{"id":1486,"date":"2024-03-26T00:50:28","date_gmt":"2024-03-25T16:50:28","guid":{"rendered":"https:\/\/www.tchepai.com\/?p=1486"},"modified":"2024-03-26T00:50:28","modified_gmt":"2024-03-25T16:50:28","slug":"bot","status":"publish","type":"post","link":"https:\/\/www.kdjingpai.com\/de\/bot\/","title":{"rendered":"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898"},"content":{"rendered":"

\u6458\u8981<\/h2>\n

 <\/p>\n

\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\u5728\u5e7f\u6cdb\u95ee\u9898\u4e0a\u7684\u63a8\u7406\u6027\u80fd\u4e25\u91cd\u4f9d\u8d56\u4e8e\u94fe\u5f0f\u601d\u7ef4\u63d0\u793a\uff0c\u8fd9\u6d89\u53ca\u5728\u63d0\u793a\u4e2d\u63d0\u4f9b\u4e00\u4e9b\u94fe\u5f0f\u601d\u7ef4\u793a\u8303\u4f5c\u4e3a\u793a\u4f8b\u3002\u6700\u8fd1\u7684\u7814\u7a76\u8868\u660e\uff0c\u4f8b\u5982\u601d\u7ef4\u6811\uff0c\u5df2\u7ecf\u6307\u51fa\u4e86\u63a2\u7d22\u548c\u81ea\u6211\u8bc4\u4f30\u5728\u590d\u6742\u95ee\u9898\u89e3\u51b3\u4e2d\u7684\u63a8\u7406\u6b65\u9aa4\u9009\u62e9\u7684\u91cd\u8981\u6027\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u540d\u4e3aBoosting of Thoughts\uff08BoT\uff09\u7684\u81ea\u52a8\u5316\u63d0\u793a\u6846\u67b6\uff0c\u901a\u8fc7\u8fed\u4ee3\u63a2\u7d22\u548c\u81ea\u6211\u8bc4\u4f30\u5927\u91cf\u601d\u7ef4\u6811\uff0c\u4ee5\u83b7\u53d6\u4e00\u7cfb\u5217\u8bd5\u9519\u63a8\u7406\u7ecf\u9a8c\u7684\u96c6\u5408\uff0c\u8fd9\u5c06\u4f5c\u4e3a\u4e00\u79cd\u65b0\u7684\u63d0\u793a\u5f62\u5f0f\u6765\u89e3\u51b3\u590d\u6742\u95ee\u9898\u3002\u4ece\u4e0d\u9700\u8981\u793a\u4f8b\u7684\u7b80\u5355\u63d0\u793a\u5f00\u59cb\uff0cBoT\u8fed\u4ee3\u5730\u63a2\u7d22\u548c\u8bc4\u4f30\u5927\u91cf\u63a8\u7406\u6b65\u9aa4\uff0c\u5e76\u4e14\u66f4\u91cd\u8981\u7684\u662f\uff0c\u4f7f\u7528LLM\u5bf9\u5b83\u4eec\u7684\u8bef\u5dee\u5206\u6790\u6765\u660e\u786e\u4fee\u8ba2\u63d0\u793a\uff0c\u4ece\u800c\u589e\u5f3a\u63a8\u7406\u6b65\u9aa4\u7684\u751f\u6210\uff0c\u76f4\u5230\u83b7\u5f97\u6700\u7ec8\u7b54\u6848\u3002\u6211\u4eec\u4f7f\u7528GPT-4\u548cLlama2\u5728\u5e7f\u6cdb\u7684\u590d\u6742\u6570\u5b66\u95ee\u9898\u4e0a\u7684\u5b9e\u9a8c\u8868\u660e\uff0cBoT\u59cb\u7ec8\u5b9e\u73b0\u6bd4\u5176\u4ed6\u5148\u8fdb\u63d0\u793a\u65b9\u6cd5\u66f4\u9ad8\u6216\u53ef\u6bd4\u7684\u95ee\u9898\u89e3\u51b3\u7387\u3002\u6e90\u4ee3\u7801\u53ef\u5728https:\/\/github.com\/iQua\/llmpebase\u7684examples\/BoTReasoning\u6587\u4ef6\u5939\u4e0b\u83b7\u5f97\u3002<\/p>\n

 <\/p>\n

1.\u5f15\u8a00<\/h2>\n

 <\/p>\n

\u5177\u6709\u81ea\u56de\u5f52\u8303\u5f0f\u7684\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\u7531\u4e8e\u5176\u6f5c\u5728\u7684\u63a8\u7406\u80fd\u529b\uff0c\u5728\u5404\u79cd\u4efb\u52a1\u4e0a\u53d6\u5f97\u4e86\u663e\u8457\u7684\u6027\u80fd\u3002\u8fd9\u79cd\u80fd\u529b\u5728\u590d\u6742\u4efb\u52a1\u4e2d\u7684\u4fdd\u8bc1\u4e25\u91cd\u4f9d\u8d56\u4e8e\u94fe\u5f0f\u601d\u7ef4\uff08CoT\uff09\u63d0\u793a\uff0c\u8fd9\u63d0\u4f9b\u4e86\u9010\u6b65\u63a8\u7406\u793a\u4f8b\u3002\u8fd9\u79cd\u65b9\u6cd5\u8868\u660e\uff0c\u53ef\u4ee5\u901a\u8fc7\u4e00\u7cfb\u5217\u601d\u7ef4\u6765\u6fc0\u53d1\u63a8\u7406\u80fd\u529b\uff0c\u5176\u4e2d\u601d\u7ef4\u4f5c\u4e3a\u89e3\u51b3\u95ee\u9898\u7684\u4e2d\u95f4\u6b65\u9aa4\u3002<\/p>\n

 <\/p>\n

\u56e0\u6b64\uff0c\u540e\u7eed\u7814\u7a76\uff0c\u7279\u522b\u662f\u601d\u7ef4\u6811\uff08ToT\uff09\u63d0\u51fa\u4e86\u6539\u8fdbCoT\u7684\u65b9\u6cd5\u3002\u4e3a\u4e86\u4fdd\u8bc1\u6709\u6548\u6027\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u7684\u63d0\u793a\u901a\u5e38\u5305\u62ec\u5bf9\u7279\u5b9a\u4efb\u52a1\u7684\u4eba\u7c7b\u6ce8\u91ca\u3002\u8fd9\u79cd\u4f9d\u8d56\u9650\u5236\u4e86\u5b83\u4eec\u7684\u53ef\u6269\u5c55\u6027\u3002\u6700\u8fd1\u7684\u5de5\u4f5c\uff0c\u8981\u4e48\u5229\u7528LLMs\u8fdb\u884c\u53cc\u91cd\u68c0\u67e5\u4ee5\u6539\u8fdb\u7b54\u6848\uff0c\u8981\u4e48\u57fa\u4e8e\u53cd\u9988\u63d0\u5347\u63d0\u793a\uff0c\u5df2\u7ecf\u663e\u793a\u51fa\u663e\u8457\u7684\u524d\u666f\u3002\u73b0\u6709\u6587\u732e\u901a\u5e38\u503e\u5411\u4e8e\u4e22\u5f03\u63d0\u793a\u4e2d\u7684\u65e0\u6548\u601d\u7ef4\u3002\u7136\u800c\uff0c\u4eba\u7c7b\u901a\u5e38\u53ef\u4ee5\u901a\u8fc7\u4ed4\u7ec6\u5206\u6790\u9519\u8bef\u6765\u4e0d\u65ad\u5b66\u4e60\uff0c\u4ece\u800c\u83b7\u5f97\u7ecf\u9a8c\uff0c\u9010\u6b65\u63d0\u9ad8\u6027\u80fd\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u4e2a\u95ee\u9898\uff1aLLMs\u7684\u601d\u7ef4\u751f\u6210\u662f\u5426\u53ef\u4ee5\u6446\u8131\u4eba\u7c7b\u6ce8\u91ca\uff0c\u6a21\u4eff\u4eba\u7c7b\u7684\u95ee\u9898\u89e3\u51b3\u65b9\u5f0f\uff0c\u4ee5\u5728\u5404\u79cd\u4efb\u52a1\u4e2d\u5b9e\u73b0\u6709\u6548\u63a8\u7406\uff1f<\/p>\n

 <\/p>\n

\u672c\u6587\u63d0\u51fa\u4e86\u4e00\u4e2a\u65b0\u9896\u7684\u6846\u67b6\uff0c\u5982\u56fe1\u6240\u793a\uff0c\u79f0\u4e3aBoosting of Thoughts\uff08BoT\uff09\uff0c\u5b83\u5b9e\u73b0\u4e86\u4e00\u79cd\u63d0\u5347\u673a\u5236\uff0c\u5305\u62ec\u805a\u5408\u548c\u7ecf\u9a8c\uff0c\u4ece\u800c\u901a\u8fc7\u4ece\u9519\u8bef\u4e2d\u5b66\u4e60\u6765\u9010\u6b65\u6539\u8fdb\u4e0d\u53ef\u9760\u7684\u63a8\u7406\u6b65\u9aa4\uff08\u5f31\u601d\u7ef4\uff09\uff0c\u6700\u7ec8\u89e3\u51b3\u5404\u79cd\u95ee\u9898\u3002\u4ece\u4e00\u4e2a\u7b80\u5355\u7684\u63d0\u793a\u5f00\u59cb\uff0c\u4e0d\u9700\u8981\u4eba\u7c7b\u6ce8\u91ca\uff0cBoT\u53ef\u80fd\u4f1a\u5f97\u5230\u5f31\u601d\u7ef4\u3002\u901a\u8fc7\u805a\u5408\uff0cBoT\u80fd\u591f\u4ece\u5b83\u4eec\u4e2d\u6d3e\u751f\u51fa\u66f4\u5408\u903b\u8f91\u548c\u6709\u6548\u7684\u601d\u7ef4\u94fe\uff0c\u4ece\u800c\u5f15\u5bfc\u540e\u7eed\u7684\u6539\u8fdb\u3002\u6211\u4eec\u6846\u67b6\u4e2d\u7684\u8fd9\u79cd\u6307\u5bfc\u662f\u901a\u8fc7\u8c03\u6574\u63d0\u793a\u6765\u5b9e\u73b0\u7684\uff0c\u8fd9\u662f\u901a\u8fc7\u5229\u7528LLMs\u5206\u6790\u805a\u5408\u94fe\u83b7\u5f97\u7684\u8be6\u7ec6\u9519\u8bef\u62a5\u544a\u3001\u5efa\u8bae\u548c\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\u7684\u6307\u5bfc\u3002\u5f53\u8fd9\u6837\u7684\u7ecf\u9a8c\u5728\u63d0\u793a\u4e2d\u79ef\u7d2f\u65f6\uff0c\u5b83\u9010\u6e10\u5bfc\u81f4\u66f4\u5f3a\u7684\u601d\u7ef4\u3002<\/p>\n

 <\/p>\n

\"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-1\"<\/p>\n

 <\/p>\n

\"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-2\"<\/p>\n

\u56fe1\uff1a\u901a\u8fc7\u9010\u6b65\u589e\u5f3a\u4f53\u9a8c\u6765\u589e\u5f3a\u63d0\u793a\uff0c\u8fd9\u5305\u62ec\u7531\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff08LLM\u6216LM\uff09\u5bf9\u751f\u6210\u7684\u601d\u7ef4\u94fe\u8fdb\u884c\u7684\u5206\u6790\u3002\u7ecf\u9a8c\u660e\u786e\u5305\u542b\u601d\u7ef4\u94fe\u672c\u8eab\uff0c\u76f8\u5e94\u7684\u9519\u8bef\u62a5\u544a\u4ee5\u53ca\u5173\u4e8e\u4fee\u8ba2\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\u7684\u8be6\u7ec6\u5efa\u8bae\u3002\u56e0\u6b64\uff0c\u90a3\u4e9b\u4ee5\u7ea2\u8272\u5341\u5b57\u6807\u8bb0\u7684\u65e0\u6548\u601d\u7ef4\u4e5f\u53ef\u4ee5\u4fc3\u8fdb\u63d0\u793a\u7684\u5b8c\u5584\u3002\u901a\u8fc7\u5728\u63d0\u793a\u4e2d\u79ef\u7d2f\u7ecf\u9a8c\uff0cBoT \u6700\u7ec8\u53ef\u4ee5\u4ece\u7b80\u5355\u63d0\u793a\u5f00\u59cb\u751f\u6210\u6b63\u786e\u7684\u601d\u7ef4\u94fe\u3002\u8fd9\u91cc\u5448\u73b0\u7684\u793a\u4f8b\u662f\u901a\u8fc7\u5c06 GPT-4 \u4e0e BoT \u5e94\u7528\u4e8e24\u70b9\u6e38\u620f\u4efb\u52a1\u6240\u83b7\u5f97\u7684\u7ed3\u679c\u3002<\/p>\n

 <\/p>\n

\u5177\u4f53\u6765\u8bf4\uff0cBoT\u5b9e\u73b0\u4e86\u8fd9\u6837\u4e00\u4e2a\u63d0\u5347\u673a\u5236\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u7ecf\u9a8c\u9a71\u52a8\u7684\u8fed\u4ee3\u8fc7\u7a0b\uff0c\u5982\u56fe1\u6240\u793a\u3002\u5728\u6bcf\u6b21\u8fed\u4ee3\u4e2d\uff0c\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u63d0\u793a\uff0cBoT\u4e0eLLM\u5e76\u884c\u6784\u5efa\u5927\u91cf\u7684\u7b80\u5355\u601d\u7ef4\u7ed3\u6784\u3002\u6211\u4eec\u9009\u62e9\u6811\u7ed3\u6784\uff0c\u5982ToT\u4e2d\u6240\u793a\uff0c\u4f46\u4e3a\u4e86\u6211\u4eec\u7684\u63d0\u5347\u76ee\u7684\uff0c\u6211\u4eec\u5bf9\u5176\u8fdb\u884c\u4e86\u91cd\u5927\u4fee\u6539\uff0c\u4f7f\u5176\u6210\u4e3a\u52a0\u6743\u4e8c\u53c9\u6811\uff0c\u5e76\u91c7\u7528\u4e86\u5404\u79cd\u751f\u957f\u7b56\u7565\u3002\u5728\u63d0\u53d6\u6bcf\u68f5\u6811\u7684\u6839\u5230\u53f6\u5206\u652f\u7684\u6700\u9ad8\u5206\u540e\uff0cBoT\u7684\u805a\u5408\u7ec4\u4ef6\u88ab\u6267\u884c\uff0c\u5c06\u5b83\u4eec\u805a\u5408\u6210\u4e00\u4e2a\u5355\u4e00\u7684\u601d\u7ef4\u94fe\u3002\u968f\u540e\uff0c\u8fd9\u4e2a\u94fe\u88ab\u540c\u4e00LLM\u8bc4\u4f30\uff0c\u4ee5\u83b7\u5f97\u7ecf\u9a8c\uff0c\u8fd9\u4e9b\u7ecf\u9a8c\u88ab\u6dfb\u52a0\u5230\u63d0\u793a\u4e2d\uff0c\u4f5c\u4e3a\u4e0b\u4e00\u6b21\u8fed\u4ee3\u4e2d\u601d\u7ef4\u751f\u6210\u7684\u6307\u5bfc\u3002<\/p>\n

 <\/p>\n

\u6211\u4eec\u7684\u8d21\u732e\u53ef\u4ee5\u6982\u62ec\u4e3a\u4e09\u4e2a\u65b9\u9762\u3002\u9996\u5148\uff0c\u4e0e\u4f7f\u7528\u7cbe\u5fc3\u8bbe\u8ba1\u7684\u63d0\u793a\u751f\u6210\u66f4\u590d\u6742\u7684\u601d\u7ef4\u7ed3\u6784\u4e0d\u540c\uff0c\u672c\u6587\u8868\u660e\uff0c\u4ec5\u4f9d\u8d56\u4e8e\u7b80\u5355\u7684\u521d\u59cb\u63d0\u793a\uff0c\u5f31\u601d\u7ef4\u53ef\u4ee5\u6839\u636e\u4ee5\u524d\u7684\u7ecf\u9a8c\u9010\u6b65\u6539\u8fdb\u4ee5\u89e3\u51b3\u95ee\u9898\u3002\u5176\u6b21\uff0c\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u79cd\u63d0\u5347\u673a\u5236\uff0c\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u4e2a\u540d\u4e3aBoosting of Thoughts\uff08BoT\uff09\u7684\u65b0\u9896\u6846\u67b6\uff0c\u5b83\u6267\u884c\u4e00\u4e2a\u7ecf\u9a8c\u9a71\u52a8\u7684\u8fed\u4ee3\u8fc7\u7a0b\u3002\u7531\u4e8e\u4ece\u7b80\u5355\u7684\u63d0\u793a\u5f00\u59cb\uff0cBoT\u53ef\u6269\u5c55\u5230\u5404\u79cd\u4efb\u52a1\u3002\u5728\u4fdd\u8bc1\u6709\u6548\u6027\u7684\u540c\u65f6\uff0cBoT\u5f88\u5feb\uff0c\u56e0\u4e3a\u5b83\u5e76\u884c\u6784\u5efa\u7b80\u5355\u7684\u601d\u7ef4\u7ed3\u6784\uff0c\u5e76\u5728\u51e0\u6b21\u8fed\u4ee3\u540e\u6536\u655b\u5230\u89e3\u51b3\u65b9\u6848\u3002\u6700\u540e\uff0c\u6211\u4eec\u4f7f\u7528GPT-4\u548cLlamaV2\u8bc4\u4f30\u4e86BoT\u5728\u590d\u6742\u6570\u5b66\u95ee\u9898\u4e0a\u7684\u6027\u80fd\u3002\u4f9d\u9760GPT-4 OpenAI (2023)\u548cLlamaV2 Touvron\u7b49\u4eba(2023)\uff0c\u6211\u4eec\u8bc4\u4f30\u4e86BoT\u5728\u590d\u6742\u6570\u5b66\u95ee\u9898\u4e0a\u7684\u6027\u80fd\u3002\u95ee\u9898\u89e3\u51b3\u7387\u8868\u660e\uff0c\u91c7\u7528\u4e8c\u53c9\u6811\u601d\u7ef4\u7ed3\u6784\u7684BoT\uff0c\u5728GSM8K\u548cAQuA\u4e0a\u663e\u8457\u8d85\u8fc7\u4e86\u5f53\u524d\u6700\u5148\u8fdb\u7684\u6280\u672f\uff0c\u540c\u65f6\u5728\u5176\u4ed6\u6570\u636e\u96c6\u4e0a\u53d6\u5f97\u4e86\u7b2c\u4e8c\u597d\u7684\u7ed3\u679c\u3002\u7279\u522b\u662f\u5728\u65b0\u7684\u5177\u6709\u6311\u6218\u6027\u7684\u4efb\u52a1Game of 24\u4e2d\uff0cBoT\u6bd4\u9886\u5148\u7684\u65b9\u6cd5ToT\u9ad8\u51fa9.7%\u3002\u6211\u4eec\u7684BoT\u56e0\u6b64\u8bc1\u660e\u4e86\uff0c\u901a\u8fc7\u589e\u5f3a\u63d0\u793a\uff0c\u79ef\u7d2f\u65e0\u6548\u601d\u7ef4\u94fe\u7684\u8bef\u5dee\u5206\u6790\u548c\u76f8\u5e94\u7684\u5efa\u8bae\uff0c\u5373\u4f7f\u6ca1\u6709\u4eba\u7c7b\u6ce8\u91ca\uff0cLLMs\u4e5f\u80fd\u5728\u5404\u79cd\u4efb\u52a1\u4e2d\u4fdd\u6301\u9ad8\u6027\u80fd\u3002<\/p>\n

 <\/p>\n

2.\u76f8\u5173\u5de5\u4f5c<\/span><\/h2>\n

 <\/p>\n

\u591a\u6b65\u63a8\u7406<\/strong>\u3002\u7a81\u51fa\u7684\u5de5\u4f5c\u94fe\u5f0f\u601d\u7ef4\uff08CoT\uff09\u63d0\u793a\u8868\u660e\uff0c\u53ef\u4ee5\u901a\u8fc7\u5728\u6bcf\u4e2a\u95ee\u9898\u7684\u63d0\u793a\u4e2d\u63d0\u4f9b\u4e2d\u95f4\u63a8\u7406\u6b65\u9aa4\u6765\u6fc0\u53d1LLMs\u7684\u9010\u6b65\u63a8\u7406\u884c\u4e3a\u3002\u6700\u8fd1\u7684\u5de5\u4f5c\uff0c\u601d\u7ef4\u6811\uff08ToT\uff09\u5c06\u987a\u5e8f\u63a8\u7406\u8fc7\u7a0b\u8f6c\u6362\u4e3a\u6811\u7ed3\u6784\uff0c\u5728\u8be5\u7ed3\u6784\u4e2d\uff0c\u6bcf\u4e2a\u601d\u7ef4\uff08\u8282\u70b9\uff09\u53ef\u80fd\u8003\u8651\u4ee5\u524d\u7684\u63a8\u7406\u8def\u5f84\u4ee5\u4ea7\u751f\u591a\u4e2a\u4e0b\u4e00\u6b65\u601d\u7ef4\u3002\u901a\u8fc7\u63a8\u7406\u8fc7\u7a0b\u4e2d\u7684\u56de\u6eaf\u548c\u6269\u5c55\u63a2\u7d22\uff0cToT\u5728\u751a\u81f3\u6311\u6218GPT-4\u7684\u95ee\u9898\u4e0a\u8868\u73b0\u826f\u597d\u3002\u8003\u8651\u5230\u5176\u9ad8\u80fd\u529b\uff0cBoT\u7684\u57fa\u7840\u601d\u7ef4\u7ed3\u6784\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u5229\u7528\u4e86ToT\u7684\u601d\u7ef4\u6811\u7ed3\u6784\u3002\u5e76\u4e14\uff0c\u7531\u4e8e\u63d0\u5347\u6846\u67b6\uff0cBoT\u5728\u6bcf\u6b21\u8fed\u4ee3\u4e2d\u751f\u6210\u7684\u6811\u7ed3\u6784\u662f\u4e8c\u5143\u7684\u548c\u6d45\u7684\uff0c\u800c\u4e0d\u662fToT\u7684\u590d\u6742\u6811\uff0c\u5176\u4e2d\u6bcf\u4e2a\u8282\u70b9\u5bf9\u5e94\u7740\u5927\u91cf\u7684\u5b50\u8282\u70b9\u3002\u7136\u800c\uff0c\u57fa\u7840\u7ed3\u6784\u4e0d\u4ec5\u9650\u4e8eToT\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0cBoT\u662f\u7075\u6d3b\u7684\uff0c\u56e0\u4e3a\u57fa\u7840\u601d\u7ef4\u7ed3\u6784\u53ef\u4ee5\u662fToT\uff0cGoT Besta\u7b49\u4eba\uff082023\uff09\uff0c\u6216\u8005CR Zhang\u7b49\u4eba\uff082023b\uff09\uff0c\u5176\u4e2d\u601d\u7ef4\u56fe\uff08GoT\uff09Besta\u7b49\u4eba\uff082023\uff09\u662f\u5c06\u601d\u7ef4\u7ed3\u6784\u6269\u5c55\u4e3a\u56fe\u5f62\u683c\u5f0f\u7684\u6700\u65b0\u5de5\u4f5c\u3002\u672c\u6587\u5c06\u4ec5\u5173\u6ce8ToT\u4f5c\u4e3a\u57fa\u7840\u601d\u7ef4\u7ed3\u6784\uff0c\u5e76\u7559\u4e0bGoT\u7684\u4f7f\u7528\u4f5c\u4e3a\u672a\u6765\u7684\u5de5\u4f5c\u3002<\/p>\n

 <\/p>\n

\u81ea\u52a8\u63d0\u793a<\/strong>\u3002\u91ca\u653e\u4eba\u7c7b\u4ece\u7279\u5b9a\u4efb\u52a1\u7684\u63d0\u793a\u4e2d\u5438\u5f15\u4e86\u5f88\u591a\u5173\u6ce8\u3002\u4e3a\u4e86\u4fdd\u8bc1LLMs\u7684\u63a8\u7406\u80fd\u529b\uff0c\u4f20\u7edf\u7684CoT\u4f9d\u8d56\u4e8e\u4eba\u7c7b\u5148\u9a8c\u77e5\u8bc6\u6765\u624b\u52a8\u751f\u6210\u7279\u5b9a\u4efb\u52a1\u7684\u6f14\u793a\u4f5c\u4e3a\u63d0\u793a\u3002\u7136\u800c\uff0c\u96f6\u6b21CoT\u8868\u660e\uff0c\u5373\u4f7f\u6ca1\u6709\u624b\u5de5\u5236\u4f5c\u7684\u4f8b\u5b50\uff0c\u901a\u8fc7\u5728\u63d0\u793a\u4e2d\u7b80\u5355\u5730\u6dfb\u52a0\u201c\u8ba9\u6211\u4eec\u4e00\u6b65\u4e00\u6b65\u5730\u601d\u8003\u201d\uff0cLLMs\u4e5f\u80fd\u591f\u8fdb\u884c\u9010\u6b65\u63a8\u7406\u4ee5\u83b7\u5f97\u51c6\u786e\u7b54\u6848\u3002\u8fd9\u4e9b\u89c1\u89e3\u50ac\u751f\u4e86\u4e00\u7cfb\u5217\u540e\u7eed\u7814\u7a76\u3002Auto-CoT\u6d88\u9664\u4e86\u624b\u52a8\u52aa\u529b\uff0c\u901a\u8fc7\u68c0\u7d22\u96f6\u6b21CoT\u751f\u6210\u7684\u53ef\u7528\u63a8\u7406\u94fe\u3002Active-Prompt\u9996\u5148\u6d4b\u91cf\u4e00\u7ec4\u95ee\u9898\u7684\u4e0d\u786e\u5b9a\u6027\uff0c\u56e0\u6b64\u53ea\u9009\u62e9\u4e0d\u786e\u5b9a\u7684\u95ee\u9898\u7531\u4eba\u7c7b\u6ce8\u91ca\u3002ToT\u4e5f\u53ef\u4ee5\u51cf\u5c11\u624b\u52a8\u52aa\u529b\uff0c\u4f46\u5bf9\u4e8e\u6bcf\u4e2a\u4efb\u52a1\uff0c\u5b83\u4ecd\u7136\u9700\u8981\u4e13\u5bb6\u5728\u63d0\u793a\u4e2d\u63d0\u4f9b\u53ef\u80fd\u7684\u4e0b\u4e00\u6b65\u601d\u7ef4\u3002\u6211\u4eec\u7684\u8bba\u6587\u5f15\u5165\u4e86\u4e00\u79cd\u65b0\u9896\u7684\u65e0\u624b\u52a8\u63d0\u793a\u63d0\u5347\u65b9\u6cd5\u3002\u4ece\u7b80\u5355\u7684\u63d0\u793a\u5f00\u59cb\uff0cBoT\u6839\u636eLLMs\u5bf9\u601d\u7ef4\u7684\u5206\u6790\u8fed\u4ee3\u589e\u5f3a\u5b83\u3002<\/p>\n

 <\/p>\n

\u901a\u8fc7\u53cd\u9988\u8fdb\u884c\u63d0\u793a\u5de5\u7a0b<\/strong>\u3002\u5229\u7528LLMs\u5bf9\u8f93\u5165\u63d0\u793a\u7684\u54cd\u5e94\u4f5c\u4e3a\u8fdb\u4e00\u6b65\u63d0\u793a\u4fee\u8ba2\u7684\u53cd\u9988\u5df2\u7ecf\u5f15\u8d77\u4e86\u5f88\u591a\u5173\u6ce8\u3002\u90a3\u4e9b\u6839\u636eLLMs\u5bf9\u8f93\u51fa\u7684\u8bc4\u4f30\u63cf\u8ff0\u4e0d\u65ad\u4fee\u8ba2\u7ed9\u5b9a\u63d0\u793a\u7684\u4eba\u65e8\u5728\u83b7\u5f97\u51c6\u786e\u7b54\u6848\u3002\u4f7f\u7528\u4e0e\u6211\u4eec\u8bba\u6587\u7c7b\u4f3c\u7684\u9ad8\u7ea7\u601d\u60f3\uff0cSELF-REFINE\u63d0\u51fa\u4e86\u4e00\u79cd\u8fed\u4ee3\u81ea\u7cbe\u70bc\u7b97\u6cd5\uff0c\u8ba9LLM\u4ea7\u751f\u53cd\u9988\u4ee5\u8fdb\u4e00\u6b65\u7cbe\u70bc\u5176\u8f93\u51fa\u3002PHP\u901a\u8fc7\u76f4\u63a5\u5c06\u524d\u4e00\u4e2a\u7b54\u6848\u7684\u89e3\u51b3\u65b9\u6848\u4f5c\u4e3a\u63d0\u793a\u6dfb\u52a0\u5230\u540e\u7eed\u63d0\u793a\u4e2d\u6765\u7b80\u5316\u8fd9\u4e2a\u8fc7\u7a0b\u3002REFINER\u4e5f\u4e0e\u6211\u4eec\u7684\u8bba\u6587\u76f8\u5173\uff0c\u5b83\u8bc4\u4f30\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\u4f5c\u4e3a\u53cd\u9988\u4ee5\u4ea7\u751f\u66f4\u5408\u7406\u7684\u4e00\u4e2a\u3002\u53e6\u4e00\u7cfb\u5217\u7814\u7a76\u63a2\u7d22\u4e86\u96c6\u6210\uff0c\u7279\u522b\u662f\u5229\u7528\u63d0\u5347\u673a\u5236Freund\u7b49\u4eba\uff081996\uff09\u901a\u8fc7\u4e00\u7ec4\u793a\u4f8b\u7684\u53cd\u9988\u6765\u7cbe\u70bc\u63d0\u793a\u3002\u4ed6\u4eec\u901a\u8fc7\u5728\u524d\u4e00\u6b21\u8fed\u4ee3\u4e2d\u6dfb\u52a0\u51e0\u4e2a\u4e0d\u786e\u5b9a\u7684\u793a\u4f8b\u6765\u8c03\u6574\u63d0\u793a\uff0c\u6216\u8005\u4f9d\u8d56\u4e8e\u4e00\u4e2a\u53cd\u9988-\u53cd\u601d-\u7cbe\u70bc\u8fc7\u7a0b\u3002APO Pryzant\u7b49\u4eba\uff082023\uff09\u8fed\u4ee3\u5730\u7cbe\u70bc\u63d0\u793a\uff0c\u4f7f\u7528\u524d\u4e00\u4e2a\u63d0\u793a\u7684\u6027\u80fd\u6765\u5f62\u6210\u4f18\u5316\u7684\u81ea\u7136\u8bed\u8a00\u3002\u8fd9\u4e9b\u5de5\u4f5c\u8bc1\u660e\u4e86\u63d0\u5347\u673a\u5236\u5728\u63d0\u793a\u5de5\u7a0b\u4e2d\u7684\u6709\u6548\u6027\u3002\u7136\u800c\uff0c\u6211\u4eec\u7684\u5de5\u4f5c\u662f\u7b2c\u4e00\u4e2a\u5f3a\u8c03\u9519\u8bef\u5206\u6790\u5728\u589e\u5f3a\u63d0\u793a\u4ee5\u751f\u6210\u6709\u6548\u63a8\u7406\u94fe\u4e2d\u7684\u91cd\u8981\u6027\u3002\u6240\u63d0\u51fa\u7684BoT\u5c06\u8fd9\u4e00\u89c1\u89e3\u6269\u5c55\u5230\u901a\u8fc7\u8fed\u4ee3\u7d2f\u79ef\u4e00\u7cfb\u5217\u8bd5\u9519\u63a8\u7406\u7ecf\u9a8c\u7684\u96c6\u5408\u6765\u5b9e\u73b0\u81ea\u52a8\u5316\u63d0\u793a\u6846\u67b6\u3002<\/p>\n

 <\/p>\n

3.\u63d0\u5347\u601d\u7ef4<\/span><\/h2>\n

 <\/p>\n

3.1\u80cc\u666f<\/span><\/h3>\n

 <\/p>\n

\u63d0\u793a\u5de5\u7a0b\u7684\u76ee\u6807\u662f\u8bbe\u8ba1\u4e00\u4e2a\u63d0\u793aI\uff0c\u5305\u542b\u591a\u4e2a\u8bed\u8a00\u5e8f\u5217\uff0c\u4ee5\u4fbf\u901a\u8fc7\u8fd9\u4e2a\u63d0\u793a\u4f5c\u4e3a\u8f93\u5165\uff0c\u9884\u8bad\u7ec3\u7684\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff08LLM\uff09\u8868\u793a\u4e3ap\u03b8\uff0c\u7531\u03b8\u53c2\u6570\u5316\uff0c\u53ef\u4ee5\u83b7\u5f97\u6240\u9700\u7684\u8bed\u8a00\u5e8f\u5217y\u3002\u56e0\u6b64\uff0c\u6807\u51c6\u7684\u8f93\u5165\u8f93\u51fa\uff08IO\uff09\u53ef\u4ee5\u8868\u8ff0\u4e3ay \u223c p\u03b8 (y|I (X, Q))\uff0c\u5176\u4e2dI (\u00b7)\u8868\u793a\u63d0\u793a\u5305\u88c5\u4efb\u52a1\u6307\u4ee4X\u548c\u76f8\u5e94\u7684\u95ee\u9898Q\u3002<\/p>\n

 <\/p>\n

\"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-3\"<\/p>\n

 <\/p>\n

\"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-4\"<\/p>\n

 <\/p>\n

\u56fe\u7247\u63cf\u7ed8\u4e86\u4f7f\u7528\u7b97\u672f\u8fd0\u7b97\u89e3\u51b3\u95ee\u9898\u80cc\u540e\u7684\u601d\u7ef4\u8fc7\u7a0b\u7684\u89c6\u89c9\u8868\u73b0\u3002\u5b83\u5206\u4e3a\u4e09\u4e2a\u4e3b\u8981\u90e8\u5206\uff1a\u601d\u7ef4\u7ed3\u6784\u805a\u5408\u3001\u4e0b\u4e00\u601d\u7ef4\u751f\u6210\u53ca\u601d\u7ef4\u94fe\u5206\u6790 – \u53cd\u9988\u3002<\/p>\n

\u601d\u7ef4\u7ed3\u6784\u805a\u5408\u4ee3\u8868\u4e0d\u540c\u63a8\u7406\u9636\u6bb5\uff08\u9636\u6bb51\uff0c\u9636\u6bb52\uff0c\u9636\u6bb53\uff09\u7684\u7ed3\u5408\uff0c\u6bcf\u4e2a\u9636\u6bb5\u90fd\u6709\u81ea\u5df1\u7684\u6570\u7ed3\u6784\uff0c\u8bf4\u660e\u4e86\u5f97\u51fa\u7ed3\u8bba\u6240\u91c7\u53d6\u7684\u6b65\u9aa4\u3002<\/p>\n

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\u601d\u7ef4\u94fe\u5206\u6790 – \u53cd\u9988\u63d0\u4f9b\u4e86\u5bf9\u91c7\u53d6\u7684\u63a8\u7406\u6b65\u9aa4\u7684\u8be6\u7ec6\u5206\u6790\uff0c\u6307\u51fa\u53ef\u80fd\u7684\u9519\u8bef\u5e76\u63d0\u4f9b\u6539\u8fdb\u5efa\u8bae\u3002\u5b83\u901a\u8fc7\u8bc4\u4f30\u8fd9\u4e9b\u6b65\u9aa4\u662f\u5426\u8ba9\u89e3\u51b3\u8005\u66f4\u63a5\u8fd1\u76ee\u6807\u6570\u5b57\uff08\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u662f24\uff09\u6765\u6279\u5224\u6b65\u9aa4\uff0c\u5e76\u5efa\u8bae\u5c1d\u8bd5\u5176\u4ed6\u7b97\u672f\u8fd0\u7b97\u3002<\/p>\n

\u6b64\u5916\uff0c\u8fd8\u6709\u4e00\u4e2a\u7b80\u5355\u63d0\u793a\u90e8\u5206\uff0c\u6982\u8ff0\u4e86\u601d\u7ef4\u8fc7\u7a0b\u7684\u8f93\u5165\uff0c\u5176\u4e2d\u5305\u62ec\u4efb\u52a1\u4e0d\u7279\u5b9a\u7684\u63cf\u8ff0\u3001\u4efb\u52a1\u4fe1\u606f\u548c\u95ee\u9898\uff0c\u4ee5\u53ca\u4ece\u5148\u524d\u7684\u63a8\u7406\u94fe\u6761\u83b7\u53d6\u7684\u7ecf\u9a8c\uff0c\u8be5\u7ecf\u9a8c\u5145\u5f53\u751f\u6210\u65b0\u601d\u7ef4\u7684\u5360\u4f4d\u7b26\u3002<\/p>\n

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 <\/p>\n

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 <\/p>\n

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 <\/p>\n

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 <\/p>\n

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 <\/p>\n

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 <\/p>\n

\u7b80\u5355\u63d0\u793a<\/strong>\u3002\u5bf9\u4e8e\u4efb\u4f55\u4efb\u52a1\uff0c\u5728\u8fed\u4ee3t=0\u65f6\uff0c\u6211\u4eec\u521b\u5efa\u4e00\u4e2a\u7b80\u5355\u7684\u521d\u59cb\u63d0\u793aI0 \u2261 {S, X, Q, F0, {Gi}}\uff0c\u5176\u4e2dS\u8868\u793a\u4efb\u52a1\u65e0\u5173\u7684\u63cf\u8ff0\uff0c\u800cX\u548cQ\u5206\u522b\u8868\u793a\u4efb\u52a1\u4fe1\u606f\u548c\u95ee\u9898\u3002\u63d0\u793a\u7684\u7ecf\u9a8c\u90e8\u5206\u8bb0\u4e3aF0\uff0c\u5728\u5f00\u59cb\u65f6\u5e94\u8be5\u662f\u7a7a\u7684\u3002{Gi}\u662f\u4e00\u4e2a\u5360\u4f4d\u7b26\uff0c\u5728\u6784\u5efa\u601d\u7ef4\u7ed3\u6784\u65f6\u5c06\u88ab\u586b\u5145\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5728\u751f\u6210\u4e0b\u4e00\u4e2a\u601d\u7ef4zi\u65f6\uff0c{Gi}\u5c06\u88ab\u66ff\u6362\u4e3a\u524d\u9762\u7684\u601d\u7ef4\u94fez1..,i-1\u3002<\/p>\n

 <\/p>\n

\u601d\u7ef4\u7ed3\u6784\u751f\u6210<\/strong>\u3002\u5728\u6536\u96c6\u7ecf\u9a8cFt-1\u540e\uff0c\u8fed\u4ee3t\u7684\u63d0\u793a\u53ef\u4ee5\u662fIt \u2261 {S, X, Q, F1,…,t-1, {Gi}}\u3002\u57fa\u4e8e\u8fd9\u4e2a\u63d0\u793a\uff0cBoT\u5e76\u884c\u751f\u6210M\u4e2a\u601d\u7ef4\u7ed3\u6784\u3002BoT\u672c\u8d28\u4e0a\u80fd\u591f\u5305\u542b\u4efb\u4f55\u601d\u7ef4\u7ed3\u6784\uff0c\u4f8b\u5982\u94fe\u5f0fWei\u7b49\u4eba\u7684\u7ed3\u6784\u6216\u6811\u72b6Yao\u7b49\u4eba\u7684\u7ed3\u6784\u3002\u8003\u8651\u5230\u63a8\u7406\u6b65\u9aa4\u7684\u63a2\u7d22\u548c\u5b9e\u9a8c\u7ed3\u679c\uff0c\u6211\u4eec\u7814\u7a76\u4e86\u6811\u72b6\u601d\u7ef4\u7ed3\u6784\u3002\u7136\u800c\uff0cBoT\u5f15\u5165\u4e86\u4e24\u4e2a\u65b0\u9896\u7684\u4fee\u6539\uff0c\u4f7f\u5176\u66f4\u9002\u5408\u63d0\u5347\u6846\u67b6\u3002<\/p>\n

    \n
  • \u52a0\u6743\u4e8c\u53c9\u6811<\/strong>\u3002\u5728\u6bcf\u8f6e\u4e2d\u4f7f\u7528\u7b80\u5355\u7684\u63d0\u793a\uff0cBoT\u6784\u5efa\u4e86\u7ed3\u6784\u7b80\u5355\u3001\u590d\u6742\u5ea6\u4f4e\u7684\u5f31\u601d\u7ef4\uff0c\u56e0\u4e3a\u5b83\u4eec\u53ef\u4ee5\u5728\u63d0\u5347\u673a\u5236\u4e2d\u8fdb\u4e00\u6b65\u4fee\u8ba2\u3002\u56e0\u6b64\uff0cBoT\u7684\u6bcf\u4e2a\u601d\u7ef4\u7ed3\u6784\u90fd\u662f\u4e00\u4e2a\u6d45\u5c42\u52a0\u6743\u4e8c\u53c9\u6811\u3002\u4e3a\u4e86\u7b80\u5355\u8d77\u89c1\uff0c\u6211\u4eec\u4fdd\u7559\u7b26\u53f7z1…i-1\u6765\u8868\u793a\u4ece\u6839\u8282\u70b9\u5230\u8282\u70b9i\u7684\u7236\u8282\u70b9\u7684\u601d\u7ef4\u3002\u9664\u4e86\u4e3a\u6bcf\u4e2a\u8282\u70b9i\u63d0\u4f9b\u4e00\u4e2a\u601d\u7ef4zi\u548c\u5176\u601d\u7ef4\u8bc4\u4f30\u5206\u6570Vi \u223c p\u03b8 (z1…i, Ia, X, Q)\uff0c\u6211\u4eec\u8fd8\u52a0\u5165\u4e86\u5b50\u8282\u70b9\u4e0e\u5176\u7236\u8282\u70b9\u4e4b\u95f4\u7684\u8fb9\u5206\u6570Vi-1,i \u223c p\u03b8 (zi-1, zi, Ie, X, Q)\uff0c\u5176\u4e2dIa\u548cIe\u5206\u522b\u6307\u4ee3\u601d\u7ef4\u548c\u8fb9\u8bc4\u4f30\u7684\u6307\u5bfc\u63cf\u8ff0\u3002Vi-1,i\u8868\u793aLLMs\u751f\u6210\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u7684\u4fe1\u5fc3\u6c34\u5e73\u3002\u56e0\u6b64\uff0cBoT\u5728\u8fd9\u4e2a\u6811\u7ed3\u6784\u4e2d\u7684\u4e0b\u4e00\u4e2a\u601d\u7ef4\u751f\u6210\u88ab\u5f62\u5f0f\u5316\u4e3ap\u03b8 (zi| (Vi-1,i, Vi, It, X, Q))\u3002<\/li>\n
  • \u6811\u5f02\u8d28\u6027<\/strong>\u3002\u4e0eToT\u4e0d\u540c\uff0c\u5b83\u5bfb\u6c42\u5728\u4e00\u4e2a\u5927\u578b\u590d\u6742\u6811\u4e2d\u5bfb\u627e\u89e3\u51b3\u65b9\u6848\uff0cBoT\u65e8\u5728\u6784\u5efa\u9ad8\u5ea6\u5f02\u8d28\u7684\u6811\u72b6\u601d\u7ef4\u7ed3\u6784\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u589e\u52a0\u5f02\u8d28\u6027\uff0c\u601d\u7ef4\u7ed3\u6784\u751f\u6210\u91c7\u7528\u4e86\u4e0d\u540c\u7684\u6811\u751f\u957f\u7b56\u7565\uff0c\u4f8b\u5982\u9010\u5c42\u751f\u957f\u548c\u9010\u53f6\u751f\u957f\u3002\u524d\u8005\u5f3a\u8c03\u63a2\u7d22\u4f46\u5229\u7528\u8f83\u5c11Chen & Guestrin (2016)\uff0c\u800c\u540e\u8005\u5219\u76f8\u53cdKe\u7b49\u4eba(2017)\u3002\u56e0\u6b64\uff0c\u9010\u53f6\u7b56\u7565\u503e\u5411\u4e8e\u4ece\u5f53\u524d\u6700\u4f73\u601d\u7ef4\u7ee7\u7eed\u63a8\u7406\uff0c\u4ee5\u8fbe\u5230\u66f4\u597d\u7684\u6700\u7ec8\u601d\u7ef4\uff0c\u76f8\u6bd4\u4e4b\u4e0b\u9010\u5c42\u751f\u957f\uff0c\u4f46\u5b83\u4e5f\u503e\u5411\u4e8e\u5f97\u5230\u5355\u8c03\u7684\u63a8\u7406\u94fe\u3002\u6b64\u5916\uff0c\u5e94\u7528\u4e86\u4e0d\u540c\u7684\u6e29\u5ea6\u548cTop p\u8bbe\u7f6e\u7684LLMs\u3002\u6700\u540e\uff0c\u6211\u4eec\u5728BoT\u4e2d\u4f7f\u7528\u4e86\u4e00\u4e2a\u5c0f\u7684\u6700\u5927\u6df1\u5ea6\u503c\uff0c\u5e76\u5728Vi-1,i\u548cVi\u503c\u8d85\u51fa\u6307\u5b9a\u8303\u56f4[0.3, 0.8]\u65f6\u5c06\u4e00\u4e2a\u8282\u70b9\u6807\u8bb0\u4e3a\u53f6\u5b50\u3002<\/li>\n<\/ul>\n

     <\/p>\n

    \u601d\u7ef4\u7ed3\u6784\u805a\u5408<\/strong>\u3002\u5728\u83b7\u5f97M\u4e2a\u601d\u7ef4\u7ed3\u6784\u540e\uff0cBoT\u5c06\u5b83\u4eec\u805a\u5408\u6210\u4e00\u4e2a\u601d\u7ef4\u94fe\uff0c\u8bb0\u4e3az1…n\u3002\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e00\u70b9\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u601d\u7ef4\u7ed3\u6784\u7d22\u5f15m\uff0cBoT\u9996\u5148\u9009\u62e9\u5177\u6709\u6700\u9ad8\u8bc4\u4f30\u5206\u6570\u7684\u94fe\uff0c\u5373zm 1…nm := arg maxz1…n\u2208Zm \u2211i=1 Vi + Vi-1,i\uff0c\u5176\u4e2dZm\u8868\u793a\u7b2cm\u68f5\u6811\u7684\u6240\u6709\u601d\u7ef4\u94fe\u7684\u96c6\u5408\u3002\u968f\u540e\uff0c\u5b58\u5728\u4e24\u79cd\u7b56\u7565\u6765\u83b7\u5f97z1…n\u3002<\/p>\n

      \n
    • \u6700\u4f73\u4f18\u5148\u805a\u5408<\/strong>\u3002BoT\u4f9d\u8d56\u4e8earg maxz1…n\u2208{Zm}M m=1 \u2211i=1 Vi + Vi-1,i\uff0c\u4eceM\u4e2a\u601d\u7ef4\u7ed3\u6784\u4e2d\u9009\u62e9\u6700\u597d\u7684\u4e00\u4e2a\u4f5c\u4e3az1…n\u3002\u8fd9\u79cd\u7b97\u6cd5\u901f\u5ea6\u5feb\uff0c\u4f46\u53ef\u80fd\u5bfc\u81f4\u4e00\u4e2a\u4e0d\u5408\u7406\u7684\u94fe\uff0c\u96be\u4ee5\u5f15\u5bfc\u540e\u7eed\u7684\u6539\u8fdb\u3002<\/li>\n
    • \u8d2a\u5a6a\u805a\u5408<\/strong>\u3002BoT\u88ab\u5141\u8bb8\u5728{Zm}M m=1\u4e0a\u6267\u884c\u8d2a\u5a6a\u641c\u7d22\uff0c\u4ee5\u7ec4\u88c5\u4e00\u4e2a\u65b0\u7684\u601d\u7ef4\u94fe\uff0c\u8fd9\u4e2a\u94fe\u53ef\u80fd\u4e0d\u5b58\u5728\uff0c\u4f46\u53ef\u80fd\u662f\u5168\u5c40\u6700\u4f18\u7684\u3002\u4ece\u521d\u59cb\u601d\u7ef4\u5f00\u59cb\uff0c\u901a\u5e38\u662f\u6811\u7684\u6839\u8282\u70b9\uff0cBoT\u83b7\u5f97z1 = arg maxzj\u2208{zm 1 } M m=1 Vj + Vj-1,j\u3002\u968f\u540e\uff0c\u4e3a\u4e86\u83b7\u5f97zi\uff0cBoT\u5728{Zm}M m=1\u4e2d\u641c\u7d22\u524d\u4e00\u6b65\u662fzi-1\u7684\u6240\u6709\u601d\u7ef4\u3002<\/li>\n<\/ul>\n

       <\/p>\n

      \u601d\u7ef4\u94fe\u5206\u6790<\/strong>\u3002\u4e3a\u4e86\u83b7\u5f97\u6d1e\u5bdf\u529b\uff0c\u4e86\u89e3\u5e94\u8be5\u8c03\u6574\u4ec0\u4e48\u4ee5\u589e\u5f3a\u63d0\u793a\u4ee5\u751f\u6210\u66f4\u597d\u7684\u601d\u7ef4\uff0cBoT\u5229\u7528LLMs\u7684\u81ea\u6211\u8bc4\u4f30\u80fd\u529b\u6765\u8bc4\u4f30z1…n\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u4ee5\u63d0\u793aIt f (z1…n, X, Q)\u4f5c\u4e3a\u8f93\u5165\uff0cLLM\u8f93\u51fa\u4e00\u4e2a\u53cd\u9988\u6bb5\u843d\uff0c\u5305\u542b\u5173\u4e8e\u8fd9\u4e2a\u601d\u7ef4\u94fez1…n\u7684\u95ee\u9898\u62a5\u544a\u548c\u8be6\u7ec6\u5efa\u8bae\u3002\u8fd9\u4e2a\u53cd\u9988\u5c06\u88ab\u6dfb\u52a0\u5230F1,…,t-1\u4e2d\uff0c\u4f5c\u4e3a\u601d\u7ef4\u751f\u6210\u4e2d\u7684\u65b0\u7ecf\u9a8c\uff0c\u7ed3\u679c\u4e3aF1,…,t\u3002<\/p>\n

      \u8fed\u4ee3\u7cbe\u70bc<\/strong>\u3002\u901a\u8fc7\u63d0\u5347\u673a\u5236\uff0cF1,…,t\u88ab\u7528\u6765\u8fed\u4ee3\u589e\u5f3a\u63d0\u793a\uff0c\u7ed3\u679c\u4e3a\u7b2c(t+1)\u6b21\u8fed\u4ee3\u7684\u63d0\u793aIt+1 \u2261 {S, X, Q, F1,…,t, {Gi}}\u3002\u968f\u7740\u8fed\u4ee3\u7684\u8fdb\u884c\uff0cF1,…,t\u53ef\u80fd\u5305\u542b\u8bb8\u591a\u5178\u578b\u7684\u3001\u4e0d\u5408\u7406\u7684\u601d\u7ef4\u94fe\uff0c\u4ee5\u53ca\u90a3\u4e9b\u66f4\u63a5\u8fd1\u89e3\u51b3\u65b9\u6848\u7684\u601d\u7ef4\u94fe\uff0c\u6240\u6709\u8fd9\u4e9b\u90fd\u5177\u6709\u660e\u786e\u5b9a\u4e49\u7684\u5206\u6790\u7ed3\u679c\u3002\u56e0\u6b64\uff0c\u5373\u4f7f\u4ece\u7b80\u5355\u7684\u63d0\u793a\u5f00\u59cb\uff0cBoT\u4e5f\u4f1a\u8fed\u4ee3\u5730\u5b8c\u5584\u8fd9\u4e2a\u63d0\u793a\uff0c\u4ee5\u4ea7\u751f\u6b63\u786e\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u4ece\u800c\u5f97\u51fa\u51c6\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002\u7ecf\u8fc7T\u6b21\u8fed\u4ee3\u540e\uff0c\u6211\u4eec\u4f7f\u7528It+1\u4f5c\u4e3aLLM\u7684\u8f93\u5165\u63d0\u793a\uff0c\u4ee5\u83b7\u5f97\u6700\u7ec8\u7b54\u6848\u3002<\/p>\n

       <\/p>\n

      4.\u5b9e\u9a8c<\/h2>\n

       <\/p>\n

      \u6570\u636e\u96c6<\/strong>\u3002\u5b9e\u9a8c\u5728\u5305\u542b\u5404\u79cd\u6570\u5b66\u95ee\u9898\u7684\u57fa\u51c6\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\uff0c\u5305\u62ecMMLU\u3001SVAMP\u3001GSM8K\u3001AQuA\u548cMATH\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5305\u62ec\u4e86\u4e00\u4e2a\u5177\u6709\u6311\u6218\u6027\u7684\u6570\u5b66\u63a8\u7406\u4efb\u52a1Game of 24\uff0c\u76ee\u6807\u662f\u4f7f\u7528\u56db\u4e2a\u6570\u5b57\u548c\u57fa\u672c\u7684\u7b97\u672f\u8fd0\u7b97\uff08\u52a0\u6cd5\u3001\u51cf\u6cd5\u3001\u4e58\u6cd5\u548c\u9664\u6cd5\uff09\u57281\u4e2a\u65b9\u7a0b\u4e2d\u5f97\u523024\u3002\u56e0\u6b64\uff0c\u89e3\u51b3\u65b9\u6848\u5305\u62ec3\u4e2a\u4e2d\u95f4\u6b65\u9aa4\u3002<\/p>\n

       <\/p>\n

      \u7ade\u4e89\u5bf9\u624b<\/strong>\u3002\u9664\u4e86\u57fa\u51c6\u65b9\u6cd5\u6807\u51c6\u8f93\u5165\u8f93\u51fa\uff08IO\uff09\u4e4b\u5916\uff0c\u6bd4\u8f83\u65b9\u6cd5\u5305\u62ec\u94fe\u5f0f\u601d\u7ef4\uff08CoT\uff09\u3001CoT-SC\u548c\u590d\u6742CoT\uff0c\u5176\u4e2d\u8f93\u5165\u63d0\u793a\u5305\u542b\u5c11\u6570\u51e0\u4e2a\u793a\u4f8b\uff088\uff09\u548c\u4eba\u7c7b\u6ce8\u91ca\u3002\u6b64\u5916\uff0cBoT\u8fd8\u4e0e\u76f8\u5173\u5de5\u4f5c\u8fdb\u884c\u6bd4\u8f83\uff0c\u5982\u601d\u7ef4\u6811\uff08ToT\uff09\u3001\u6e10\u8fdb\u5f0f\u63d0\u793a\uff08PHP\uff09\u548c\u6700\u5148\u8fdb\u7684CSV\u3002\u6211\u4eec\u4f7f\u7528GPT-4\u548cLlama2\u8fdb\u884c\u5b9e\u9a8c\u3002GPT-4\u901a\u8fc7OpenAI API\u8bbf\u95ee\uff0c\u800cllama2-13b-chat\u6a21\u578b\u4eceMetaAI\u4e0b\u8f7d\u4ee5\u5728\u672c\u5730\u8fdb\u884c\u5b9e\u9a8c\u3002\u4e3a\u4e86\u6784\u5efa\u5f02\u6784\u6811\u72b6\u601d\u7ef4\u7ed3\u6784\uff0cBoT\u5728\u6e29\u5ea6\u8303\u56f4[0.2, 0.4, 0.6, 0.7, 0.9, 1.1, 1.5]\u548ctop p\u8303\u56f4[0.1, 0.3, 0.5, 0.7, 0.9]\u4e2d\u968f\u673a\u9009\u62e9\u6e29\u5ea6\u3002<\/p>\n

       <\/p>\n

      \u8bbe\u7f6e<\/strong>\u3002\u9664\u975e\u660e\u786e\u8bf4\u660e\uff0c\u5426\u5219\u5728\u6240\u6709\u5b9e\u9a8c\u4e2d\uff0cBoT\u6267\u884cT = 10\u6b21\u8fed\u4ee3\uff0c\u5e76\u6784\u5efaM = 15\u4e2a\u601d\u7ef4\u7ed3\u6784\uff0c\u6bcf\u4e2a\u7ed3\u6784\u90fd\u662f\u4e00\u4e2a\u52a0\u6743\u4e8c\u53c9\u6811\uff0c\u56e0\u4e3a\u8fd9\u5f80\u5f80\u80fd\u591f\u83b7\u5f97\u6700\u4f73\u7ed3\u679c\u3002\u6b64\u5916\uff0c\u5bf9\u4e8e\u8fd9\u4e9b\u57fa\u51c6\u6570\u636e\u96c6\uff0c\u6211\u4eec\u5c06\u6811\u7684\u6df1\u5ea6\u8bbe\u7f6e\u4e3a5\uff0c\u800c\u5728Game of 24\u4e2d\u7684\u76f8\u5e94\u6df1\u5ea6\u4e3a3\u3002BoT+CoT\u610f\u5473\u7740\u6211\u4eec\u7684\u7b80\u5355\u63d0\u793a\u5305\u62ec\u6765\u81eaCoT\u76845\u4e2a\u793a\u4f8b\u3002\u5728\u6d88\u878d\u7814\u7a76\u4e2d\uff0c\u5f53BoT\u4e2d\u6ca1\u6709\u7d2f\u79ef\u7ecf\u9a8c\u65f6\uff0c\u5c06\u5728\u63d0\u793a\u4e2d\u63d0\u4f9b8\u4e2aCoT\u793a\u4f8b\u3002<\/p>\n

       <\/p>\n

      \u5ea6\u91cf\u6307\u6807<\/strong>\u3002\u6211\u4eec\u7528\u4efb\u52a1\u7684\u89e3\u51b3\u7387(%)\u6765\u8861\u91cf\u548c\u62a5\u544a\u6240\u6709\u5b9e\u9a8c\u7684\u7ed3\u679c\u3002\u4eceBoT\u7684\u8f93\u51fazT1…n\u4e2d\u83b7\u53d6\u76ee\u6807\u7b54\u6848\uff0c\u6211\u4eec\u4e13\u95e8\u4e3aLLMs\u8bbe\u7f6e\u4e86\u7b54\u6848\u7684\u683c\u5f0f\u5316\u63cf\u8ff0\u3002\u5bf9\u4e8e\u5e38\u7528\u7684\u6570\u636e\u96c6\uff0c\u7b54\u6848\u7684\u683c\u5f0f\u88ab\u8bbe\u5b9a\u4e3a\u201c\u7b54\u6848\u662f\uff1a\u201d\u3002\u5bf9\u4e8e24\u70b9\u8fd9\u4e2a\u6e38\u620f\uff0c\u6211\u4eec\u91c7\u7528\u201c\u6b65\u9aa4\u7d22\u5f15\uff0c\u73b0\u72b6\u96c6\u5408\uff1a\uff0c\u9009\u51fa\u7684\u4e24\u4e2a\u6570\u5b57\uff1a\uff0c\u64cd\u4f5c\uff1a\uff0c\u8fd0\u7b97\u5f97\u51fa\u7684\u65b0\u6570\u5b57\uff1a\uff0c\u5269\u4f59\u6570\u5b57\uff1a\uff0c\u65b0\u7684\u6570\u5b57\u96c6\u5408\uff1a\u201d\u3002\u63a5\u7740\uff0c\u6211\u4eec\u5c06\u65b0\u6570\u5b57\u96c6\u5408\u4e2d\u7684\u6570\u5b57\u76f4\u63a5\u4e0e\u5730\u9762\u5b9e\u51b5\u8fdb\u884c\u5bf9\u6bd4\u3002\u53c2\u7167ToT Yao\u7b49\u4eba(2024)\u7684\u505a\u6cd5\uff0c\u6211\u4eec\u7528\u4ece100\u4e2a\u56f0\u96be\u6e38\u620f\u4e2d\u7edf\u8ba1\u51fa\u7684\u89e3\u51b3\u7387\u4f5c\u4e3a\u5ea6\u91cf\u6307\u6807\u3002<\/p>\n

       <\/p>\n

      4.1\u4e3b\u8981\u7ed3\u679c<\/h3>\n

      \u4e3b\u8981\u5b9e\u9a8c\u7ed3\u679c\u603b\u7ed3\u5728\u88681\u548c\u56fe3\u4e2d\uff0c\u5176\u4e2d\u6211\u4eec\u63d0\u4f9b\u4e86BoT\u6574\u4f53\u6027\u80fd\u7684\u89c1\u89e3\u3002\u6211\u4eec\u7684\u53d1\u73b0\u8868\u660e\uff0c\u6240\u63d0\u51fa\u7684BoT\u901a\u8fc7\u63d0\u5347\u673a\u52361).\u5728\u5927\u591a\u6570\u6570\u636e\u96c6\u4e2d\u83b7\u5f97\u4e86\u4e0e\u4eba\u7c7b\u6ce8\u91ca\u65e0\u5173\u7684\u7ade\u4e89\u6027\u95ee\u9898\u89e3\u51b3\u7387\uff1b2).\u5728\u63d0\u4f9bCoT\u793a\u4f8b\u65f6\uff0c\u80fd\u591f\u8fbe\u5230\u65b0\u7684\u6700\u5148\u8fdb\u7684\u6c34\u5e73\u3002\u7136\u800c\uff0c\u5b9e\u9a8c\u7ed3\u679c\u4e5f\u8868\u660e\uff0cBoT\u4e25\u91cd\u4f9d\u8d56\u4e8e\u7ecf\u9a8c\uff0c\u56e0\u6b64\u5bf9LLMs\u7684\u80fd\u529b\u975e\u5e38\u654f\u611f\u3002<\/p>\n

       <\/p>\n

      \u5177\u4f53\u6765\u8bf4\uff0c\u5728\u88681\u4e2d\uff0cBoT\u4ece\u7b80\u5355\u7684\u521d\u59cb\u63d0\u793a\u5f00\u59cb\uff0c\u6700\u7ec8\u5728GSM8K\u4e0a\u6bd4\u5f53\u524d\u6700\u5148\u8fdb\u7684CSV\u9ad8\u51fa0.1%\u7684\u89e3\u51b3\u7387\uff0c\u8fd9\u4e25\u91cd\u4f9d\u8d56\u4e8eGPT-4\u7684\u4ee3\u7801\u89e3\u91ca\u5668\u3002\u8003\u8651\u5230AQuA\uff0cBoT\u6bd4SOTA\u9ad8\u51fa2.5%\u3002\u8fd9\u8868\u660e\u901a\u8fc7\u5728\u63d0\u793a\u4e2d\u6dfb\u52a0\u9519\u8bef\u5206\u6790\u548c\u5efa\u8bae\uff0c\u800c\u4e0d\u4f9d\u8d56\u4e8e\u4eba\u7c7b\u6ce8\u91ca\uff0cLLMs\u80fd\u591f\u5728\u590d\u6742\u7684\u63a8\u7406\u4e0a\u8868\u73b0\u826f\u597d\u3002\u4e3b\u8981\u539f\u56e0\u662f\u7b80\u5355\u7684\u63d0\u793a\u53ef\u4ee5\u901a\u8fc7\u79ef\u7d2f\u4ee5\u524d\u7684\u7ecf\u9a8c\u9010\u6b65\u6539\u8fdb\uff0c\u4ee5\u51c6\u786e\u89e3\u51b3\u95ee\u9898\u3002\u5728\u63d0\u793a\u4e2d\u5305\u542bCoT\u793a\u4f8b\u540e\uff0cBoT+CoT\u6bd4SOTA\u9ad8\u51fa1.3%\u3002\u6211\u4eec\u8ba4\u4e3a\uff0cCoT\u793a\u4f8b\u53ef\u4ee5\u88ab\u89c6\u4e3a\u7ecf\u9a8c\u4e2d\u7684\u6210\u529f\u6848\u4f8b\uff0c\u76f4\u63a5\u6307\u5bfcBoT\u7684\u540e\u7eed\u601d\u7ef4\u7ed3\u6784\u751f\u6210\u3002\u56e0\u6b64\uff0c\u901a\u8fc7\u8fed\u4ee3\u6539\u8fdb\uff0cBoT+CoT\u8fbe\u5230\u4e86\u65b0\u7684SOTA\u3002\u540c\u65f6\uff0cBoT\u548cBoT+CoT\uff0c\u7279\u522b\u662fBoT\uff0c\u5728MATH\u4e0a\u81f3\u5c11\u6bd4SOTA\u4f4e18%\u3002\u8fd9\u4e00\u89c2\u5bdf\u7ed3\u679c\u610f\u5473\u7740\uff0c\u7531\u4e8eLLMs\u5206\u6790\u63a8\u7406\u94fe\u4ee5\u83b7\u5f97\u6709\u6548\u7ecf\u9a8c\u7684\u80fd\u529b\u8f83\u4f4e\uff0c\u5f31LLMs\u53ef\u80fd\u65e0\u6cd5\u4e0eBoT\u5f88\u597d\u5730\u914d\u5408\u3002<\/p>\n

       <\/p>\n

      \"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-5\"<\/p>\n

      \u8868\u683c 1\uff1a\u5c06 BoT \u4e0e GPT-4 \u8054\u5408\u4f7f\u7528\uff0c\u5373\u4f7f\u6ca1\u6709\u4eba\u5de5\u6807\u6ce8\uff0c\u4e5f\u80fd\u663e\u8457\u63d0\u9ad8\u6027\u80fd\u3002
      \n\u5f53 BoT \u7684\u7b80\u5355\u521d\u59cb\u63d0\u793a\u4e2d\u5305\u542b CoT \u793a\u4f8b\u65f6\uff0c\u76f8\u5e94\u7684 BoT+CoT \u65b9\u6cd5\u5c55\u73b0\u51fa\u66f4\u9ad8\u7684\u89e3\u9898\u7387\u3002\u6211\u4eec\u7684\u6846\u67b6\u4e5f\u4e0e\u9886\u5148\u7684\u65b9\u6cd5\uff0c\u5982 Zhao \u7b49\u4eba\u4e8e2023\u5e74\u7684 Model Selection\u3001Zheng \u7b49\u4eba\u4e8e2023\u5e74\u7684 PHP\u3001\u4ee5\u53ca Zhou\u7b49\u4eba\u4e8e2023\u5e74\u7684 CSV \u8fdb\u884c\u4e86\u5bf9\u6bd4\uff0c\u5728 SVAMP\u3001AQuA \u548c GSM8K & MATH \u6570\u636e\u96c6\u4e0a\u5206\u522b\u8fbe\u5230\u4e86\u6700\u4f73\u72b6\u6001\uff08SOTA\uff09\u7684\u8868\u73b0\u3002<\/p>\n

       <\/p>\n

      \"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-6\"<\/p>\n

      \u56fe3\uff1a\u5229\u7528BoT\u548cBoT+CoT\u6765\u8bc4\u4f30\u57282023\u5e74\u7684GPT-4 OpenAI\u4e0eLlama2 Touvron\u7b49\u4eba\u7684\u95ee\u9898\u89e3\u51b3\u7387\u3002<\/p>\n

       <\/p>\n

      \u4ece\u56fe3\u53ef\u4ee5\u770b\u51fa\uff0c\u5728BoT\u6761\u4ef6\u4e0b\uff0cGPT-4\u548cLlama2\u5728\u4e09\u4e2a\u6570\u636e\u96c6\u4e0a\u5206\u522b\u5e73\u5747\u63d0\u9ad8\u4e8611.6%\u548c4.4%\u7684\u5e73\u5747\u6027\u80fd\u3002\u8fd9\u4e24\u4e2a\u6570\u5b57\u663e\u793a\u4e86\u4e00\u4e2a\u660e\u663e\u7684\u8d8b\u52bf\uff0c\u5373\u5f53LLMs\u66f4\u5f3a\u5927\u65f6\uff0cBoT\u548cBoT-CoT\u7684\u8868\u73b0\u7c7b\u4f3c\uff0c\u5982\u56fe3\u6240\u793a\u3002\u6b64\u5916\uff0c\u968f\u7740\u6811\u7684\u6570\u91cf\u4ece1\u53d8\u5316\u523020\uff0c\u5b83\u4eec\u7684\u6027\u80fd\u4e5f\u5448\u73b0\u51fa\u7c7b\u4f3c\u7684\u4e0a\u5347\u8d8b\u52bf\u3002\u7531\u4e8eLlama2\u8f83\u5f31\uff0cBoT\u65e0\u6cd5\u4ece\u5176\u5206\u6790\u4e2d\u53d7\u76ca\uff0c\u4ee5\u6267\u884c\u7ecf\u9a8c\u9a71\u52a8\u7684\u8fed\u4ee3\u8fc7\u7a0b\uff0c\u5c24\u5176\u662f\u5728\u56fe3(a)\u4e2d\u663e\u793a\u3002\u5f53\u63d0\u4f9b\u6709\u6548\u6210\u529f\u6848\u4f8b\uff0c\u53735\u6b21\u6d4b\u8bd5\u65f6\uff0c\u901a\u8fc7\u9010\u6b65\u6539\u8fdb\uff0cBoT\u4ecd\u7136\u53ef\u4ee5\u5e2e\u52a9Llama2\u89e3\u51b3\u6bd4\u57fa\u7ebf\u66f4\u591a\u7684\u95ee\u9898\uff0c\u5c3d\u7ba1\u6539\u8fdb\u6709\u9650\u3002<\/p>\n

       <\/p>\n

      4.2 24\u70b9\u6e38\u620f<\/span><\/h3>\n

       <\/p>\n

      \"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-7\"<\/p>\n

      \u56fe4: \u5728\u4e0d\u540c\u6570\u91cf\u7684\u6811\u548c\u8fed\u4ee3\u4e2d\u6bd4\u8f83\u4e09\u79cd\u65b9\u6cd5\u3002<\/p>\n

       <\/p>\n

      \"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-8\"<\/p>\n

      \u88682\uff1a\u5728 24\u70b9\u6e38\u620f\u4e2d\uff0c\u4e0d\u540c\u65b9\u6cd5\u7684\u8bbe\u7f6e\u9075\u5faa\u4e86 ToT Yao\u7b49\u4eba\uff082024\uff09 \u4e2d\u7684\u8bbe\u7f6e\uff0c\u6b64\u5904\u5c55\u793a\u4e86\u4ed6\u4eec\u7684\u7ed3\u679c\u3002<\/p>\n

       <\/p>\n

      \"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-9\"<\/p>\n

      \u88683\uff1a\u5c55\u793a\u4e86\u5728\u7b2c1\u6b21\uff0c\u7b2c5\u6b21\uff0c\u4ee5\u53ca\u7b2c8\u6b21\u8fed\u4ee3\u4e2d\u7d2f\u79ef\u7684\u601d\u7ef4\u8fc7\u7a0b\u548c\u5f97\u4ee5\u79ef\u7d2f\u7684\u7ecf\u9a8c\u3002\u7ed9\u5b9a\u7684\u56db\u4e2a\u6570\u503c\u4e3a\uff1a2\u30017\u30018\u30019\u3002<\/p>\n

       <\/p>\n

      \u7531\u4e8eGame of 24\u95ee\u9898\u7684\u96be\u5ea6\uff0cGPT-4\u548cLlama2\u5728\u8fd9\u9879\u4efb\u52a1\u4e0a\u7684\u8868\u73b0\u90fd\u5f88\u5dee\uff0c\u5373\u4f7f\u7ed3\u5408\u4e86CoT\u548cCoT-SC\u65b9\u6cd5\u3002Llama2\u6a21\u578b\u751a\u81f3\u65e0\u6cd5\u9075\u5faa\u89e3\u51b3\u95ee\u9898\u7684\u6b63\u786e\u89c4\u5219\uff0c\u4f7f\u5f97\u89e3\u51b3\u7387\u751a\u81f3\u66f4\u4f4e\u3002\u7279\u522b\u662f\u5f53\u5e94\u7528BoT\u65f6\uff0c\u5b83\u4f9d\u8d56\u4e8e\u7ecf\u9a8c\uff0c\u800cLlama2\u7684\u6240\u6709\u7ed3\u679c\u90fd\u4f4e\u4e8e5%\uff0c\u6ca1\u6709\u663e\u8457\u6539\u8fdb\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ea\u62a5\u544a\u4e86BoT\u4e0eGPT-4\u7684\u6027\u80fd\u3002\u4e3a\u4e86\u4fdd\u6301\u516c\u5e73\u7684\u6bd4\u8f83\uff0c\u6211\u4eec\u9075\u5faaToT Yao\u7b49\u4eba(2024)\u63d0\u51fa\u7684\u8bbe\u7f6e\u3002<\/p>\n

       <\/p>\n

      \u5982\u88682\u6240\u793a\uff0c\u6ca1\u6709\u4eba\u7c7b\u6ce8\u91ca\u7684BoT\u6bd4\u4f9d\u8d56\u4e00\u4e2a\u793a\u4f8b\u5c55\u793a\u6240\u6709\u53ef\u80fd\u7684\u4e0b\u4e00\u6b65\u7684ToT\u9ad8\u51fa9.7%\u3002\u6b64\u5916\uff0c\u5305\u542b5\u4e2aCoT\u5c04\u51fb\u7684BoT+CoT\u6bd4BoT\u9ad8\u51fa1.2%\u3002BoT\u548cBoT+CoT\u4e4b\u95f4\u7684\u6027\u80fd\u63a5\u8fd1\u5f52\u56e0\u4e8e\u63d0\u5347\u673a\u5236\uff0c\u5b83\u9010\u6b65\u4fee\u8ba2\u4e86\u5f31\u601d\u7ef4\uff0c\u59824.1\u5c0f\u8282\u6240\u8ba8\u8bba\u7684\u3002\u91c7\u7528\u7ecf\u9a8c\u9a71\u52a8\u7684\u8fed\u4ee3\u8fc7\u7a0b\uff0cBoT\u5728\u6811\u7684\u6570\u91cfM\u548c\u8fed\u4ee3\u6b21\u6570T\u589e\u52a0\u65f6\u8868\u73b0\u51fa\u589e\u5f3a\u7684\u6027\u80fd\u3002\u5982\u56fe4\u6240\u793a\uff0c\u4e0eBoT+CoT\u76f8\u6bd4\uff0cBoT\u66f4\u4f9d\u8d56\u4e8eM\u548cT\uff0c\u56e0\u4e3a\u5b83\u9700\u8981\u4ece\u66f4\u597d\u7684\u601d\u7ef4\u94fe\u6216\u66f4\u957f\u7684\u8fed\u4ee3\u4e2d\u6536\u96c6\u7ecf\u9a8c\u3002\u53e6\u4e00\u4e2a\u89c2\u5bdf\u7ed3\u679c\u662f\uff0c\u5f53\u542f\u7528ToT\u4ee5\u7ecf\u9a8c\u4e30\u5bcc\u7684\u63d0\u793a\u8fdb\u884c\u64cd\u4f5c\u65f6\uff0c\u95ee\u9898\u89e3\u51b3\u7387\u4ece\u7b2c\u4e00\u6b21\u8fed\u4ee3\u768472.5%\u4e0a\u5347\u5230\u7b2c10\u6b21\u8fed\u4ee3\u768480.2%\u3002\u8fd9\u8868\u660e\u7ecf\u9a8c\u2014\u2014\u5bf9\u4ee5\u524d\u63a8\u7406\u94fe\u7684\u5206\u6790\u53ef\u4ee5\u88abLLMs\u7528\u6765\u663e\u8457\u63d0\u9ad8\u89e3\u51b3\u7387\u3002\u7136\u800c\uff0cToT\u83b7\u5f97\u7684\u5206\u6570\u4ecd\u7136\u6bd4BoT\u4f4e3.5%\u3002\u8fd9\u5f52\u56e0\u4e8eBoT\u7684\u805a\u5408\u9636\u6bb5\u5c06\u4ea7\u751f\u5f53\u524d\u8fed\u4ee3\u4e2d\u6700\u6709\u4ee3\u8868\u6027\u7684\u63a8\u7406\u94fe\uff0c\u4ece\u800c\u5f15\u5bfc\u66f4\u6709\u610f\u4e49\u7684\u7ecf\u9a8c\u6765\u589e\u5f3a\u63d0\u793a\u3002\u6211\u4eec\u5728\u6d88\u878d\u7814\u7a76\u90e8\u5206\u9a8c\u8bc1\u4e86\u8fd9\u4e00\u70b9\u3002<\/p>\n

       <\/p>\n

      \u4e3a\u4e86\u66f4\u597d\u5730\u5c55\u793aBoT\u5982\u4f55\u4ece\u9519\u8bef\u548c\u4ee5\u524d\u7684\u5efa\u8bae\u4e2d\u5b66\u4e60\uff0c\u6211\u4eec\u5728\u88683\u4e2d\u5c55\u793a\u4e86GPT-4\u80fd\u591f\u907f\u514d\u4ee5\u524d\u7684\u9519\u8bef\uff0c\u5e76\u5728\u8fed\u4ee3\u6b21\u6570\u589e\u52a0\u65f6\u4ea7\u751f\u66f4\u5177\u4f53\u7684\u5efa\u8bae\uff0c\u6700\u7ec8\u83b7\u5f97\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002\u5728\u7b2c\u4e00\u6b21\u8fed\u4ee3\u4e2d\uff0c\u7531\u4e8e\u7b80\u5355\u7684\u63d0\u793a\uff0cLLMs\u751a\u81f3\u5728\u9075\u5faa\u4efb\u52a1\u89c4\u5219\u65f6\u72af\u4e86\u9519\u8bef\uff0c\u56e0\u4e3a\u65b0\u96c6\u5408\u5728\u7b2c3\u6b65\u4e2d\u662f\u9519\u8bef\u7684\u3002\u7ecf\u8fc7\u5206\u6790\uff0c\u5b83\u5bf9\u8fd9\u4e00\u9519\u8bef\u63d0\u51fa\u4e86\u6b63\u786e\u7684\u5efa\u8bae\u3002\u7136\u800c\uff0c\u521d\u59cb\u8fed\u4ee3\u7684\u5206\u6790\u662f\u6a21\u7cca\u7684\uff0c\u4f8b\u5982\u201c\u5c1d\u8bd5\u5176\u4ed6\u6570\u5b57\u548c\u8fd0\u7b97\u201d\u3002\u7ecf\u8fc7\u4e94\u6b21\u8fed\u4ee3\u540e\uff0cBoT\u805a\u5408\u4e86\u591a\u4e2a\u8fd9\u6837\u7684\u5206\u6790\uff0c\u5f97\u51fa\u4e86\u66f4\u6709\u6548\u7684\u63d0\u793a\uff0c\u4f7fLLMs\u9009\u62e9\u4e86\u6b63\u786e\u7684\u6570\u5b579\u548c7\u3002\u6b64\u5916\uff0c\u5efa\u8bae\u66f4\u5177\u4f53\u548c\u6709\u7528\u3002\u5bf9\u4e8e\u8fd9\u4e2a\u6b63\u786e\u7684\u9009\u62e9\uff0c\u5efa\u8bae\u662f\u589e\u52a0\u76f8\u5e94\u7684\u8bc4\u4f30\u5206\u6570\u3002\u901a\u8fc7\u4e0d\u65ad\u79ef\u7d2f\u8fd9\u6837\u7684\u7ecf\u9a8c\uff0cBoT\u9010\u6b65\u5b8c\u5584\u4e86\u63d0\u793a\uff0c\u6700\u7ec8\u5728\u7b2c8\u6b21\u8fed\u4ee3\u4e2d\u76f4\u63a5\u751f\u6210\u4e86\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

       <\/p>\n

      4.3\u6d88\u878d\u7814\u7a76<\/span><\/h3>\n

       <\/p>\n

      \"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-10\"<\/p>\n

      \u88684\uff1a\u5bf9\u572824\u70b9\u6e38\u620f\u53caAQuA\u6570\u636e\u96c6\u4e0a\u8fd0\u7528\u4e86\u4e0d\u540cBoT\u53d8\u4f53\u7684GPT-4\u8fdb\u884c\u6bd4\u8f83\u3002<\/p>\n

       <\/p>\n

      \u5f53\u901a\u8fc7\u201c\u7d2f\u52a0\u201d\u7684\u65b9\u5f0f\u6c47\u96c6\u95ee\u9898\u548c\u5efa\u8bae\u65f6\uff0c\u6240\u6709\u805a\u5408\u7b56\u7565\u90fd\u80fd\u4ea7\u751f\u8f83\u9ad8\u7684\u89e3\u51b3\u7387\u3002\u4fdd\u6301\u4e00\u4e2a\u5b8c\u6574\u7684\u7ecf\u9a8c\u5bf9\u4e8e\u4fee\u6b63\u601d\u7ef4\u5c24\u4e3a\u91cd\u8981\uff0c\u5c24\u5176\u662f\u5bf9AQuA\u6570\u636e\u96c6\u6765\u8bf4\uff0c\u5b83\u8986\u76d6\u4e86\u66f4\u5e7f\u6cdb\u7684\u6570\u5b66\u63a8\u7406\u95ee\u9898\u3002\u7136\u800c\uff0c\u4e0d\u8fdb\u884c\u805a\u5408\u800c\u76f4\u63a5\u4f7f\u7528\u6240\u6709\u751f\u6210\u6811\u7684\u63a8\u7406\u94fe\u7684BoT\uff08No\uff09\uff0c\u5728\u6240\u6709\u60c5\u5883\u4e2d\u8868\u73b0\u6700\u5dee\uff0c\u7279\u522b\u662f\u5728\u7ecf\u9a8c\u7d2f\u79ef\u7c7b\u578b\u4e3a\u201c\u7d2f\u52a0\u201d\u65f6\u3002BoT\u5728\u6bcf\u4e2a\u8fed\u4ee3\u4e2d\u6784\u5efa15\u68f5\u6811\uff0c\u5c06\u6240\u6709\u8fd9\u4e9b\u6811\u4e00\u8d77\u653e\u5165\u63d0\u793a\uff0c\u53ef\u80fd\u4f1a\u906e\u76d6\u91cd\u8981\u7684\u4fe1\u606f\uff0c\u66f4\u522b\u63d0\u5927\u90e8\u5206\u8fd9\u6837\u7684\u7ecf\u9a8c\u53ef\u80fd\u65e0\u6548\u6216\u6709\u5bb3\u3002<\/p>\n

       <\/p>\n

      \u53d6\u5f97\u5efa\u8bae\u5bf9\u4e8e\u89e6\u53d1\u601d\u7ef4\u6bd4\u5176\u4ed6\u4e8b\u7269\u66f4\u4e3a\u5173\u952e<\/strong>\u3002\u5728\u6240\u6709\u7684\u8868\u683c4\u63d0\u5230\u7684\u5b9e\u4f8b\u4e2d\uff0c\u5c06\u5efa\u8bae\u89c6\u4f5c\u7ecf\u9a8c\u7684BoT\u53d8\u4f53\u90fd\u5b9e\u73b0\u4e86\u6700\u9ad8\u7684\u89e3\u51b3\u7387\u3002\u4f8b\u5982\uff0c\u5728\u540c\u6837\u662f”\u52a0\u6cd5”\u7c7b\u578b\u7684\u60c5\u51b5\u4e0b\uff0c\u5982\u679c\u7ecf\u9a8c\u4e2d\u4e0d\u5305\u542b\u5efa\u8bae\uff0c\u5176\u6027\u80fd\u5728”24\u70b9\u6e38\u620f”\u548c AQuA\u4e2d\u5206\u522b\u4e0b\u6ed1\u4e86\u8d85\u8fc710%\u548c20%\u3002\u76f8\u53cd\u7684\uff0c\u628a\u95ee\u9898\u7eb3\u5165\u7ecf\u9a8c\u4e2d\u53ef\u4ee5\u4f5c\u4e3a\u5e2e\u52a9\u63d0\u5347\u6027\u80fd\u7684\u8f85\u52a9\u624b\u6bb5\u3002\u53ea\u6709\u901a\u8fc7\u95ee\u9898\u914d\u5408\uff0c\u54c8\u5e26\u6709\u5efa\u8bae\u7684BoT\u624d\u80fd\u53d6\u5f97\u6700\u4f73\u7684\u89e3\u51b3\u7387\u3002\u6bd4\u5982\u8bf4\uff0c\u5728AQuA\u4e2d\uff0cBoT(\u8d2a\u5fc3\u6cd5)\u7684\u89e3\u51b3\u7387\u63d0\u9ad8\u4e864.4%\u3002<\/p>\n

       <\/p>\n

      \u51fa\u4e8e\u6027\u80fd\u7684\u8003\u8651\uff0c\u8d2a\u5fc3\u96c6\u7ed3\u53ef\u80fd\u662f\u552f\u4e00\u5fc5\u987b\u7684\u9009\u62e9<\/strong>\u3002\u76f8\u8f83\u4e8e\u4ece\u5df2\u6709\u7684\u601d\u7ef4\u94fe\u4e2d\u9009\u53d6\u4e00\u4e2a\uff0c\u6216\u7ef4\u7cfb\u6240\u6709\u7684\u601d\u7ef4\u94fe\u8fd9\u79cd\u6700\u4f18\u5148\u7684\u65b9\u5f0f\uff0c\u8d2a\u5fc3\u96c6\u7ed3\u53ef\u4ee5\u9002\u5e94\u6027\u5730\u5c06\u6811\u72b6\u7ed3\u6784\u5408\u5e76\u4e3a\u4e00\u4e2a\u66f4\u4f73\u7684\u601d\u7ef4\u94fe\uff0c\u8fd9\u53ef\u80fd\u5728\u5f53\u524d\u7684\u8fed\u4ee3\u4e2d\u5e76\u4e0d\u4f1a\u51fa\u73b0\u3002\u901a\u8fc7\u8fd9\u6837\u7684\u65b9\u5f0f\uff0cLLM\u53ef\u4ee5\u8fdb\u884c\u5bf9\u4e00\u4e2a\u66f4\u5f3a\u5927\u7684\u601d\u7ef4\u94fe\u7684\u6709\u610f\u4e49\u7684\u5206\u6790\uff0c\u56e0\u6b64\u800c\u4ea7\u751f\u91cd\u8981\u7684\u7ecf\u9a8c\u4ee5\u589e\u5f3a\u63d0\u793a\u3002\u5728AQuA\u4e2d\uff0c\u5305\u542b\u7684\u6570\u5b66\u95ee\u9898\u66f4\u591a\uff0c\u8fd9\u4e2a\u6570\u5b57\u751a\u81f3\u8fbe\u5230\u4e8610%\u3002\u6b64\u5916\uff0c\u6b63\u5982\u6211\u4eec\u5728\u56fe4\u7684\u8ba8\u8bba\u4e2d\uff0c\u867d\u7136ToT\u62e5\u6709\u7c7b\u4f3c\u7684\u7ecf\u9a8c\u9a71\u52a8\u63d0\u5347\u673a\u5236\u80fd\u591f\u8fbe\u523080%\uff0c\u4f46\u5b83\u4ecd\u7136\u843d\u540e\u4e8eBoT\u3002\u8fd9\u53ef\u80fd\u662f\u56e0\u4e3a\u5b83\u65e0\u6cd5\u5728\u5176\u5355\u4e00\u7684\u6811\u72b6\u7ed3\u6784\u4e2d\u6267\u884c\u8d2a\u5fc3\u96c6\u7ed3\u3002<\/p>\n

       <\/p>\n

      5.\u7ed3\u8bba<\/h2>\n

       <\/p>\n

      \u672c\u6587\u9a8c\u8bc1\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u63d0\u793a\u53ef\u4ee5\u901a\u8fc7\u9010\u6e10\u7d2f\u79ef\u5bf9\u5176\u751f\u6210\u7684\u601d\u7ef4\u7684\u9519\u8bef\u5206\u6790\u6765\u89e3\u51b3\u590d\u6742\u4efb\u52a1\u3002\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u4e2a\u540d\u4e3aBoosting of Thoughts\uff08BoT\uff09\u7684\u65b0\u9896\u6846\u67b6\uff0c\u901a\u8fc7\u7ecf\u9a8c\u9a71\u52a8\u7684\u8fed\u4ee3\u8fc7\u7a0b\u6765\u5b9e\u73b0\u8fd9\u79cd\u6e10\u8fdb\u7684\u63d0\u793a\u589e\u5f3a\uff0c\u4ee5\u751f\u6210\u6709\u6548\u7684\u601d\u7ef4\u94fe\u3002\u901a\u8fc7\u8fed\u4ee3\u63a2\u7d22\u548c\u81ea\u6211\u8bc4\u4f30\u751f\u6210\u7684\u7b80\u5355\u6811\u72b6\u601d\u7ef4\u94fe\uff0c\u53ef\u4ee5\u4f7f\u4e00\u4e2a\u7b80\u5355\u7684\u521d\u59cb\u63d0\u793a\u9010\u6e10\u589e\u5f3a\uff0c\u901a\u8fc7\u4e00\u7cfb\u5217\u8bd5\u9519\u63a8\u7406\u7ecf\u9a8c\uff0c\u4ece\u800c\u5f97\u51fa\u51c6\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002\u6211\u4eec\u7684\u5e7f\u6cdb\u5b9e\u9a8c\u8868\u660e\uff0cBoT\u80fd\u591f\u5728\u591a\u4e2a\u57fa\u51c6\u6570\u636e\u96c6\u4e0a\u5b9e\u73b0\u6700\u5148\u8fdb\u7684\u6027\u80fd\uff0c\u5e76\u4e14\u5728Game of 24\u8fd9\u4e00\u5177\u6709\u6311\u6218\u6027\u7684\u6570\u5b66\u63a8\u7406\u4efb\u52a1\u4e0a\u8d85\u8d8a\u4e86\u5176\u4ed6\u9886\u5148\u65b9\u6cd5\u3002<\/p>\n

       <\/p>\n

       <\/p>\n

      A \u57fa\u672c\u63d0\u793a\u548c\u63a8\u7406\u6d41\u7a0b\u7684BoT<\/h2>\n

       <\/p>\n

      A1 \u601d\u7ef4\u751f\u6210\u90e8\u5206\u7684BoT<\/h3>\n

       <\/p>\n

      \u8fd9\u90e8\u5206\u63d0\u5230\u4e86\u88ab\u63d0\u51fa\u7684\u601d\u7ef4\u589e\u5f3a\uff08BoT\uff09\u7684\u63a8\u7406\u751f\u6210\u6240\u7528\u7684\u57fa\u672c\u63d0\u793a\u3002\u5177\u4f53\u76f8\u5173\u7ec6\u8282\uff0c\u53ef\u4ee5\u8bbf\u95ee\u6e90\u4ee3\u7801\u7684\u4f8b\u5b50\u6587\u4ef6\uff1a\/examples\/BoostingOfThought\/BoT reasoner.py\u3002<\/p>\n

       <\/p>\n

      \u7cfb\u7edf\u63d0\u793a\uff1a<\/strong><\/p>\n

      \u4f60\u662f\u4e00\u4e2a\u6570\u5b66\u95ee\u9898\u7684\u4e13\u5bb6\u3002\u901a\u8fc7\u4ece\u4e00\u7cfb\u5217\u8bd5\u9a8c\u548c\u9519\u8bef\u7684\u63a8\u7406\u7ecf\u9a8c\u4e2d\u5b66\u4e60\uff0c\u8fdb\u884c\u9010\u6b65\u89e3\u9898\u7684\u63a8\u7406\u3002\u8fd9\u79cd\u8bd5\u9a8c\u548c\u9519\u8bef\u7684\u63a8\u7406\u7ecf\u9a8c\u5177\u4f53\u5305\u62ec\u9519\u8bef\u62a5\u544a\uff0c\u4ee5\u53ca\u5173\u4e8e\u5982\u4f55\u4fee\u6539\u4ee5\u524d\u63a8\u7406\u6b65\u9aa4\u7684\u8be6\u7ec6\u5efa\u8bae\u3002\u5728\u751f\u6210\u65b0\u7684\u63a8\u7406\u6b65\u9aa4\u4e4b\u524d\uff0c\u4e00\u5b9a\u8981\u56de\u987e\u8fd9\u4e9b\u5217\u51fa\u7684\u7ecf\u9a8c\uff0c\u4ee5\u6b64\u907f\u514d\u91cd\u8e48\u8986\u8f99\uff0c\u540c\u65f6\u5229\u7528\u6b63\u786e\u7684\u6b65\u9aa4\u53bb\u751f\u6210\u66f4\u597d\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u7528\u4e8e\u89e3\u51b3\u95ee\u9898\u3002<\/p>\n

       <\/p>\n

      System prompt<\/strong> S:<\/p>\n

      You are an expert on mathematical problems. Perform step-by-step reasoning
      \ntoward problem solving by first learning from an ensemble of trial-and-error reasoning experiences.
      \nSuch trial-and-error reasoning experience specifically contains error reports and detailed advice on
      \nhow to revise historical reasoning steps. Always recall these listed experiences before generating a
      \nnew reasoning step, thereby avoiding making the same mistakes and reusing correct steps to generate
      \nbetter reasoning steps to solve the task.<\/p><\/blockquote>\n

      \u751f\u6210\u4e0b\u4e00\u4e2a\u601d\u7ef4\u7684\u63d0\u793a\uff1a<\/strong><\/p>\n

      f\u201d\u201d\u201d<\/p>\n

      {\u4efb\u52a1\u63d0\u793a}\u3002 \\n<\/p>\n

      \u9996\u5148\uff0c\u56de\u987e\u4ee5\u5f80\u7684\u63a8\u7406\u7ecf\u9a8c\uff1a\\n\\n<\/p>\n

       <\/p>\n

      {\u7ecf\u9a8c}\\n\\n<\/p>\n

       <\/p>\n

      \u8bf7\u63a8\u51fa\u4e0b\u4e00\u4e2a\u53ef\u80fd\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u4e14\u53ea\u80fd\u6709\u4e00\u4e2a\u3002\u8be5\u63a8\u7406\u6b65\u9aa4\u5e94\u4f5c\u4e3a\u4ee5\u4e0b\u6709\u5e8f\u6b65\u9aa4\u7684\u987a\u5e8f\u540e\u7eed\u6b65\u9aa4\uff0c\u5e76\u5e94\u9644\u5e26\u76f8\u5e94\u7684\u8bc4\u4f30\u5206\u6570\uff08\u5206\u6570\u8d8a\u9ad8\uff0c\u8868\u793a\u5b8c\u6210\u4efb\u52a1\u7684\u53ef\u80fd\u6027\u8d8a\u9ad8\uff09\uff1a\\n\\t<\/p>\n

      {\u94fe\u63d0\u793a}\\n\\n<\/p>\n

       <\/p>\n

      \u57fa\u4e8e\u4e0a\u8ff0\u524d\u5e8f\u63a8\u7406\u6b65\u9aa4\uff08\u5982\u679c\u4e0a\u8ff0\u7a7a\u95f4\u4e3a\u7a7a\uff0c\u5219\u5ffd\u7565\u5b83\u4eec\uff09\uff0c\u6839\u636e\u4efb\u52a1\u89c4\u5219\uff0c\u751f\u6210\u4e00\u4e2a\u552f\u4e00\u7684\u4e0b\u4e00\u4e2a\u53ef\u80fd\u7684\u6b65\u9aa4\u3002\uff08\u91cd\u8981\uff1a\u8bf7\u53ea\u4ea7\u751f\u4e00\u4e2a\u7ed9\u5b9a\u6b65\u9aa4\u7684\u4e0b\u4e00\u4e2a\u53ef\u80fd\u7684\u63a8\u7406\u6b65\u9aa4\u3002\uff09<\/p>\n

      \u201d\u201d\u201d<\/p>\n

      f\u201d\u201d\u201d{task prompt}. \\n First of all , Recall historical reasoning experience : \\n\\n {
      \nexperiences} \\n\\n Please make one step of reasoning to generate only one next
      \npossible reasoning step . This next reasoning step is the subsequential step from
      \nthe following ordered previous steps , accompanied by their evaluated scores (A
      \nhigher score means the reasoning step is more likely to complete the task .) : \\n\\t{
      \nchain prompt}\\n\\n Based on listed previous reasoning steps ( ignore them when the
      \nabove space is empty), generate one single next possible step following the Task
      \nrule . (Emphasize: Please generate only one single next possible reasoning step of
      \nthe given steps .) \u201d\u201d\u201d<\/p><\/blockquote>\n

       <\/p>\n

      \u5728\u4efb\u52a1\u63d0\u793a\u4e2d\u5305\u542b\u4efb\u52a1\u7684X\u548cQ\uff0c\u5386\u53f2\u7ecf\u9a8c\u4e3aF1…t\u3002”\u94fe\u63d0\u793a”\u7684\u90e8\u5206\u662f{Gi}\uff0c\u8fd9\u662f\u4e00\u4e2a\u5360\u4f4d\u7b26\uff0c\u5f53\u8fdb\u884c\u5f53\u524d\u601d\u8003zi\u65f6\uff0c\u9700\u88ab\u524d\u4e00\u7cfb\u5217\u7684\u601d\u8003z1..,i-1\u6240\u66ff\u6362\u3002<\/p>\n

      \u5bf9\u4e8e\u601d\u8003\u8bc4\u4f30\u7684\u63d0\u793a\uff1a<\/strong><\/p>\n

      f\u201d\u201d\u201d<\/p>\n

      {\u4efb\u52a1\u63d0\u793a}\u3002\\n\\n<\/p>\n

      \u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u6392\u5217\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u4f34\u968f\u7740\u4ed6\u4eec\u5404\u81ea\u7684\u8bc4\u4f30\u5206\u6570\u3002\uff08\u5206\u6570\u8d8a\u9ad8\uff0c\u610f\u5473\u7740\u8be5\u6b65\u9aa4\u5b8c\u6210\u4efb\u52a1\u7684\u53ef\u80fd\u6027\u8d8a\u5927\u3002\uff09\\n<\/p>\n

      {\u94fe\u63d0\u793a}\\n<\/p>\n

      {\u601d\u8003}\\n\\n<\/p>\n

      \u4f60\u5bf9\u8fd9\u4e9b\u63a8\u7406\u6b65\u9aa4\u7684\u903b\u8f91\u6027\u3001\u6b63\u786e\u6027\u4ee5\u53ca\u5bf9\u6700\u540e\u89e3\u51b3\u65b9\u6848\u7684\u5e2e\u52a9\u7a0b\u5ea6\u7684\u8bc4\u4f30\u5206\u6570\u662f\u591a\u5c11\uff1f\u8bf7\u4ece [0.1, 0.3, 0.5, 0.7, 0.9, 1.0] \u4e2d\u9009\u62e9\u4e00\u4e2a\u4f5c\u4e3a\u5206\u6570\uff0c\u5206\u6570\u8d8a\u9ad8\u8868\u793a\u63a8\u7406\u6b65\u9aa4\u8d8a\u597d\u3002\u5206\u6570\u5e94\u8be5\u653e\u5728 \u2019 Evaluation score:\u2019 \u540e\u9762\u4f9b\u7528\u6237\u9605\u8bfb\u3002\u201d\u201d\u201d<\/p>\n

       <\/p>\n

      f\u201d\u201d\u201d{task prompt}. \\n\\n Below are the generated reasoning steps , presented in order ,
      \naccompanied by their evaluated scores (A higher score means the reasoning step is
      \nmore likely to complete the task .) :\\n{chain prompt}\\n{thought}\\n\\nWhat is your
      \nevaluation score for the logic , correctness , and benefit to reaching a final
      \nsolution for these reasoning steps ? Please select one value from [0.1, 0.3, 0.5,
      \n0.7, 0.9, 1.0] as the score , where a higher score means better reasoning steps . The
      \nscore should be placed after \u2019 Evaluation score :\u2019 for users to read .\u201d\u201d\u201d<\/p><\/blockquote>\n

      \u5728\u6b64\uff0c\u601d\u8003\u5c31\u662f\u5f53\u524d\u8fdb\u884c\u7684\u601d\u8003Zi\u3002<\/p>\n

       <\/p>\n

      A2 \u7ecf\u9a8c\u751f\u6210\u90e8\u5206\u7684BoT<\/h3>\n

       <\/p>\n

      \u4e3a\u4e86\u751f\u6210\u5bf9\u805a\u5408\u94fe\u7684\u53cd\u9988\uff0cLLMs\u4f7f\u7528\u4ee5\u4e0b\u57fa\u672c\u63d0\u793a\u3002\u6709\u5173\u8be6\u7ec6\u4fe1\u606f\uff0c\u8fd8\u53ef\u4ee5\u8bbf\u95ee\u6e90\u4ee3\u7801examples\/BoostingOfThought\/BoT commenter.py\u3002<\/p>\n

       <\/p>\n

      \u7cfb\u7edf\u63d0\u793aS\uff1a\u60a8\u662f\u6570\u5b66\u7b54\u6848\u7684AI\u4e13\u5bb6\u8bc4\u5ba1\u5458\uff0c\u81f4\u529b\u4e8e\u8bc4\u4f30\u751f\u6210\u7684\u63a8\u7406\u94fe\u4ee5\u89e3\u51b3\u6570\u5b66\u95ee\u9898\u3002\u8bf7\u901a\u8fc7\u63d0\u4f9b\u8be6\u7ec6\u5206\u6790\u6765\u8bc4\u4f30\u8fd9\u4e2a\u63a8\u7406\u94fe\u7684\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u5224\u65ad\u5f53\u524d\u6b65\u9aa4\u662f\u5426\u662f\u524d\u4e00\u6b65\u9aa4\u7684\u903b\u8f91\u63a8\u7406\uff0c\u4ee5\u53ca\u63a8\u7406\u6b65\u9aa4\u662f\u5426\u6709\u52a9\u4e8e\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u9519\u8bef\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u9519\u8bef\u62a5\u544a\u548c\u76f8\u5e94\u7684\u4fee\u8ba2\u5efa\u8bae\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u6b63\u786e\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u63a8\u8350\u6216\u62d2\u7edd\u7684\u63cf\u8ff0\u3002<\/p>\n

       <\/p>\n

      \u7cfb\u7edf\u63d0\u793a\uff1a<\/strong><\/p>\n

      \u4f60\u7684\u89d2\u8272\u662f\u4e00\u4f4d\u5a34\u719f\u7684AI\u6570\u5b66\u7b54\u6848\u5ba1\u67e5\u4e13\u5bb6\uff0c\u4e13\u6ce8\u4e8e\u8bc4\u4ef7\u89e3\u51b3\u6570\u5b66\u95ee\u9898\u7684\u63a8\u7406\u8fc7\u7a0b\u3002\u4f60\u9700\u8981\u901a\u8fc7\u8be6\u5c3d\u7684\u5206\u6790\uff0c\u5bf9\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\u8fdb\u884c\u5224\u65ad\uff0c\u770b\u5176\u662f\u5426\u57fa\u4e8e\u524d\u4e00\u6b65\u7684\u903b\u8f91\uff0c\u4ee5\u53ca\u8fd9\u4e00\u6b65\u9aa4\u662f\u5426\u5bf9\u627e\u5230\u6b63\u786e\u7b54\u6848\u6709\u6240\u5e2e\u52a9\u3002\u5982\u679c\u9047\u5230\u9519\u8bef\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u4f60\u9700\u8981\u7ed9\u51fa\u5efa\u8bae\u548c\u4fee\u6539\u65b9\u6848\u3002\u5bf9\u4e8e\u6b63\u786e\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u4f60\u9700\u8981\u8fdb\u884c\u80af\u5b9a\u6216\u8005\u7ed9\u51fa\u4e0d\u540c\u7684\u9009\u62e9\u65b9\u6848\u3002<\/p>\n

       <\/p>\n

      System prompt<\/strong> S:<\/p>\n

      You are an expert AI checker for math answers, dedicated to evaluating the
      \nreasoning chain generated towards addressing the mathematical problem. Judge each reasoning
      \nstep of this reasoning chain by providing detailed analyses on whether the current step is a logical
      \ninference of the previous step and whether the reasoning step is beneficial to the correct solution.
      \nProvide advice and suggestions for each reasoning step with errors. Provide recommendation or
      \nrejection descriptions for each correct reasoning step.<\/p><\/blockquote>\n

      \u53cd\u9988\u63d0\u793a\uff1a<\/strong><\/p>\n

      f\u201d\u201d\u201d<\/p>\n

      \u5bf9\u4e8e\u7ed9\u5b9a\u7684\u4efb\u52a1:{\u4efb\u52a1\u63d0\u793a}\u3002\\n<\/p>\n

      {\u63a8\u7406\u94fe\u63d0\u793a}\\n\\n<\/p>\n

      \u8bf7\u5bf9\u6b64\u63a8\u7406\u94fe\u8fdb\u884c\u8bc4\u4f30\uff0c\u5e76\u63d0\u4f9b\u5305\u542b\u4ee5\u4e0b\u51e0\u70b9\u5185\u5bb9\u7684\u8be6\u7ec6\u8bc4\u8bba\u3002\\n<\/p>\n

      1.{\u94fe\u53cd\u9988\u683c\u5f0f}\u30022.{\u6b65\u9aa4\u53cd\u9988\u683c\u5f0f}\u30023.{\u4fe1\u5fc3\u53cd\u9988\u683c\u5f0f}\u3002\\n\\n<\/p>\n

      \u6ce8\u610f\u4e8b\u9879\uff1a{\u6ce8\u610f\u4e8b\u9879}\u3002<\/p>\n

       <\/p>\n

      f\u201d\u201d\u201dGiven task:{task prompt}.\\n{chain prompt}\\n\\n Please evaluate this reasoning chain
      \nby giving detailed comments containing the following content .\\n 1.{
      \nchain feedback format }. 2.{ step feedback format }. 3.{ confidence feedback format }.\\n
      \n\\n Notice: {Notice}.<\/p><\/blockquote>\n

      \u5176\u4e2d\u63a8\u7406\u94fe\u63d0\u793a<\/strong>\u662f\u805a\u5408\u7684\u63a8\u7406\u94fez1…n\u3002<\/p>\n

      \u94fe\u53cd\u9988\u683c\u5f0f<\/strong>\uff1a\u8fd9\u4e2a\u63a8\u7406\u94fe\u80fd\u5426\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\uff1f\u4e3a\u4ec0\u4e48\uff1f\u5728\u201c\u5206\u6790\u62a5\u544a\uff1a\u201d\u4e0b\u5199\u4e0b\u7ed3\u8bba\u5206\u6790\u62a5\u544a\u3002<\/p>\n

      \u6b65\u9aa4\u53cd\u9988\u683c\u5f0f<\/strong>\uff1a\u5bf9\u4e8e\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u8be6\u7ec6\u5206\u6790\uff0c\u5224\u65ad\u5f53\u524d\u6b65\u9aa4\u662f\u5426\u662f\u524d\u4e00\u6b65\u9aa4\u7684\u903b\u8f91\u63a8\u7406\uff0c\u4ee5\u53ca\u63a8\u7406\u6b65\u9aa4\u662f\u5426\u6709\u52a9\u4e8e\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u9519\u8bef\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u9519\u8bef\u62a5\u544a\u548c\u76f8\u5e94\u7684\u4fee\u8ba2\u5efa\u8bae\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u63a8\u8350\u6216\u62d2\u7edd\u7684\u63cf\u8ff0\u3002\u8bc4\u8bba\u5e94\u7b80\u6d01\uff0c\u5e76\u6309\u7167\u4ee5\u4e0b\u683c\u5f0f\uff1a\u63a8\u7406\u6b65\u9aa4\u27e8idx\u27e9\u3002\u5206\u6790\u62a5\u544a\uff1a\u3002\u5efa\u8bae\uff1a\u3002\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0\uff1a\u3002<\/p>\n

      \u4fe1\u5fc3\u53cd\u9988\u683c\u5f0f<\/strong>\uff1a\u60a8\u5bf9\u8fd9\u4e9b\u8bc4\u4f30\u548c\u8bc4\u8bba\u7684\u4fe1\u5fc3\u5206\u6570\u662f\u591a\u5c11\uff1f\u8bf7\u4ece[0.1, 0.3, 0.5, 0.7, 0.9, 1.0]\u4e2d\u9009\u62e9\u4e00\u4e2a\u503c\u4f5c\u4e3a\u5206\u6570\uff0c\u4f9b\u7528\u6237\u9605\u8bfb\u3002<\/p>\n

      \u901a\u8fc7\u53cd\u9988\u63d0\u793a\uff0cLLMs\u751f\u6210\u5305\u542b\u5bf9\u63a8\u7406\u94fe\u548c\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\u7684\u7ed3\u8bba\u548c\u5206\u6790\u7684\u7ecf\u9a8cFt\u3002<\/p>\n

       <\/p>\n

      A3 \u63a8\u7406\u6d41\u7a0b<\/h3>\n

       <\/p>\n

      \u4e3a\u4e86\u4fbf\u4e8e\u7406\u89e3\u6240\u63d0\u51fa\u7684Boosting of Thoughts\uff0c\u6211\u4eec\u603b\u7ed3\u4e86\u63a8\u7406\u6d41\u7a0b\u5728\u7b97\u6cd5\u88681\u4e2d\u3002\u8fd9\u4e2a\u6d41\u7a0b\u7684\u6e90\u4ee3\u7801\u53ef\u4ee5\u5728\u6587\u4ef6examples\/BoostingOfThought\/BoT core.py\u4e2d\u627e\u5230\u3002<\/p>\n

       <\/p>\n

      \"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-1\"

      BoT\u539f\u6587<\/p><\/div>\n

      \u56fe\u7247\u5185\u5bb9\u662f\u5173\u4e8e\u4e00\u79cd\u540d\u4e3a “BoT” \u7684\u7406\u8bba\u7684\u7b97\u6cd5\u6b65\u9aa4\u8868\u8ff0\uff0c\u4ee5\u4e0b\u662f\u5176\u4e2d\u6587\u8bd1\u6587\uff0c\u5bf9\u5e94\u7684\u7b97\u6cd5\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n

      \u7b97\u6cd51\uff1aBoT\u7684\u4e3b\u8981\u63a8\u7406\u6d41\u7a0b<\/p>\n

      \u8f93\u5165\uff1a\u8fed\u4ee3\u6b21\u6570 T\uff0c\u6811\u7ed3\u6784\u7684\u6570\u91cf M\uff0c\u95ee\u9898 Q\u3002
      \n\u8f93\u51fa\uff1a\u805a\u5408\u7684\u94fe z\u0304_1…n^T<\/p>\n

      1. \u521d\u59cb\u5316\u4e00\u4e2a\u7b80\u5355\u7684\u63d0\u793aI^0 (S, X, Q, F^0, {Gi})\uff0c\u5176\u4e2d F^0\u5c06\u662f\u4e00\u4e2a\u7a7a\u5b57\u7b26\u4e32\u3002
      \n2. \u6bcf\u6b21\u8fed\u4ee3 t = 1, 2, …, T\uff0c
      \n3. \u4f7f\u7528\u63d0\u793aI^t-1 (S, X, Q, F^t-1, {Gi}) \u4e0eLLMS\uff08\u4f4e\u6f5c\u5728\u91cf\u6df7\u5408\u6a21\u578b\uff09\u521b\u5efa M\u4e2a\u4e0d\u540c\u7684\u6811\u72b6\u601d\u7ef4\u7ed3\u6784\uff0c\u5176\u8fc7\u7a0b\u79f0\u4e3a\u201cThought Structure Generation\u201d\u3002
      \n4. \u4ece M\u4e2a\u601d\u7ef4\u7ed3\u6784\u4e2d\u63d0\u53d6\u601d\u7ef4\u94fe{z\u0304_i=1…n^m}\uff0c\u6bcf\u4e2a z\u0304_i=1…n^m \u662f m-th\u6811\u7ed3\u6784\u7684\u6700\u4f73\u601d\u7ef4\u94fe\u3002
      \n5. \u4f7f\u7528\u201cBest-First Aggregation\u201d\u6216\u201cGreedy aggregation\u201d\u65b9\u6cd5\u5c06{z\u0304_i=1…n^m} \u5e76\u5165\u5355\u4e00\u601d\u7ef4\u94fe z\u0304_1…n^t\u3002
      \n6. \u4f7f\u7528LLMS\u5728 z\u0304_1…n^t \u4e0a\u8fdb\u884c\u201cThought Chain Analysis\u201d\uff0c\u83b7\u5f97\u53cd\u9988\uff0c\u5e76\u4e0e z\u0304_1…n^t \u7ed3\u5408\uff0c\u83b7\u5f97\u7ecf\u9a8cF^t\u3002
      \n7. \u901a\u8fc7\u7d2f\u79efF^t \u66f4\u65b0\u63d0\u793a\uff0c\u4f7f\u5176\u53d8\u4e3a I^t (S, X, Q, F^t-1,t, {Gi})\u3002
      \n8. \u7ed3\u675f
      \n9. \u83b7\u5f97\u89e3\u51b3\u65b9\u6848 z\u0304_1…n^T<\/p><\/blockquote>\n

       <\/p>\n

       <\/p>\n

      B \u589e\u5f3a\u601d\u7ef4\u7684\u89c1\u89e3<\/h2>\n

       <\/p>\n

      Boosting of Thoughts\u6e90\u4e8e\u6211\u4eec\u7684\u89c1\u89e3\uff0c\u5373\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\u89e3\u51b3\u6570\u5b66\u95ee\u9898\u7684\u63a8\u7406\u80fd\u529b\u76f4\u63a5\u6765\u81ea\u4e8e\u7ecf\u9a8c\uff0c\u8fd9\u4e9b\u7ecf\u9a8c\u5305\u542b\u4e86\u5bf9\u5148\u524d\u9519\u8bef\u7684\u5206\u6790\u548c\u5efa\u8bae\u3002\u4e00\u65e6\u63d0\u793a\u5305\u542b\u6709\u6548\u7684\u5386\u53f2\u63a8\u7406\u7ecf\u9a8c\u4f9bLLMs\u5728\u6267\u884c\u63a8\u7406\u524d\u56de\u5fc6\uff0c\u6240\u4ea7\u751f\u7684\u63a8\u7406\u6b65\u9aa4\u901a\u5e38\u66f4\u52a0\u903b\u8f91\u548c\u5408\u7406\uff0c\u5982\u88685\u548c6\u7684\u6bd4\u8f83\u6240\u793a\u3002\u8fd9\u4e9b\u89c1\u89e3\u8fd8\u4f7f\u6211\u4eec\u8003\u8651\u5230\uff0cLLMs\u4e0d\u9700\u8981\u4e25\u91cd\u4f9d\u8d56\u4e8e\u6bcf\u4e2a\u4efb\u52a1\u7684\u7cbe\u5fc3\u51c6\u5907\u7684\u63d0\u793a\uff08\u63d0\u793a\u4e2d\u7684\u51e0\u4e2a\u601d\u7ef4\u94fe\u793a\u8303\u4f5c\u4e3a\u793a\u4f8b\uff09\u3002\u7136\u800c\uff0c\u7531\u4e8eLLMs\u80fd\u591f\u4ece\u7ecf\u9a8c\u4e2d\u5b66\u4e60\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u4e00\u4e2a\u7b80\u5355\u7684\u63d0\u793a\u5f00\u59cb\uff0c\u4e0d\u9700\u8981\u793a\u4f8b\u6216\u624b\u52a8\u8bbe\u8ba1\u7684\u5185\u5bb9\uff0c\u5728\u63a8\u7406\u8fc7\u7a0b\u4e2d\u9010\u6e10\u6536\u96c6\u7ecf\u9a8c\u3002\u6700\u7ec8\uff0c\u901a\u8fc7\u5728\u63d0\u793a\u4e2d\u7d2f\u79ef\u7ecf\u9a8c\uff0cLLMs\u5b9e\u73b0\u4e86\u89e3\u51b3\u590d\u6742\u95ee\u9898\u7684\u5f3a\u6709\u529b\u63a8\u7406\u3002\u6709\u4e86\u8fd9\u4e9b\u89c1\u89e3\uff0cBoosting of Thoughts\u88ab\u8bbe\u8ba1\u4e3a\u4e00\u4e2a\u81ea\u52a8\u5316\u7684\u63d0\u793a\u6846\u67b6\uff0c\u5b83\u901a\u8fc7\u8fed\u4ee3\u6536\u96c6\u8bd5\u9519\u63a8\u7406\u7ecf\u9a8c\u7684\u96c6\u5408\u6765\u89e3\u51b3\u95ee\u9898\u3002\u6211\u4eec\u8ba4\u4e3a\u6240\u63d0\u51fa\u7684BoT\u4e0d\u662fLLMs\u5e94\u7528\u4e8e\u7279\u5b9a\u4efb\u52a1\uff0c\u800c\u662f\u5efa\u7acb\u5728\u8fd9\u6837\u7684\u89c1\u89e3\u4e0a\uff0c\u5373LLMs\u7684\u63a8\u7406\u80fd\u529b\u53ef\u4ee5\u76f4\u63a5\u4ece\u5206\u6790\u4e0d\u6b63\u786e\u63a8\u7406\u94fe\u7684\u9519\u8bef\u5206\u6790\u4e2d\u83b7\u5f97\uff0c\u800c\u65e0\u9700\u4f9d\u8d56\u4eba\u7c7b\u5148\u9a8c\u77e5\u8bc6\u3002<\/p>\n

       <\/p>\n

      \u4e3a\u4e86\u5f3a\u8c03\u6211\u4eec\u7684\u89c1\u89e3\uff0c\u6211\u4eec\u5206\u4eab\u4e86\u4ee5\u4e0b\u4e09\u4e2a\u5173\u952e\u89c2\u5bdf\uff0c\u8fd9\u4e9b\u89c2\u5bdf\u662f\u57fa\u4e8e\u4ee5\u4e0b24\u5c40\u6e38\u620f\u6570\u636e\u96c6\u4e0a\u4f7f\u7528gpt-3.5-turbo\u6a21\u578b\uff0c\u6e29\u5ea6\u4e3a0.7\uff0ctop p\u503c\u4e3a0.7\u7684\u5e94\u7528\u5f97\u51fa\u7684\u3002<\/p>\n

       <\/p>\n

      \u63d0\u793a\u4e2d\u7684\u7ecf\u9a8c\u9f13\u52b1LLMs\u5728\u56de\u7b54\u4e2d\u63a2\u7d22\u66f4\u591a\u7684\u903b\u8f91\u3002<\/strong>\u5982\u88685\u6240\u793a\uff0c\u5f53\u63d0\u793a\u4e2d\u4e0d\u5305\u542b\u7ecf\u9a8c\u65f6\uff0c\u6a21\u578b\u751f\u6210\u4e86\u76f8\u540c\u7684\u63a8\u7406\u6b65\u9aa4\u4e94\u6b21\u3002\u8fd9\u4e00\u89c2\u5bdf\u663e\u793a\u4e86LLMs\u7684\u4e00\u4e2a\u5e38\u89c1\u95ee\u9898\uff0c\u5373\u7f3a\u4e4f\u81ea\u6211\u6fc0\u52b1\u53bb\u63a2\u7d22\u4e0d\u540c\u7684\u63a8\u7406\u903b\u8f91\u3002\u56e0\u6b64\uff0c\u5c3d\u7ba1LLMs\u5177\u6709\u5f3a\u5927\u7684\u63a8\u7406\u6f5c\u529b\uff0c\u4f46\u5b83\u4eec\u53ef\u80fd\u4f1a\u9677\u5165\u4e00\u4e2a\u5faa\u73af\uff0c\u5f00\u59cb\u4e8e\u6700\u7b80\u5355\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u8fd9\u53ef\u80fd\u6c38\u8fdc\u4e0d\u4f1a\u5bfc\u81f4\u627e\u5230\u6700\u7ec8\u89e3\u51b3\u65b9\u6848\u3002\u88685\u7684\u201c\u83b7\u5f97\u7684\u63a8\u7406\u94fe\u201d\u90e8\u5206\u5c55\u793a\u4e86\u9519\u8bef\u7684\u63a8\u7406\u94fe\u3002\u6211\u4eec\u8ba4\u4e3a\uff0c\u6b63\u5982Tree of Thoughts Yao\u7b49\u4eba\uff082024\uff09\u901a\u8fc7\u751f\u6210\u591a\u4e2a\u54cd\u5e94\u4f5c\u4e3a\u601d\u7ef4\u6765\u6784\u5efa\u6811\u7684\u8282\u70b9\uff0c\u8fd9\u6837\u7684\u91cd\u590d\u63a8\u7406\u6b65\u9aa4\u53ef\u80fd\u4f1a\u5bfc\u81f4\u8be5\u7b97\u6cd5\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u5931\u8d25\u3002\u7136\u800c\uff0c\u5728BoT\u7684\u7b2c\u4e8c\u6b21\u8fed\u4ee3\u4e2d\uff0c\u5f15\u5165\u7ecf\u9a8c\u5230\u63d0\u793a\u4e2d\uff0c\u5bfc\u81f4\u751f\u6210\u4e86\u4e0d\u540c\u7684\u521d\u59cb\u63a8\u7406\u6b65\u9aa4\uff0c\u5982\u88686\u6240\u793a\u3002\u6700\u7ec8\u7684\u63a8\u7406\u94fe\u6700\u7ec8\u53ef\u4ee5\u901a\u8fc7\u4ece\u66f4\u5e7f\u6cdb\u7684\u6f5c\u5728\u903b\u8f91\u8303\u56f4\u5f00\u59cb\uff0c\u5230\u8fbe\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002Weng\u7b49\u4eba\uff082023\uff09<\/p>\n

       <\/p>\n

      LLMs\u907f\u514d\u72af\u7ecf\u9a8c\u4e2d\u5f3a\u8c03\u7684\u7c7b\u4f3c\u9519\u8bef\u3002<\/strong>\u5982\u679c\u4e0d\u5728\u63d0\u793a\u4e2d\u5305\u542b\u7ecf\u9a8c\uff0c\u5176\u4e2d\u5305\u542b\u9519\u8bef\u5206\u6790\uff0cLLMs\u5c06\u72af\u5f88\u591a\u9519\u8bef\uff0c\u4f8b\u5982\u504f\u79bb\u4efb\u52a1\u89c4\u5219\u548c\u5728\u6700\u540e\u8fc7\u7a0b\u4e2d\u9000\u56de\u5230\u521d\u59cb\u63a8\u7406\u6b65\u9aa4\uff0c\u5982\u88685\u7684\u201c\u83b7\u5f97\u7684\u63a8\u7406\u94fe\u201d\u90e8\u5206\u6240\u793a\u3002\u5728\u5206\u6790\u8fd9\u4e2a\u63a8\u7406\u94fe\u5e76\u5c06\u5176\u53cd\u9988\u4f5c\u4e3a\u7ecf\u9a8c\u7eb3\u5165\u5230BoT\u7684\u7b2c\u4e8c\u6b21\u8fed\u4ee3\u7684\u63d0\u793a\u4e2d\u4e4b\u540e\uff0c\u4ece\u88686\u53ef\u4ee5\u770b\u51fa\uff0cLLMs\u5c06\u5728\u8fdb\u884c\u63a8\u7406\u4e4b\u524d\u5145\u5206\u5b66\u4e60\u7ecf\u9a8c\u3002\u9996\u5148\uff0c\u6ca1\u6709\u4e00\u4e2a\u54cd\u5e94\u590d\u5236\u4e86\u76f8\u540c\u7684\u9519\u8bef\u63a8\u7406\u6b65\u9aa4\uff0c\u6b63\u5982\u201c\u6765\u81eagpt-3.5-turbo\u7684\u4e94\u4e2a\u54cd\u5e94\u201d\u4e2d\u6240\u793a\u7684\u591a\u6837\u5316\u7684\u521d\u59cb\u63a8\u7406\u6b65\u9aa4\u3002\u5176\u6b21\uff0cLLMs\u6210\u529f\u907f\u514d\u4e86\u6240\u6709\u5148\u524d\u786e\u5b9a\u7684\u9519\u8bef\uff0c\u901a\u8fc7\u4e25\u683c\u9075\u5b88\u4efb\u52a1\u89c4\u5219\uff0c\u6d88\u9664\u4e0d\u6b63\u786e\u7684\u63a8\u7406\uff0c\u5e76\u6267\u884c\u903b\u8f91\u63a8\u7406\u6b65\u9aa4\u3002\u7b2c\u4e09\uff0c\u6700\u7ec8\u5bfc\u81f4\u201c1 1 4 6\u201dGame of 24\u4efb\u52a1\u7684\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u3002\u5176\u4ed6\u5de5\u4f5c\uff0c\u5982Weng\u7b49\u4eba\uff082023\uff09\uff1bMadaan\u7b49\u4eba\uff082023\uff09\uff1bZheng\u7b49\u4eba\uff082023\uff09\uff0c\u4e5f\u5f3a\u8c03\u4e86\u901a\u8fc7\u53cd\u9988\u589e\u5f3a\u63d0\u793a\u7684\u91cd\u8981\u6027\uff0c\u8fd9\u662f\u5bf9\u5148\u524d\u7b54\u6848\u7684\u81ea\u6211\u8bc4\u4f30\u3002\u7136\u800c\uff0cBoT\u662f\u5f00\u521b\u6027\u7684\u5de5\u4f5c\uff0c\u57fa\u4e8e\u8fd9\u6837\u7684\u89c1\u89e3\uff0c\u5373\u5305\u542b\u9519\u8bef\u5206\u6790\u7684\u7ecf\u9a8c\u53ef\u4ee5\u4f7fLLMs\u83b7\u5f97\u5f3a\u5927\u7684\u63a8\u7406\u80fd\u529b\u3002<\/p>\n

       <\/p>\n

      \u6ca1\u6709\u4eba\u7c7b\u6ce8\u91ca\uff0cLLMs\u6839\u636e\u7ecf\u9a8c\u81ea\u52a8\u7ec4\u7ec7\u6709\u6548\u7684\u63a8\u7406\u94fe\u6765\u89e3\u51b3\u590d\u6742\u95ee\u9898\u3002<\/strong>BoT\u662f\u5f00\u521b\u6027\u7684\u5021\u8bae\uff0c\u63d0\u51fa\u4e86\u4e00\u4e2a\u81ea\u52a8\u5316\u7684\u63d0\u793a\u6846\u67b6\uff0c\u5229\u7528\u8fd9\u6837\u7684\u89c1\u89e3\uff0c\u5373LLMs\u53ef\u4ee5\u901a\u8fc7\u9519\u8bef\u5206\u6790\u548c\u6307\u5bfc\uff0c\u4ec5\u901a\u8fc7\u7ecf\u9a8c\u83b7\u5f97\u89e3\u51b3\u95ee\u9898\u7684\u6709\u6548\u63a8\u7406\u6280\u80fd\uff0c\u800c\u65e0\u9700\u4eba\u7c7b\u6ce8\u91ca\u3002\u5982\u88685\u6240\u793a\uff0c\u8fd9\u662fBoT\u7684\u7b2c\u4e00\u6b21\u8fed\u4ee3\uff0c\u521d\u59cb\u63d0\u793a\u53ea\u5305\u542b\u57fa\u672c\u4efb\u52a1\u6307\u5bfc\u548c\u95ee\u9898\uff0c\u800c\u6ca1\u6709\u50cfCoT\u4e2d\u7684\u4e0a\u4e0b\u6587\u5b66\u4e60\u793a\u4f8b\u3002\u5373\u4f7fLLMs\u4f7f\u7528\u8fd9\u79cd\u63d0\u793a\u83b7\u5f97\u7684\u63a8\u7406\u94fe\u5305\u542b\u8bb8\u591a\u9519\u8bef\u548c\u65e0\u6548\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u5176\u9519\u8bef\u5206\u6790\u548c\u5efa\u8bae\u53ef\u4ee5\u4f5c\u4e3a\u7ecf\u9a8c\u5305\u542b\u5728\u8f93\u5165\u63d0\u793a\u4e2d\uff0c\u4ee5\u4f7f\u7b2c\u4e8c\u6b21\u8fed\u4ee3\u7684\u63a8\u7406\u53d7\u76ca\uff0c\u5982\u88686\u6240\u793a\u3002\u53ef\u4ee5\u89c2\u5bdf\u5230\uff0c\u6ca1\u6709\u5173\u4e8e\u6b63\u786e\u63a8\u7406\u7a0b\u5e8f\u7684\u4eba\u7c7b\u6307\u5bfc\uff0cLLMs\u53ef\u4ee5\u4ece\u7ecf\u9a8c\u4e2d\u83b7\u53d6\u77e5\u8bc6\uff0c\u5305\u62ec\u9519\u8bef\u5206\u6790\u548c\u6307\u5bfc\uff0c\u8fd9\u4e9b\u7ecf\u9a8c\u662f\u4ece\u4ee5\u524d\u751f\u6210\u7684\u63a8\u7406\u94fe\u4e2d\u83b7\u5f97\u7684\uff0c\u4ece\u800c\u5bfc\u81f4\u63a8\u7406\u95ee\u9898\u89e3\u51b3\u7684\u9010\u6b65\u6539\u8fdb\u3002<\/p>\n

       <\/p>\n

      \u56e0\u6b64\uff0c\u6211\u4eec\u7684BoT\u4e3a\u7814\u7a76\u63d0\u4f9b\u4e86\u957f\u671f\u6307\u5bfc\uff0c\u56e0\u4e3a\u5b83\u5c55\u793a\u4e86\u5728\u4f7fLLMs\u751f\u6210\u590d\u6742\u4efb\u52a1\u7684\u6709\u6548\u63a8\u7406\u8fc7\u7a0b\u65f6\uff0c\u56de\u5fc6\u9519\u8bef\u5206\u6790\u548c\u5efa\u8bae\u7684\u91cd\u8981\u6027\u3002\u6709\u4e86\u8fd9\u4e9b\u89c1\u89e3\uff0c\u8bf1\u5bfcLLMs\u63a8\u7406\u80fd\u529b\u7684\u63d0\u793a\u5de5\u7a0b\u7814\u7a76\u53ef\u4ee5\u4e13\u6ce8\u4e8e\u5982\u4f55\u751f\u6210\u7ecf\u9a8c\uff0c\u800c\u4e0d\u662f\u5f15\u5165\u66f4\u591a\u7684\u4eba\u7c7b\u5148\u9a8c\u77e5\u8bc6\u3002<\/p>\n

       <\/p>\n

       <\/p>\n

      C\u601d\u7ef4\u7ed3\u6784\u751f\u6210<\/h2>\n

       <\/p>\n

      BoT\u662f\u4e00\u4e2a\u81ea\u52a8\u5316\u7684\u63d0\u793a\u6846\u67b6\uff0c\u8fed\u4ee3\u5730\u7d2f\u79ef\u4ece\u63a8\u7406\u94fe\u5206\u6790\u4e2d\u5f97\u5230\u7684\u7ecf\u9a8c\u3002\u56e0\u6b64\uff0cBoT\u88ab\u6982\u62ec\u4e3a\u5404\u79cd\u601d\u7ef4\u751f\u6210\u65b9\u6cd5\u548c\u80fd\u591f\u751f\u6210\u548c\u8bc4\u4f30\u63a8\u7406\u6b65\u9aa4\u7684LLMs\u3002\u800c\u4e14\uff0cBoT\u7684\u6027\u80fd\u53d6\u51b3\u4e8e\u5176\u601d\u7ef4\u751f\u6210\u7ed3\u6784\u7684\u6709\u6548\u6027\u3002\u56e0\u6b64\uff0cBoT\u4f7f\u7528\u6700\u65b0\u7684\u7ed3\u6784\u2014\u2014\u601d\u7ef4\u6811\uff08ToT\uff09Yao\u7b49\u4eba\uff082024\uff09\u4f5c\u4e3a\u5176\u57fa\u7840\u6a21\u578b\uff0c\u5728\u6bcf\u6b21\u8fed\u4ee3\u4e2d\u751f\u6210\u63a8\u7406\u94fe\u3002\u6b63\u5982\u4e3b\u8981\u8bba\u6587\u4e2d\u63d0\u5230\u7684\uff0c\u57fa\u7840\u601d\u7ef4\u751f\u6210\u6a21\u578b\u4e5f\u53ef\u4ee5\u662f\u601d\u7ef4\u56fe\uff08GoT\uff09Besta\u7b49\u4eba\uff082023\uff09\uff0c\u5373BoT\u4e0eGoT\u3002\u7136\u800c\uff0c\u7531\u4e8e\u65f6\u95f4\u9650\u5236\u4ee5\u53ca\u5f53\u524dGoT\u5c1a\u672a\u5e94\u7528\u4e8e\u6570\u5b66\u95ee\u9898\uff0cBoT\u8bbe\u8ba1\u4e13\u95e8\u91c7\u7528ToT\u3002\u6b64\u5916\uff0c\u5f53\u4f5c\u4e3a\u63d0\u5347\u673a\u5236\u4e2d\u7684\u57fa\u7840\u6a21\u578b\u65f6\uff0c\u6bcf\u6b21\u8fed\u4ee3\u4e2d\u7684\u601d\u7ef4\u7ed3\u6784\u53ef\u4ee5\u4fdd\u6301\u8f7b\u91cf\u7ea7\u3002\u6700\u7ec8\uff0c\u6240\u63d0\u51fa\u7684BoT\u751f\u6210\u5f02\u6784\u6811\u7ed3\u6784\uff0c\u6bcf\u68f5\u6811\u90fd\u662f\u4e00\u4e2a\u6d45\u52a0\u6743\u4e8c\u53c9\u6811\u3002<\/p>\n

       <\/p>\n

      C1 \u4e0b\u4e00\u4e2a\u601d\u7ef4\u751f\u6210\u548c\u8fb9\u6743\u91cd\u8ba1\u7b97<\/h3>\n

      \u4f7f\u7528\u7b2cA\u8282\u4e2d\u8ba8\u8bba\u7684\u4e0b\u4e00\u4e2a\u601d\u7ef4\u751f\u6210\u63d0\u793a\uff0cLLMs\u53ef\u4ee5\u901a\u8fc7\u7ed3\u5408\u7ecf\u9a8cF1…t\u5e76\u7528z1..,i-1\u66ff\u6362{Gi}\u6765\u751f\u6210\u63a8\u7406\u6b65\u9aa4zi\u7684\u4e0b\u4e00\u4e2a\u53ef\u80fd\u601d\u7ef4\u3002\u5bf9\u4e8e\u4e00\u4e2a\u63a8\u7406\u6b65\u9aa4zi\uff0cLLMs\u4f7f\u7528\u601d\u7ef4\u8bc4\u4f30\u63d0\u793a\u6765\u751f\u6210\u8bc4\u4f30\u5206\u6570\u4f5c\u4e3azi\u548czi-1\u4e4b\u95f4\u7684\u8fb9\u6743\u91cd\u3002\u6709\u5173\u8be6\u7ec6\u8fc7\u7a0b\uff0c\u8bf7\u53c2\u89c1examples\/BoostingOfThought\/BoT reasoner.py\u4e2d\u7684\u6e90\u4ee3\u7801\u3002\u76f4\u63a5\u4e3e\u4f8b\u8bf4\u660eBoT\u5e94\u7528\u4e8eGame of 24\u4e2d\u7684’3 5 6 8’\uff0c\u4f7f\u7528gpt-3.5-turbo\uff0c\u88687\u548c\u88688\u5c55\u793a\u4e86\u601d\u7ef4\u7684\u751f\u6210\uff0c\u800c\u88689\u5c55\u793a\u4e86\u5982\u4f55\u8ba1\u7b97\u3002<\/p>\n

       <\/p>\n

      C2 \u5f02\u6784\u6811\u7ed3\u6784\u7684\u5fc5\u8981\u6027<\/h3>\n

      \u5728\u6bcf\u6b21\u8fed\u4ee3\u7684BoT\u4e2d\uff0c\u5f02\u6784\u6811\u7ed3\u6784\u7684\u6784\u5efa\u662f\u4e3a\u4e86\u63a2\u7d22\u66f4\u5e7f\u6cdb\u7684\u63a8\u7406\u641c\u7d22\u7a7a\u95f4\u5e76\u63d0\u9ad8\u9c81\u68d2\u6027\u3002\u6b63\u5982\u5728examples\/BoostingOfThought\/BoT core.py\u4e0b\u7684\u6e90\u4ee3\u7801\u4e2d\u770b\u5230\u7684\u90a3\u6837\uff0cLLMs\u5728\u6bcf\u68f5\u6811\u4e2d\u7684\u6e29\u5ea6\u548cTop p\u503c\u5206\u522b\u4ece\u8303\u56f4[0.2, 0.4, 0.6, 0.7, 0.9, 1.1, 1.5]\u548c[0.1, 0.3, 0.5, 0.7, 0.9]\u4e2d\u9009\u62e9\u3002\u6811\u751f\u957f\u7b56\u7565\u53ef\u4ee5\u662f\u9010\u5c42\u751f\u957f\u6216\u9010\u53f6\u751f\u957f\u3002\u6211\u4eec\u89c2\u5bdf\u5230\u4fdd\u8bc1\u8fd9\u79cd\u5f02\u6784\u6027\u7684\u4ee5\u4e0b\u4e24\u4e2a\u597d\u5904\u3002<\/p>\n

       <\/p>\n

      \u5f02\u6784\u6027\u6269\u5c55\u4e86\u63a8\u7406\u641c\u7d22\u7a7a\u95f4\uff0c\u4ece\u800c\u589e\u52a0\u4e86\u6536\u655b\u901f\u5ea6\u3002<\/strong>\u5f53\u4e0d\u540c\u7684\u6811\u4e3a\u4e0d\u540c\u7684\u76ee\u7684\u6784\u5efa\u65f6\uff0c\u4f8b\u5982\u4f7f\u7528\u9010\u5c42\u7b56\u7565\u8fdb\u884c\u63a2\u7d22\u6216\u4f7f\u7528\u9010\u53f6\u7b56\u7565\u8fdb\u884c\u5229\u7528\uff0c\u5e76\u4e14\u57fa\u4e8e\u968f\u673a\u6216\u786e\u5b9a\u6027\u7684LLMs\uff0c\u751f\u6210\u7684\u63a8\u7406\u6b65\u9aa4\u548c\u7ed3\u679c\u7684\u63a8\u7406\u94fe\u53ef\u4ee5\u8868\u73b0\u51fa\u663e\u7740\u5dee\u5f02\uff0c\u6709\u6548\u5730\u8986\u76d6\u4e86\u66f4\u5e7f\u6cdb\u7684\u63a8\u7406\u53ef\u80fd\u6027\u3002\u4f8b\u5982\uff0c\u5728\u4e00\u6b21\u8fed\u4ee3\u4e2d\uff0c\u5f53LLMs\u4ee5\u66f4\u591a\u4fe1\u5fc3\u751f\u6210\u4e0b\u4e00\u4e2a\u601d\u7ef4\u65f6\uff0c\u7c7b\u4f3c\u7684\u601d\u7ef4\u5c06\u4e0d\u65ad\u88ab\u63a2\u7d22\uff1b\u5426\u5219\uff0c\u5177\u6709\u66f4\u591a\u968f\u673a\u6027\u7684LLMs\u503e\u5411\u4e8e\u751f\u6210\u591a\u6837\u5316\u7684\u601d\u7ef4\u3002\u901a\u5e38\u5f88\u96be\u9884\u6d4b\u786e\u5b9a\u6027\u63a8\u7406\u6216\u968f\u673a\u6027\u662f\u5426\u6709\u52a9\u4e8e\u89e3\u51b3\u65b9\u6848\u3002\u56e0\u6b64\uff0c\u901a\u8fc7\u6df7\u5408\u4e0d\u540c\u7c7b\u578b\u7684\u903b\u8f91\u63a8\u7406\u6b65\u9aa4\u6765\u4fdd\u8bc1\u5f02\u6784\u6027\uff0c\u4f7f\u6211\u4eec\u80fd\u591f\u5728\u5355\u4e2a\u8fed\u4ee3\u4e2d\u5168\u9762\u63a2\u7d22\u63a8\u7406\u7a7a\u95f4\uff0c\u6700\u7ec8\u4fc3\u8fdb\u540e\u7eed\u8fed\u4ee3\u3002\u5728\u6d88\u878d\u7814\u7a76\u4e2d\uff0c\u6211\u4eec\u6bd4\u8f83\u4e86\u5f02\u6784\u548c\u540c\u8d28\u6811\u7ed3\u6784\u4e4b\u95f4\u7684BoT\u6027\u80fd\u3002<\/p>\n

       <\/p>\n

      \u5f02\u6784\u6027\u51cf\u5c11\u4e86\u751f\u6210\u65e0\u6548\u6216\u9519\u8bef\u63a8\u7406\u94fe\u7684\u53ef\u80fd\u6027\uff0c\u4ece\u800c\u589e\u5f3a\u4e86\u9c81\u68d2\u6027\u3002<\/strong>\u4e0e\u5f02\u6784\u6027\u4e0d\u540c\uff0c\u5728\u5177\u6709\u540c\u8d28\u8bbe\u7f6e\u7684\u6811\u4e2d\uff0c\u5355\u4e2a\u6811\u503e\u5411\u4e8e\u9075\u5faa\u4e00\u81f4\u7684\u903b\u8f91\u751f\u6210\u601d\u7ef4\uff0c\u5e76\u6784\u5efa\u5177\u6709\u76f8\u540c\u6811\u7ed3\u6784\u7684\u63a8\u7406\u94fe\u3002\u7136\u540e\uff0c\u5f53\u903b\u8f91\u9519\u8bef\u6216\u5e95\u5c42\u7ed3\u6784\u5bf9\u5f53\u524d\u95ee\u9898\u65e0\u6548\u65f6\uff0cBoT\u5728\u6bcf\u6b21\u8fed\u4ee3\u4e2d\u83b7\u5f97\u7684\u6240\u6709\u6811\u7684\u63a8\u7406\u94fe\u53ea\u80fd\u5305\u542b\u566a\u58f0\u548c\u4e0d\u6b63\u786e\u7684\u63a8\u7406\u6b65\u9aa4\u3002\u5373\u4f7f\u5728\u805a\u5408\u5b83\u4eec\u4ee5\u83b7\u5f97\u66f4\u7cbe\u70bc\u7684\u63a8\u7406\u94fe\u8fdb\u884c\u8bc4\u4f30\u65f6\uff0c\u7ecf\u9a8c\u53ef\u80fd\u4ecd\u7136\u4e0e\u63d0\u4f9b\u9002\u5f53\u7684\u95ee\u9898\u89e3\u51b3\u5efa\u8bae\u6709\u5f88\u5927\u7684\u504f\u5dee\u3002\u56e0\u6b64\uff0c\u5c06\u6811\u72b6\u601d\u7ef4\u7ed3\u6784\u8bbe\u8ba1\u4e3a\u5f02\u6784\u6027\u53ef\u4ee5\u5e2e\u52a9\u51cf\u5c11\u5728\u540e\u7eedBoT\u8fed\u4ee3\u4e2d\u6ca1\u6709\u6709\u6548\u7684\u63a8\u7406\u94fe\u53ef\u7528\u4e8e\u8bc4\u4f30\u7684\u53ef\u80fd\u6027\u3002\u8fd9\u79cd\u589e\u5f3a\u7684\u9c81\u68d2\u6027\u4f7fBoT\u80fd\u591f\u89e3\u51b3\u4e0d\u540c\u96be\u5ea6\u7ea7\u522b\u7684\u95ee\u9898\u3002<\/p>\n

       <\/p>\n

      \"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-12\"<\/p>\n

       <\/p>\n

      \u8fd9\u662f\u4e00\u5f20\u63cf\u8ff0\u4e86”\u6700\u4f18\u5148\u805a\u5408”\u548c”\u8d2a\u5a6a\u805a\u5408”\u8fc7\u7a0b\u7684\u56fe\u7247\u3002<\/p>\n

      \u8f93\u5165\uff1aM\u6761\u63a8\u8bba\u94fe\uff0c\u5176\u4e2dm-th\u94fe\u7684\u63a8\u8bba\u6b65\u9aa4\u8bb0\u4e3az1i=1m\u3002
      \n\u8f93\u51fa\uff1a\u805a\u5408\u94fez1..n\u3002<\/p>\n

      1 – \u6700\u4f18\u5148\u805a\u5408
      \n2 \u5bf9\u4e8e\u6bcf\u4e2a\u94fe m = 1, 2, …, M \u505a
      \n3 \u8ba1\u7b97m-th\u94fe\u7684\u8fb9\u7f18\u6743\u91cd\u4e4b\u548c\u4e3a Vm = \u2211i\u5728m1m\u8303\u56f4\u5185 Vi-1,i\u3002
      \n4 \u7ed3\u675f
      \n5 \u901a\u8fc7\u6267\u884c m* = arg maxm {Vm} \u83b7\u53d6M\u4e2a\u94fe\u4e2d\u6700\u4f18\u7684\u94fe
      \n6 \u5c06\u805a\u5408\u94fe\u5206\u914d\u4e3a\u6700\u4f18\u94fe\uff0cz1…n := {z1i=1n*m*}<\/p>\n

      7 – \u8d2a\u5a6a\u805a\u5408
      \n8 z1 := z1 \u5176\u4e2d m* = arg maxm {V1m}.
      \n9 \u5bf9\u4e8e\u6bcf\u4e2a\u805a\u5408\u6b65\u9aa4 i = 2, …, n \u505a
      \n10 \u5bf9\u4e8e\u6bcf\u4e2a\u94fe m = 1, 2, …, M \u505a
      \n11 \u6536\u96c6 Jm = {j, sim(z1i-1, z1j) > 0.7; j \u2208 n1m}.
      \n12 \u83b7\u5f97 j*,m = arg maxj\u2208Jm {Vj,j+1m}
      \n13 \u7ed3\u675f
      \n14 \u6267\u884c\u4ee5\u4e0b\u64cd\u4f5c\u83b7\u5f97\u6700\u4f73\u4e0b\u4e00\u63a8\u7406\u6b65\u9aa4\uff1azi = z1j*+1 \u5176\u4e2d j* = arg maxj\u2208{j*m}1M {Vj,j+1m}.
      \n15 \u7ed3\u675f
      \n16 \u83b7\u5f97\u805a\u5408\u94fe z1…n\u3002<\/p>\n

      \u8fd9\u57fa\u672c\u4e0a\u662f\u4e00\u4e2a\u63cf\u8ff0\u5982\u4f55\u901a\u8fc7\u4e0d\u540c\u7684\u65b9\u6cd5\u5bf9\u6570\u636e\u94fe\u6216\u8282\u70b9\u8fdb\u884c\u4f18\u5316\u5e76\u83b7\u53d6\u6700\u4f73\u7ed3\u679c\u7684\u7b97\u6cd5\u6d41\u7a0b\u56fe\u3002<\/p><\/blockquote>\n

       <\/p>\n

       <\/p>\n

      D \u601d\u7ef4\u7ed3\u6784\u805a\u5408<\/h2>\n

      \u5728\u5b8c\u6210\u5f02\u6784\u6811\u7ed3\u6784\u4e2d\u7684\u63a8\u7406\u540e\uff0cBoT\u7684\u805a\u5408\u8fc7\u7a0b\u9996\u5148\u4ece\u6bcf\u68f5\u6811\u4e2d\u63d0\u53d6\u6700\u4f73\u63a8\u7406\u94fe\uff0c\u7136\u540e\u4f7f\u7528\u6700\u4f73\u4f18\u5148\u6216\u8d2a\u5a6a\u805a\u5408\u65b9\u6cd5\u5c06\u5b83\u4eec\u7ec4\u5408\u6210\u4e00\u4e2a\u5355\u4e00\u7684\u63a8\u7406\u94fe\u3002\u6709\u5173\u8fd9\u4e24\u79cd\u805a\u5408\u65b9\u6cd5\u7684\u66f4\u591a\u8be6\u7ec6\u4fe1\u606f\u53ef\u4ee5\u5728\u6e90\u4ee3\u7801examples\/BoostingOfThought\/BoT aggregator.py\u4e2d\u627e\u5230\u3002<\/p>\n

       <\/p>\n

      \u5982\u7b97\u6cd516\u7684\u7b2c\u4e00\u5757\u6240\u793a\uff0c\u6700\u4f73\u4f18\u5148\u805a\u5408\u662f\u4e00\u79cd\u76f4\u63a5\u7684\u805a\u5408\u65b9\u6cd5\uff0c\u5b83\u76f4\u63a5\u63d0\u53d6\u5177\u6709\u6700\u9ad8\u8fb9\u6743\u91cd\u548c\u7684\u94fe\u3002\u8fd9\u79cd\u65b9\u6cd5\u5feb\u901f\u7a33\u5b9a\u3002\u5b83\u901a\u5e38\u4fdd\u8bc1\u5177\u6709\u7ade\u4e89\u529b\u7684\u6027\u80fd\uff0c\u56e0\u4e3a\u540e\u7eed\u7684\u7ecf\u9a8c\u53ef\u4ee5\u901a\u8fc7\u5206\u6790\u83b7\u5f97\u7684\u6700\u4f18\u94fe\u6765\u751f\u6210\u3002\u7136\u800c\uff0c\u5b83\u53ea\u80fd\u9009\u62e9\u73b0\u6709\u94fe\u800c\u65e0\u6cd5\u8fdb\u884c\u6709\u6548\u7684\u8c03\u6574\u3002\u8d2a\u5a6a\u805a\u5408\u66f4\u4e3a\u5148\u8fdb\uff0c\u56e0\u4e3a\u5b83\u7ed3\u5408\u4e86\u4e0d\u540c\u94fe\u4e2d\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u4ea7\u751f\u4e86\u4e00\u4e2a\u65b0\u7684\u3001\u66f4\u597d\u7684\u63a8\u7406\u94fe\uff0c\u5177\u6709\u6700\u9ad8\u7684\u8fb9\u6743\u91cd\u3002\u7b97\u6cd516\u4e2d\u7684\u8d2a\u5a6a\u805a\u5408\u8fc7\u7a0b\u5305\u542b\u4e24\u4e2a\u6b65\u9aa4\u3002\u9996\u5148\uff0c\u5b83\u6536\u96c6\u4e0e\u805a\u5408\u63a8\u7406\u6b65\u9aa4zi-1\u76f8\u4f3c\u7684\u63a8\u7406\u6b65\u9aa4\u3002\u56e0\u6b64\uff0c\u4e0b\u4e00\u4e2a\u805a\u5408\u63a8\u7406\u6b65\u9aa4\u662f\u4ece\u8fd9\u4e2a\u6536\u96c6\u96c6\u4e2d\u7684\u4e0b\u4e00\u4e2a\u63a8\u7406\u6b65\u9aa4\u4e2d\u9009\u62e9\u7684\uff0c\u901a\u8fc7\u6700\u5927\u5316\u8fb9\u6743\u91cd\u3002sim\u662f\u4f7f\u7528LLMs\u8bc4\u4f30\u4e24\u4e2a\u6bb5\u843d\u4e4b\u95f4\u76f8\u540c\u5355\u8bcd\u548c\u6570\u5b66\u6570\u5b57\u7684\u767e\u5206\u6bd4\u7684\u76f8\u4f3c\u6027\u51fd\u6570\u30020.7\u662f\u4ece\u5b9e\u9a8c\u4e2d\u83b7\u5f97\u7684\u7ecf\u9a8c\u9608\u503c\u3002<\/p>\n

       <\/p>\n

       <\/p>\n

      E \u9519\u8bef\u53cd\u9988\u7684\u5f71\u54cd<\/h2>\n

      \u901a\u8fc7\u8bc4\u4f30\u805a\u5408\u63a8\u7406\u94fe\u83b7\u5f97\u7684\u53cd\u9988\u53ef\u80fd\u5305\u62ec\u5206\u6790\u7684\u6709\u9650\u7528\u9014\u548c\u5b8c\u5168\u9519\u8bef\u7684\u7ed3\u8bba\u548c\u9519\u8bef\u62a5\u544a\u3002\u8fd9\u4e2a\u95ee\u9898\u901a\u5e38\u662f\u7531LLMs\u7684\u6027\u8d28\u5f15\u8d77\u7684\uff0c\u5b83\u4eec\u662f\u8bed\u8a00\u6a21\u578b\uff0c\u5e76\u4e0d\u56fa\u6709\u5730\u9a8c\u8bc1\u751f\u6210\u6587\u672c\u7684\u51c6\u786e\u6027\u3002\u6b64\u5916\uff0cLLMs\u7684\u80fd\u529b\uff0c\u4f8b\u5982gpt-3.5-turbo\uff0c\u5f53\u7528\u4f5c\u6570\u5b66\u95ee\u9898\u7684\u9a8c\u8bc1\u5668\u65f6\u53d7\u5230\u9650\u5236\u3002<\/p>\n

       <\/p>\n

      \u4e00\u4e2a\u76f4\u63a5\u7684\u4f8b\u5b50\u5728\u88687\u4e2d\u5448\u73b0\u3002\u5206\u6790\u62a5\u544a\u5f97\u51fa\u7ed3\u8bba\uff1a\u201c\u7b2c\u4e09\u6b65\u4e2d\u83b7\u5f97\u7684\u6700\u7ec8\u7ed3\u679c\u662f80\uff0c\u6570\u5b66\u4e0a\u7b49\u4e8e24\u3002\u201d\u66f4\u7cdf\u7cd5\u7684\u662f\uff0c\u7ecf\u9a8c\u8fdb\u4e00\u6b65\u5305\u542b\u201c\u63a8\u7406\u94fe\u662f\u6b63\u786e\u7684\u201d\uff0c\u5e76\u4e14\u201c\u63a8\u7406\u6b65\u9aa4\u4e2d\u6ca1\u6709\u53d1\u73b0\u9519\u8bef\u201d\u3002\u4f7f\u7528\u8fd9\u4e2a\u7ecf\u9a8c\u4f5c\u4e3a\u8f93\u5165\u63d0\u793a\uff0c\u5728\u7b2c\u4e00\u6b21\u8fed\u4ee3\u4e2d\uff0cBoT\u88ab\u8bef\u5bfc\u751f\u6210\u9519\u8bef\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u76f8\u5e94\u7684\u805a\u5408\u94fe\u53ef\u4ee5\u5728\u88688\u7684\u5f00\u5934\u770b\u5230\u3002\u5f88\u660e\u663e\uff0c\u805a\u5408\u94fe\u5728\u903b\u8f91\u4e0a\u662f\u4e0d\u6b63\u786e\u7684\uff0c\u5e76\u4e14\u4e0d\u7b26\u5408Game of 24\u7684\u4efb\u4f55\u89c4\u5219\u3002<\/p>\n

       <\/p>\n

      \u7136\u800c\uff0c\u6211\u4eec\u8ba4\u4e3a\uff0c\u9519\u8bef\u7684\u53cd\u9988\u4e0d\u4f1a\u88ab\u653e\u5927\uff0c\u800c\u662f\u901a\u8fc7BoT\u7684\u8fed\u4ee3\u673a\u5236\uff0c\u5176\u5bf9\u751f\u6210\u7684\u63a8\u7406\u6b65\u9aa4\u7684\u8d1f\u9762\u5f71\u54cd\u53ef\u4ee5\u5728\u540e\u7eed\u8fed\u4ee3\u4e2d\u5f97\u5230\u7f13\u89e3\u751a\u81f3\u5b8c\u5168\u7ea0\u6b63\u3002\u4e3b\u8981\u539f\u56e0\u662f\u751f\u6210\u7684\u9519\u8bef\u63a8\u7406\u6b65\u9aa4\u5c06\u8fdb\u4e00\u6b65\u5206\u6790\u4ee5\u4ea7\u751f\u65b0\u7684\u7ecf\u9a8c\uff0c\u5c06\u88ab\u6dfb\u52a0\u5230\u63d0\u793a\u4e2d\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u7531\u4e8e\u8fd9\u4e9b\u63a8\u7406\u6b65\u9aa4\u5305\u542b\u5bb9\u6613\u8bc6\u522b\u7684\u660e\u663e\u9519\u8bef\uff0cLLMs\u503e\u5411\u4e8e\u751f\u6210\u6b63\u786e\u7684\u9519\u8bef\u5206\u6790\uff0c\u5e76\u63d0\u4f9b\u6709\u6548\u7684\u4fee\u8ba2\u5efa\u8bae\u3002\u6709\u4e86\u65b0\u7684\u7ecf\u9a8c\u5305\u542b\u5728\u63d0\u793a\u4e2d\uff0cBoT\u80fd\u591f\u751f\u6210\u6b63\u786e\u7684\u63a8\u7406\u6b65\u9aa4\u3002\u6b63\u5982\u88688\u4e2d\u7684\u7ecf\u9a8c\u6240\u793a\uff0cBoT\u4ea7\u751f\u4e86\u8be6\u7ec6\u7684\u9519\u8bef\u62a5\u544a\u548c\u4fee\u8ba2\u5efa\u8bae\uff0c\u4ece\u800c\u4ea7\u751f\u4e86\u5408\u7406\u7684\u601d\u7ef4\u751f\u6210\u8fc7\u7a0b\u3002<\/p>\n

       <\/p>\n

      BoT\u5229\u7528\u8fed\u4ee3\u6765\u7f13\u89e3\u9519\u8bef\u53cd\u9988\u7684\u4e0d\u5229\u5f71\u54cd\u7684\u4f18\u52bf\uff0c\u5728\u56fe4\u4e2d\u663e\u800c\u6613\u89c1\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u968f\u7740\u8fed\u4ee3\u6b21\u6570\u7684\u589e\u52a0\uff0cBoT\u7684\u6027\u80fd\u8868\u73b0\u51fa\u4e00\u81f4\u7684\u589e\u5f3a\u3002\u8fd9\u5f3a\u8c03\u4e86\u79ef\u7d2f\u7ecf\u9a8c\u7684\u91cd\u8981\u6027\u4ee5\u53ca\u540e\u7eed\u7ecf\u9a8c\u7ea0\u6b63\u5148\u524d\u9519\u8bef\u7684\u80fd\u529b\u3002<\/p>\n

       <\/p>\n

       <\/p>\n

      F \u66f4\u591a\u5173\u4e8e\u6570\u5b66\u7684\u7ed3\u679c<\/h2>\n

       <\/p>\n

      \"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-13\"<\/p>\n

      \u56fe5: \u63ed\u793a\u4e86\u4f7f\u7528\u4e0d\u540c\u7b56\u7565\u5728MATH\u6570\u636e\u96c6\u6240\u6709\u95ee\u9898\u5206\u7c7b\u4e2d\u7684\u89e3\u51b3\u6548\u679c\u3002\u8fd9\u4e9b\u7b56\u7565\u7684\u5bf9\u6bd4\u57fa\u4e8e\u5404\u7c7b\u522b\uff0c\u5305\u62ec\u9884\u4ee3\u6570\u3001\u4ee3\u6570\u3001\u8ba1\u6570\u4e0e\u6982\u7387\u3001\u6570\u7406\u539f\u7406\u3001\u51e0\u4f55\u3001\u9884\u5fae\u79ef\u5206\u548c\u4e2d\u7ea7\u4ee3\u6570\u7b49\u3002\u6807\u6709”\u603b\u4f53”\u7684\u5b50\u56fe\u5219\u5c55\u793a\u4e86\u6240\u6709\u7c7b\u522b\u6240\u6709\u95ee\u9898\u7684\u6574\u4f53\u89e3\u51b3\u7387\u3002<\/p>\n

       <\/p>\n

      \u5728\u56fe5\u4e2d\uff0c\u6211\u4eec\u63d0\u4f9b\u4e86\u4e0d\u540c\u65b9\u6cd5\u5728MATH\u6570\u636e\u96c6\u6bcf\u4e2a\u7c7b\u522b\u4e0a\u7684\u89e3\u51b3\u7387\u3002\u8fd9\u4e9b\u7c7b\u522b\u4e2d\u5404\u79cd\u6570\u5b66\u95ee\u9898\u7684\u590d\u6742\u6027\u548c\u591a\u6837\u6027\u4e3a\u6570\u5b66\u63a8\u7406\u63d0\u4f9b\u4e86\u4e00\u4e2a\u66f4\u5177\u6311\u6218\u6027\u7684\u57fa\u51c6\u3002\u56e0\u6b64\uff0cMATH\u4e2d\u7684\u95ee\u9898\u590d\u6742\u6027\u548c\u591a\u6837\u6027\u8981\u6c42\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\u9700\u8981\u5e7f\u6cdb\u7684\u63a8\u7406\u80fd\u529b\u3002\u56e0\u6b64\uff0c\u5728\u6211\u4eec\u7684\u80cc\u666f\u4e0b\u8be6\u7ec6\u68c0\u67e5\u6211\u4eec\u7684\u65b9\u6cd5\u53ca\u5176\u4e0e\u5176\u4ed6\u65b9\u6cd5\u7684\u6bd4\u8f83\uff0c\u53ef\u4ee5\u63d0\u4f9b\u6709\u4ef7\u503c\u7684\u89c1\u89e3\u3002<\/p>\n

      LLMs\u3002<\/strong>\u5728MATH\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u7684\u5b9e\u9a8c\u4f7f\u7528\u4e86\u8457\u540d\u7684\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\uff0c\u5373GPT-3.5-Turbo\uff0c\u4ee5\u4e0b\u7b80\u79f0\u4e3aGPT3.5\uff0c\u548cGPT-4\uff0c\u7b80\u79f0\u4e3aGPT4\u3002\u6211\u4eec\u76f4\u63a5\u4f7f\u7528\u4e86OPENAI\u53d1\u5e03\u7684API\u3002<\/p>\n

       <\/p>\n

      \u7ade\u4e89\u5bf9\u624b\u3002<\/strong>
      \n\u2022 GPT4 ComplexCoT\u3002\u8fd9\u662f\u4f7f\u7528\u590d\u6742CoT Fu\u7b49\u4eba\uff082022\uff09\u63d0\u793a\u65b9\u6cd5\u7684GPT4\u6a21\u578b\u3002\u63a8\u7406\u793a\u4f8b\u7528\u4e8e\u63a8\u7406\u63d0\u793a\u4e2d\uff0c\u8fd9\u4e9b\u793a\u4f8b\u6765\u81ea\u76f8\u5e94\u7684Complex CoT\u51fa\u7248\u7269Fu\u7b49\u4eba\uff082022\uff09\u3002\u7531\u4e8e\u4f7f\u7528\u4e86\u8d2a\u5a6a\u89e3\u7801\uff0c\u56e0\u6b64\u6211\u4eec\u4e0d\u9075\u5faa\u81ea\u6211\u4e00\u81f4\u6027\u65b9\u6cd5Wang\u7b49\u4eba\uff082022\uff09\u6765\u5bf9\u63a8\u7406\u8def\u5f84\u8fdb\u884c\u91c7\u6837\u3002
      \n\u2022 GPT3.5\u3002\u4f7f\u7528\u6807\u51c6\u63d0\u793a\uff0cGPT3.5\u6a21\u578b\u7528\u4e8e\u751f\u6210\u7b54\u6848\u3002
      \n\u2022 GPT3.5 ComplexCoT\u3002\u4e0eGPT4 ComplexCoT\u7c7b\u4f3c\uff0c\u4f46\u5c06\u6a21\u578b\u66f4\u6539\u4e3aGPT3.5\u3002
      \n\u2022 GPT4 PHP+ComplexCoT\u3002\u8fd9\u662f\u4f7f\u7528PHP Zheng\u7b49\u4eba\uff082023\uff09+Complex CoTFu\u7b49\u4eba\uff082022\uff09\u7684GPT4\u6a21\u578b\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5728PHP Zheng\u7b49\u4eba\uff082023\uff09\u6846\u67b6\u4e2d\uff0c\u4f7f\u7528Complex CoT\u63d0\u793a\u751f\u6210\u521d\u59cb\u57fa\u7840\u7b54\u6848\uff0c\u7136\u540ePHP+Complex CoT\u53ef\u4ee5\u4ece\u8fd9\u4e9b\u57fa\u7840\u7b54\u6848\u4e2d\u53d1\u5c55\u51fa\u540e\u7eed\u7684\u7b54\u6848\u751f\u6210\u63d0\u793a\u3002\u56e0\u6b64\uff0c\u5728\u4ea4\u4e92\u7684\u5f00\u59cb\uff0c\u901a\u8fc7\u5c06Complex CoT\u7684\u57fa\u7840\u63d0\u793a\u548c\u5f53\u524d\u95ee\u9898\u4f20\u9012\u7ed9LLM\uff0c\u53ef\u4ee5\u751f\u6210\u57fa\u7840\u7b54\u6848\u3002\u7136\u540e\uff0c\u4f9d\u9760\u4fee\u8ba2\u4e3aPHP\u7248\u672c\u7684Complex CoT\u63d0\u793a\uff0c\u5e76\u9644\u52a0\u63d0\u793a\u53e5\u5b50\uff0c\u9010\u6b65\u63d0\u793a\u6846\u67b6\u5728\u6b64\u57fa\u7840\u7b54\u6848\u4e0a\u6267\u884c\uff0c\u4ee5\u751f\u6210\u6b63\u786e\u7684\u7b54\u6848\u3002\u6211\u4eec\u5c06\u5176\u79f0\u4e3a\u539f\u59cb\u5de5\u4f5c\u4e2dPHP-Complex CoT\u5bf9\u5e94\u7684PHP+Complex CoT\u3002Complex CoT\u7684\u5c04\u51fb\u6b21\u6570\u4e3a8\u3002
      \n\u2022 GPT4 BoT wo\/ experience\u3002GPT4\u6a21\u578b\u7528\u4e8e\u6267\u884cBoT\u6846\u67b6\u7684\u63a8\u7406\uff0c\u800c\u4e0d\u79ef\u7d2f\u7ecf\u9a8c\u3002BoT\u7684\u57fa\u672c\u8bbe\u7f6e\u9075\u5faa\u4e3b\u8981\u8bba\u6587\u4e2d\u4ecb\u7ecd\u7684\u90a3\u4e9b\u3002\u56e0\u6b64\uff0c\u5728\u4e00\u6b21\u8fed\u4ee3\u540e\uff0c\u5c06\u4f7f\u7528\u805a\u5408\u94fe\u4f5c\u4e3a\u89e3\u51b3\u65b9\u6848\u3002
      \n\u2022 GPT4 BoT\u3002GPT4\u7528\u4e8e\u6267\u884c\u4e3b\u8981\u8bba\u6587\u4e2d\u5c55\u793a\u7684\u5b8c\u6574\u7248\u672c\u7684BoT\u3002
      \n\u2022 GPT4 BoT + CoT\u3002\u9664\u4e86BoT\u6846\u67b6\u5916\uff0c\u63d0\u793a\u4e2d\u8fd8\u5305\u62ec\u4e86\u6765\u81eaCoT Wei\u7b49\u4eba\uff082022\uff09\u51fa\u7248\u7269\u76845\u4e2a\u63a8\u7406\u793a\u4f8b\u3002\u56e0\u6b64\uff0c\u5728\u6bcf\u6b21\u8fed\u4ee3\u4e2d\uff0c\u63d0\u793a\u4e0d\u4ec5\u5305\u542b\u7ecf\u9a8c\uff0c\u8fd8\u5305\u62ec\u989d\u5916\u76845\u4e2aCoT\u63a8\u7406\u793a\u4f8b\u3002
      \n\u2022 GPT3.5 BoT\u3002\u4e0eGPT4 BoT\u7c7b\u4f3c\uff0c\u4f46\u5c06\u6a21\u578b\u66f4\u6539\u4e3aGPT3.5\u3002
      \n\u2022 GPT3.5 BoT (GPT4)\u3002\u5728\u8fd9\u4e2a\u5b9e\u9a8c\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528GPT3.5\u8fdb\u884c\u63a8\u7406\uff0c\u4ece\u800c\u5728\u601d\u7ef4\u7ed3\u6784\u751f\u6210\u4e2d\u751f\u6210\u601d\u7ef4\u94fe\u3002<\/p>\n

      \u7136\u800c\uff0c\u5728\u805a\u5408\u7684\u601d\u7ef4\u94fe\u5206\u6790\u4e2d\u8fdb\u884c\u601d\u7ef4\u8bc4\u4f30\u548c\u7ecf\u9a8c\u751f\u6210\u65f6\uff0c\u4f7f\u7528GPT4\u6a21\u578b\u6765\u83b7\u5f97\u8bc4\u4f30\u548c\u5206\u6790\u53cd\u9988\u3002<\/p><\/blockquote>\n

       <\/p>\n

      \u6211\u4eec\u4ece\u56fe5\u4e2d\u7684\u7ed3\u679c\u4e2d\u83b7\u5f97\u4e86\u4ee5\u4e0b\u989d\u5916\u7684\u89c2\u5bdf\u3002<\/strong><\/p>\n

       <\/p>\n

      BoT\u5728\u89e3\u51b3\u8f83\u4e3a\u6311\u6218\u6027\u95ee\u9898\u65b9\u9762\u7684\u7a81\u51fa\u6027\u80fd\uff0c\u4e3b\u8981\u6e90\u81ea\u4e8e\u7ecf\u9a8c\u7684\u79ef\u7d2f\u3002<\/strong>\u5982GPT4 BoT\u548cGPT4 BoT + CoT\u7b49\u4e0eBoT\u76f8\u5173\u7684\u65b9\u6cd5\uff0c\u5728MATH\u7684\u4e0d\u540c\u5b50\u7c7b\u522b\u4e2d\u59cb\u7ec8\u80fd\u5b9e\u73b0\u6700\u9ad8\u7684\u95ee\u9898\u89e3\u51b3\u7387\u3002\u5177\u4f53\u800c\u8a00\uff0cGPT4 BoT\u9886\u5148\u73b0\u6709\u6700\u4f73\u65b9\u6848GPT4 PHP+ComplexCoT8.6%\uff0c\u800cGPT4 BOT + CoT\u66f4\u662f\u9886\u514812.4%\u3002\u5728\u603b\u5171\u4e03\u4e2a\u7c7b\u522b\u4e2d\uff0cGPT4 BoT\u81f3\u5c11\u6bd4GPT4 PHP+ComplexCoT\u9ad80.8%\u51fa\u5934\uff0c\u5176\u4e2d\u5728\u4ee3\u6570\u95ee\u9898\u4e0a\u7684\u4f18\u8d8a\u6027\u66f4\u662f\u8fbe\u523012.5%\u3002\u5bf9\u4e8eGPT3.5 BoT\u548cGPT3.5 BoT + CoT\u4e5f\u540c\u6837\u5982\u6b64\u3002\u7136\u800c\uff0c\u5f53BoT\u6846\u67b6\u4e2d\u6ca1\u6709\u79ef\u7d2f\u7684\u7ecf\u9a8c\u65f6\uff0c\u6240\u6709\u7684\u6570\u5b66\u95ee\u9898\u89e3\u51b3\u6027\u80fd\u90fd\u4f1a\u5927\u5e45\u5ea6\u964d\u4f4e\uff0c\u5c31\u5982GPT4 BoT wo\/\u7ecf\u9a8c\u6240\u663e\u793a\u7684\u3002<\/p>\n

       <\/p>\n

      \u9664\u4e86\u9519\u8bef\u5206\u6790\u7ecf\u9a8c\u5916\uff0c\u5305\u62ec\u6b63\u786e\u7684\u5b9e\u4f8b\uff0c\u5982\u7b80\u5355CoT\u5b9e\u4f8b\uff0c\u5bf9\u4e8e\u63d0\u5347BoT\u5728\u89e3\u51b3\u5177\u6709\u6311\u6218\u6027\u7684\u6570\u5b66\u95ee\u9898\u65b9\u9762\u7684\u6548\u7387\u81f3\u5173\u91cd\u8981\u3002<\/strong>GPT4 BoT\u5728\u89e3\u51b3MATH\u95ee\u9898\u7684\u524d\u4e94\u4e2a\u5b50\u7c7b\u522b\u65f6\uff0c\u5176\u6027\u80fd\u5747\u5927\u5927\u9886\u5148GPT4 PHP+ComplexCoT\u3002\u7136\u800c\uff0c\u5728\u8f83\u4e3a\u590d\u6742\u63a8\u7406\u548c\u590d\u6742\u903b\u8f91\u6b65\u9aa4\u89e3\u51b3\u65b9\u9762\u7684\u9700\u6c42\u66f4\u9ad8\u7684\u9ad8\u7ea7\u4ee3\u6570\u548c\u4e2d\u7ea7\u4ee3\u6570\u9886\u57df\uff0cBoT\u7684\u6539\u8fdb\u5e45\u5ea6\u4ec5\u4e3a0.8%\u548c2.4%\u3002\u4e0e\u5728\u89e3\u51b3\u8f83\u7b80\u5355\u95ee\u9898\u7c7b\u522b\u65f6\u89c2\u5bdf\u5230\u7684\u663e\u8457\u589e\u5f3a\u76f8\u6bd4\uff0c\u8fd9\u4e9b\u589e\u76ca\u76f8\u5bf9\u6709\u9650\u3002\u7136\u800c\uff0c\u5f53\u8f93\u5165\u63d0\u793a\u4e2d\u76f4\u63a5\u52a0\u51655\u4e2a\u6b63\u786e\u7684CoT\u5b9e\u4f8b\u540e\uff0cGPT-4 BoT + CoT\u5728\u9ad8\u7ea7\u4ee3\u6570\u548c\u4e2d\u7ea7\u4ee3\u6570\u9886\u57df\u7684\u8868\u73b0\u5927\u5927\u63d0\u5347\uff0c\u5206\u522b\u8d85\u8d8aGPT-4 BoT7.7%\u548c11.5%\u3002\u8fd9\u4e9b\u89c2\u5bdf\u7ed3\u679c\u7684\u57fa\u672c\u7ed3\u8bba\u662f\uff0c\u8981\u786e\u4fddBoT\u5728\u89e3\u51b3\u590d\u6742\u6570\u5b66\u95ee\u9898\u65f6\u80fd\u8fbe\u5230\u6700\u597d\u7684\u8868\u73b0\uff0c\u4ec5\u9760\u8bd5\u9519\u8bef\u5206\u6790\u4ee5\u5b66\u4e60\u63a8\u7406\u662f\u4e0d\u8db3\u591f\u7684\uff0c\u5e94\u4f9d\u8d56\u4e8e\u5728\u8f93\u5165\u63d0\u793a\u4e2d\u63d0\u4f9b\u6b63\u786e\u7b54\u6848\u7ed9LLMs\u3002<\/p>\n

       <\/p>\n

      \u867d\u7136\u5f00\u59cb\u65f6GPT3.5\u914d\u5408BoT\u53ef\u80fd\u7a0d\u900a\u4e8eGPT-4 CoT\uff0c\u4f46\u662f\u5f53\u4f7f\u7528GPT-4\u4f5c\u4e3a\u8bc4\u4f30\u548c\u5206\u6790\u7684\u5de5\u5177\u6765\u751f\u6210\u7ecf\u9a8c\u540e\uff0c\u53ef\u4ee5\u8ba9GPT-3.5 BoT\uff08GPT-4\uff09\u7684\u6027\u80fd\u8d85\u8d8aGPT-4 Complex CoT\u3002<\/strong>\u4f7f\u7528\u5bb9\u91cf\u5c0f\u4e8eGPT4\u7684GPT3.5\u4f5c\u4e3aLLM\u65f6\uff0cBoT\u83b7\u5f97\u7684\u89e3\u51b3\u7387\u81f3\u5c11\u6bd4GPT4 ComplexCoT\u4f4e7.7%\uff08\u5c24\u5176\u662f\u5728\u4ee3\u6570\u8fd9\u95e8\u5b66\u79d1\u91cc\uff09\u3002\u5f88\u660e\u663e\uff0c\u5f53\u6027\u80fd\u8f83\u5f31\u7684LLMs\u4ea7\u751f\u7684\u8bd5\u9519\u5206\u6790\u8d28\u91cf\u8f83\u4f4e\u65f6\uff0cBoT\u65e0\u6cd5\u80dc\u8fc7GPT4 ComplexCoT\u3002\u56e0\u6b64\uff0c\u5728GPT4\u751f\u6210\u7ecf\u9a8c\u7684\u540c\u65f6\u4f7f\u7528GPT3.5\u4ec5\u751f\u6210\u63a8\u7406\u6b65\u9aa4\u540e\uff0cGPT3.5 BoT\uff08GPT4\uff09\u5728\u6240\u6709\u7c7b\u522b\u4e2d\u8868\u73b0\u51fa\u663e\u8457\u6539\u8fdb\uff0c\u5bfc\u81f4\u89e3\u51b3\u7387\u8fbe\u5230\u4e8655.8%\uff0c\u6bd4GPT4 ComplexCoT\u9ad85.5%\uff0c\u751a\u81f3\u6bd4\u5f53\u524d\u6700\u65b0\u7684GPT4 PHP+ComplexCoT\u9ad8\u51fa1.9%\u3002\u8fd9\u4e9b\u89c2\u5bdf\u7ed3\u679c\u8fdb\u4e00\u6b65\u8bc1\u660e\u4e86\u5728\u63d0\u793a\u4e2d\u901a\u8fc7\u8fed\u4ee3\u79ef\u7d2f\u7ecf\u9a8c\u662fBoT\u6846\u67b6\u6210\u529f\u7684\u4e3b\u56e0\u3002<\/p>\n

       <\/p>\n

       <\/p>\n

      G \u6e38\u620f24\u70b9\u7684\u63a8\u7406\u7ed3\u679c<\/h2>\n

       <\/p>\n

      \u9996\u5148\uff0c\u5728\u88685\u81f3\u88689\u4e2d\uff0c\u6211\u4eec\u5c55\u793a\u4e86BoT\u5728\u63a8\u7406\u8fc7\u7a0b\u4e2d\u4f7f\u7528\u7684\u8be6\u7ec6\u63d0\u793a\uff0c\u4ece\u800c\u63d0\u4f9b\u4e86\u5bf9BoT\u5728\u6bcf\u6b21\u8fed\u4ee3\u4e2d\u6240\u505a\u5de5\u4f5c\u7684\u5168\u9762\u7406\u89e3\u3002\u7136\u540e\uff0c\u4ece\u886810\u5f00\u59cb\uff0c\u6211\u4eec\u5c55\u793a\u4e86\u5305\u542bBoT\u6574\u4e2a\u63a8\u7406\u8fc7\u7a0b\u7684\u786e\u5207\u793a\u4f8b\u3002\u9075\u5faa\u5b9e\u9a8c\u90e8\u5206\u4e2d\u663e\u793a\u7684\u57fa\u672c\u8bbe\u7f6e\uff0c\u8fd9\u4e9b\u5b9e\u9a8c\u662f\u4f7f\u7528GPT-3.5-turbo\u6a21\u578b\u4e0eBoT\u83b7\u5f97\u7684\u3002<\/p>\n

       <\/p>\n

      \"BoT\uff1a\u5f3a\u5316\u601d\u8003:\u7528\u5927\u578b\u8bed\u8a00\u6a21\u578b\u89e3\u51b3\u8bd5\u9519\u95ee\u9898-14\"<\/p>\n

      \u88685\uff1a\u5728\u6ca1\u6709\u7ecf\u9a8c\u5305\u542b\u5728\u8f93\u5165\u63d0\u793a\u4e2d\u65f6\uff0cgpt-3.5-turbo\u751f\u6210\u7684\u63a8\u7406\u6b65\u9aa4\u3002<\/strong>\u6211\u4eec\u9996\u5148\u8ba9\u6a21\u578b\u751f\u6210\u4e94\u4e2a\u63a8\u7406\u6b65\u9aa4\u4ee5\u68c0\u67e5\u591a\u6837\u6027\uff0c\u7136\u540e\u5448\u73b0\u5b8c\u6210BoT\u7b2c\u4e00\u6b21\u8fed\u4ee3\u540e\u7684\u6700\u7ec8\u63a8\u7406\u94fe\u3002<\/p>\n

       <\/p>\n

      \u6e38\u620f24\u70b9\u7684\u63d0\u793a\uff0c\u6ca1\u6709\u7ecf\u9a8c<\/strong><\/p>\n

      \u572824\u70b9\u6e38\u620f\u4e2d\uff0c\u4f60\u4f1a\u5f97\u5230\u56db\u4e2a\u6570\u5b57\uff0c\u76ee\u6807\u662f\u4f7f\u7528\u57fa\u672c\u7684\u7b97\u672f\u8fd0\u7b97\uff08+\uff0c-\uff0c*\uff0c\/\uff09\u6765\u7ed3\u5408\u8fd9\u4e9b\u6570\u5b57\uff0c\u5f97\u523024\u8fd9\u4e2a\u7ed3\u679c\u3002\u4f60\u53ea\u80fd\u4f7f\u7528\u6bcf\u4e2a\u6570\u5b57\u4e00\u6b21\uff0c\u5e76\u4e14\u53ef\u4ee5\u4f7f\u7528\u62ec\u53f7\u6765\u6539\u53d8\u8fd0\u7b97\u987a\u5e8f\u3002<\/p>\n

      \u5206\u6790\u683c\u5f0f\u7684\u6bcf\u4e00\u6b65\uff1a
      \n\u7b2cX\u6b65\uff0c\u5f53\u524d\u96c6\u5408\uff1aXXXX\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1aXX XX\uff0c\u8fd0\u7b97\uff1aXX\uff0c\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b57\uff1aXX\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1aXXXX\uff0c\u65b0\u96c6\u5408\uff1aXXXX\u3002<\/p>\n

      \u7ed9\u5b9a\u7684\u56db\u4e2a\u6570\u5b57\u662f\uff1a1 1 4 6\u3002
      \n\u8ba9\u6211\u4eec\u4e00\u6b65\u4e00\u6b65\u601d\u8003\u3002<\/p>\n

      \u56de\u5fc6\u5386\u53f2\u63a8\u7406\u7ecf\u9a8c\uff08\u5f53\u7ecf\u9a8c\u4e3a\u7a7a\u65f6\u8bf7\u5ffd\u7565\uff09\uff1a<\/strong>
      \n## ############### ######## ######## # # # #######
      \n\u6ce8\u610f\u5206\u6790\u548c\u7ed3\u8bba\u5728\u7ecf\u9a8c\u4e2d\uff0c\u907f\u514d\u901a\u8fc7\u9075\u5faa\u5efa\u8bae\u800c\u72af\u7c7b\u4f3c\u7684\u9519\u8bef\u3002
      \n\u4ee5\u4e0b\u662f\u4e00\u7cfb\u5217\u6709\u5e8f\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u9644\u5e26\u5b83\u4eec\u7684\u8bc4\u4f30\u5206\u6570\uff08\u66f4\u9ad8\u7684\u5206\u6570\u610f\u5473\u7740\u63a8\u7406\u6b65\u9aa4\u66f4\u6709\u53ef\u80fd\u5b8c\u6210\u4efb\u52a1\u3002\uff09\uff1a<\/p>\n

      \u57fa\u4e8e\u4e0a\u8ff0\u201c_\u201d\u4e2d\u5217\u51fa\u7684\u63a8\u7406\u6b65\u9aa4\uff08\u5373\uff0c\u4e0d\u662f\u7ecf\u9a8c\u5757\u4e2d\u7684\u6b65\u9aa4\uff09\uff0c\u8bf7\u8fdb\u884c\u4e00\u6b65\u63a8\u7406\uff0c\u4ee5\u751f\u6210\u552f\u4e00\u7684\u4e00\u4e2a\u53ef\u80fd\u7684\u540e\u7eed\u63a8\u7406\u6b65\u9aa4\u3002<\/p>\n

      \u6765\u81eagpt-3.5-turbo\u7684\u4e94\u4e2a\u54cd\u5e94<\/strong>
      \n\u6b65\u9aa4 1\uff0c\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u8fd0\u7b97\uff1a+\uff0c\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b57\uff1a2\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a2 4 6.\uff0c\u8bc4\u4f30\u5206\u6570\uff1a0.7
      \n\u6b65\u9aa4 1\uff0c\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u8fd0\u7b97\uff1a+\uff0c\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b57\uff1a2\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a2 4 6.\uff0c\u8bc4\u4f30\u5206\u6570\uff1a0.7
      \n\u6b65\u9aa4 1\uff0c\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u8fd0\u7b97\uff1a+\uff0c\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b57\uff1a2\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a2 4 6.\uff0c\u8bc4\u4f30\u5206\u6570\uff1a0.7
      \n\u6b65\u9aa4 1\uff0c\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u8fd0\u7b97\uff1a+\uff0c\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b57\uff1a2\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a2 4 6.\uff0c\u8bc4\u4f30\u5206\u6570\uff1a0.7
      \n\u6b65\u9aa4 1\uff0c\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u8fd0\u7b97\uff1a*\uff0c\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b57\uff1a1\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a1 4 6.\uff0c\u8bc4\u4f30\u5206\u6570\uff1a0.7<\/p>\n

      \u805a\u5408\u540e\u83b7\u5f97\u7684\u63a8\u7406\u94fe<\/strong>
      \n\u6b65\u9aa4 1\uff0c\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u8fd0\u7b97\uff1a+\uff0c\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b57\uff1a2\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a2 4 6.. \u8bc4\u4f30\u5206\u6570\uff1a0.7
      \n\u6b65\u9aa4 2\uff0c\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 4\uff0c\u8fd0\u7b97\uff1a*\uff0c\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b57\uff1a4\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a1 6\uff0c\u65b0\u96c6\u5408\uff1a4 1 6.. \u8bc4\u4f30\u5206\u6570\uff1a0.7
      \n\u6b65\u9aa4 1\uff0c\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u8fd0\u7b97\uff1a*\uff0c\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b57\uff1a1\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a1 4 6.\uff0c\u8bc4\u4f30\u5206\u6570\uff1a0.7<\/p><\/blockquote>\n

       <\/p>\n

       <\/p>\n

      H \u5173\u4e8e\u201cGSM8K\u201d\u7684\u63a8\u5bfc\u7ed3\u679c<\/h2>\n

       <\/p>\n

      BoT\u7684\u64cd\u4f5c\u65b9\u5f0f\u662f\u91c7\u7528\u7c7b\u4f3c\u4e8e\u8868\u683c5\u81f3\u8868\u683c9\u6240\u793a\u7684\u57fa\u672c\u63d0\u793a\u548c\u7279\u5b9a\u683c\u5f0f\u3002\u552f\u4e00\u4f1a\u6539\u53d8\u7684\u53ea\u6709\u4efb\u52a1\u63d0\u793a\uff0c\u5982\u886815\u6240\u793a\u3002\u800c\u4ece\u886816\u5f00\u59cb\uff0c\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e9b\u8be6\u7ec6\u7684\u5b9e\u4f8b\uff0c\u8fd9\u4e9b\u5b9e\u4f8b\u5305\u542b\u4e86BoT\u5b8c\u6574\u7684\u63a8\u7406\u8fc7\u7a0b\u3002\u8fd9\u4e9b\u5b9e\u9a8c\u662f\u57fa\u4e8e\u5b9e\u9a8c\u90e8\u5206\u6240\u663e\u793a\u7684\u57fa\u7840\u8bbe\u7f6e\uff0c\u4f7f\u7528\u7684\u662fGPT-3.5-turbo\u6a21\u578b\u7684BoT\u3002<\/p>\n

       <\/p>\n

      # \u6e38\u620f24\u7684\u7ecf\u9a8c\u6027\u63a8\u7406\u63d0\u793a<\/p>\n

      ## \u9996\u5148\uff0c\u56de\u987e\u5386\u53f2\u63a8\u7406\u7ecf\u9a8c\uff1a<\/p>\n

      ### \u63a8\u7406\u94fe1\u53ca\u5176\u8bc4\u8bba<\/p>\n

      \u4e0b\u9762\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5c55\u793a\u7684\u63a8\u7406\u6b65\u9aa4\u94fe\uff1a<\/p>\n

      —<\/p>\n

      ### \u6b65\u9aa4 1
      \n\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a2\uff0c\u5269\u4f59\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a2 4 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.7<\/p>\n

      ### \u6b65\u9aa4 2
      \n\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 4\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a4\uff0c\u5269\u4f59\u6570\u5b57\uff1a1 6\uff0c\u65b0\u96c6\u5408\uff1a4 1 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.7<\/p>\n

      ### \u6b65\u9aa4 3
      \n\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a1\uff0c\u5269\u4f59\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a1 4 6. \u8bc4\u4f30\u5f97\u5206\uff1a0.7<\/p>\n

      —<\/p>\n

      ## \u5206\u6790\u62a5\u544a\uff1a\u8fd9\u4e2a\u63a8\u7406\u94fe\u65e0\u6cd5\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u63a8\u7406\u6b65\u9aa4\u5b58\u5728\u9519\u8bef\uff0c\u963b\u788d\u4e86\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u7684\u53d1\u73b0\u3002<\/p>\n

      ### \u63a8\u7406\u6b65\u9aa4 1
      \n\u8fd9\u4e00\u6b65\u662f\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u65ad\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4e86\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\u3001\u6267\u884c\u64cd\u4f5c\u5e76\u76f8\u5e94\u66f4\u65b0\u96c6\u5408\u7684\u89c4\u5219\u3002\u7136\u800c\uff0c\u8fd9\u4e00\u6b65\u5bf9\u4e8e\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u5e76\u65e0\u5e2e\u52a9\u3002\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b572\u5e76\u4e0d\u80fd\u5bfc\u81f4\u671f\u671b\u7684\u7ed3\u679c24\u3002
      \n**\u5efa\u8bae**\uff1a\u5c1d\u8bd5\u4e0d\u540c\u7684\u64cd\u4f5c\u6216\u6570\u5b57\u7ec4\u5408\uff0c\u4ee5\u83b7\u5f97\u66f4\u63a5\u8fd124\u7684\u65b0\u6570\u5b57\u3002
      \n**\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u62d2\u7edd\u3002<\/p>\n

      ### \u63a8\u7406\u6b65\u9aa4 2
      \n\u63a8\u7406\u6b65\u9aa4\u63cf\u8ff0\u4e2d\u6709\u8bef\u3002\u5b83\u88ab\u9519\u8bef\u5730\u79f0\u4e3a\u201c\u63a8\u7406\u6b65\u9aa4 2\u201d\u4e24\u6b21\u3002\u7136\u800c\uff0c\u5047\u8bbe\u5b83\u662f\u552f\u4e00\u7684\u6b65\u9aa4\uff0c\u5b83\u662f\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u65ad\u3002\u4e58\u6cd5(*)\u64cd\u4f5c\u6b63\u786e\u5e94\u7528\u4e8e\u6240\u9009\u6570\u5b57\uff0c\u5e76\u5f97\u5230\u4e86\u65b0\u6570\u5b574\u3002\u5269\u4f59\u6570\u5b57\u76f8\u5e94\u66f4\u65b0\u3002
      \n**\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u63a8\u8350\u3002<\/p>\n

      ### \u63a8\u7406\u6b65\u9aa4 3
      \n\u63a8\u7406\u6b65\u9aa4\u63cf\u8ff0\u4e2d\u6709\u8bef\u3002\u5b83\u88ab\u9519\u8bef\u5730\u79f0\u4e3a\u201c\u63a8\u7406\u6b65\u9aa4 1\u201d\uff0c\u800c\u4e0d\u662f\u201c\u63a8\u7406\u6b65\u9aa4 3\u201d\u3002\u8fd9\u4e00\u6b65\u5e76\u4e0d\u662f\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u65ad\u3002\u4e58\u6cd5(*)\u64cd\u4f5c\u5e94\u7528\u4e8e\u4e0e\u63a8\u7406\u6b65\u9aa41\u4e2d\u76f8\u540c\u7684\u6570\u5b57\uff0c\u4f46\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u6570\u5b571\u662f\u4e0d\u540c\u7684\u3002\u5269\u4f59\u6570\u5b57\u76f8\u5e94\u66f4\u65b0\u3002
      \n**\u9519\u8bef\u62a5\u544a**\uff1a\u8fd9\u4e00\u6b65\u7684\u8ba1\u7b97\u662f\u9519\u8bef\u7684\u3002\u6b63\u786e\u7684\u8ba1\u7b97\u5e94\u8be5\u662f1 * 1 = 1\u3002
      \n**\u5efa\u8bae**\uff1a\u4ed4\u7ec6\u68c0\u67e5\u8ba1\u7b97\uff0c\u786e\u4fdd\u5176\u51c6\u786e\u65e0\u8bef\u3002
      \n**\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u62d2\u7edd\u3002<\/p>\n

      **\u4fe1\u5fc3\u5f97\u5206**\uff1a0.7<\/p>\n

      —<\/p>\n

      ## \u6765\u81eagpt-3.5-turbo\u7684\u4e94\u4e2a\u56de\u5e94<\/p>\n

      —<\/p>\n

      ### \u6b65\u9aa4 1
      \n\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 4\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a4\uff0c\u5269\u4f59\u6570\u5b57\uff1a1 6\uff0c\u65b0\u96c6\u5408\uff1a1 4 6.\uff0c<\/p>\n

      ### \u6b65\u9aa4 1
      \n\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 6\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a7\uff0c\u5269\u4f59\u6570\u5b57\uff1a1 4\uff0c\u65b0\u96c6\u5408\uff1a1 4 7.\uff0c<\/p>\n

      ### \u6b65\u9aa4 1
      \n\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a1\uff0c\u5269\u4f59\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a1 4 6.\uff0c<\/p>\n

      ### \u6b65\u9aa4 1
      \n\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 4\uff0c\u64cd\u4f5c\uff1a\/\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a0.25\uff0c\u5269\u4f59\u6570\u5b57\uff1a1 6\uff0c\u65b0\u96c6\u5408\uff1a0.25 1 6.\uff0c<\/p>\n

      ### \u6b65\u9aa4 1
      \n\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u64cd\u4f5c\uff1a-\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a0\uff0c\u5269\u4f59\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a0 4 6.\uff0c<\/p>\n

      —<\/p>\n

      ## \u805a\u5408\u540e\u7684\u63a8\u7406\u94fe<\/p>\n

      —<\/p>\n

      ### \u6b65\u9aa4 1
      \n\u5f53\u524d\u96c6\u5408\uff1a1 1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 1\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a1\uff0c\u5269\u4f59\u6570\u5b57\uff1a4 6\uff0c\u65b0\u96c6\u5408\uff1a1 4 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      ### \u6b65\u9aa4 2
      \n\u5f53\u524d\u96c6\u5408\uff1a1 4 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a1 4\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a4\uff0c\u5269\u4f59\u6570\u5b57\uff1a6\uff0c\u65b0\u96c6\u5408\uff1a4 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.7<\/p>\n

      ### \u6b65\u9aa4 3
      \n\u5f53\u524d\u96c6\u5408\uff1a46\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 6\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a1\uff0c\u5269\u4f59\u6570\u5b57\uff1a\uff0c\u65b0\u96c6\u5408\uff1a24. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      —<\/p><\/blockquote>\n

      \u88686: \u5f53\u5c06\u7ecf\u9a8c\u7eb3\u5165\u8f93\u5165\u63d0\u793a\u65f6\uff0c\u7531gpt-3.5-turbo\u6240\u751f\u6210\u7684\u63a8\u7406\u6b65\u9aa4\u3002\u8fd9\u4efd\u7ecf\u9a8c\u662f\u5bf9\u88685\u63a8\u7406\u94fe\u7684\u5206\u6790\u3002\u8bbe\u5b9a\u8fd9\u4e2a\u7ecf\u9a8c\u5728\u63d0\u793a\u4e2d\u540e\uff0c\u6211\u4eec\u5c55\u793a\u4e86\u6a21\u578b\u7684\u4e94\u6b21\u56de\u5e94\u548c\u5b8c\u6210BoT\u7684\u7b2c\u4e8c\u8f6e\u8fed\u4ee3\u4e4b\u540e\u5f62\u6210\u7684\u6700\u7ec8\u63a8\u7406\u94fe\u3002<\/p>\n

       <\/p>\n

      # \u4e0b\u4e00\u4e2a\u601d\u7ef4\u751f\u6210\u7684\u63d0\u793a<\/p>\n

      \u572824\u70b9\u6e38\u620f\u4e2d\uff0c\u4f60\u4f1a\u5f97\u5230\u56db\u4e2a\u6570\u5b57\uff0c\u76ee\u6807\u662f\u4f7f\u7528\u57fa\u672c\u7684\u7b97\u672f\u8fd0\u7b97\uff08+\u3001-\u3001*\u3001\/\uff09\u6765\u7ec4\u5408\u8fd9\u4e9b\u6570\u5b57\uff0c\u5f97\u523024\u8fd9\u4e2a\u7ed3\u679c\u3002\u6bcf\u4e2a\u6570\u5b57\u53ea\u80fd\u4f7f\u7528\u4e00\u6b21\uff0c\u53ef\u4ee5\u4f7f\u7528\u62ec\u53f7\u6765\u6539\u53d8\u8fd0\u7b97\u987a\u5e8f\u3002<\/p>\n

      \u6bcf\u4e2a\u6b65\u9aa4\u7684\u5206\u6790\u683c\u5f0f\uff1a\u6b65\u9aa4 , \u5f53\u524d\u96c6\u5408: , \u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57: , \u64cd\u4f5c: , \u8ba1\u7b97\u7684\u65b0\u6570\u5b57: , \u5269\u4f59\u7684\u6570\u5b57: , \u65b0\u96c6\u5408: \u3002<\/p>\n

      \u7ed9\u51fa\u7684\u56db\u4e2a\u6570\u5b57\u662f\uff1a3 5 6 8\u3002<\/p>\n

      \u8ba9\u6211\u4eec\u4e00\u6b65\u4e00\u6b65\u5730\u601d\u8003\u3002<\/p>\n

      ## \u9996\u5148\uff0c\u56de\u987e\u5386\u53f2\u63a8\u7406\u7ecf\u9a8c\uff1a<\/p>\n

      ### \u7b2c1\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba<\/p>\n

      \u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u7684\u5305\u542b\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a<\/p>\n

      —<\/p>\n

      \u6b65\u9aa41\uff0c\u5f53\u524d\u96c6\u5408\uff1a3 5 6 8\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 6\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a30\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a3 8\uff0c\u65b0\u96c6\u5408\uff1a30 3 8.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      \u6b65\u9aa42\uff0c\u5f53\u524d\u96c6\u5408\uff1a30 3 8\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a30 3\uff0c\u64cd\u4f5c\uff1a\/\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a10\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a8\uff0c\u65b0\u96c6\u5408\uff1a10 8.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      \u6b65\u9aa43\uff0c\u5f53\u524d\u96c6\u5408\uff1a10 8\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a10 8\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a80\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a80.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9\u3002<\/p>\n

      —<\/p>\n

      ## \u5206\u6790\u62a5\u544a<\/p>\n

      \u8fd9\u6761\u63a8\u7406\u94fe\u53ef\u4ee5\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u7b2c3\u6b65\u4e2d\u5f97\u5230\u7684\u6700\u7ec8\u7ed3\u679c\u662f80\uff0c\u6570\u5b66\u4e0a\u7b49\u4e8e24\u3002<\/p>\n

      ### \u63a8\u7406\u6b65\u9aa41
      \n\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u5bfc\u3002\u4ece\u5f53\u524d\u96c6\u5408\uff083 5 6 8\uff09\u4e2d\u9009\u62e9\u6570\u5b575\u548c6\u5e76\u76f8\u4e58\u5f97\u5230\u65b0\u6570\u5b5730\u3002\u5269\u4f59\u7684\u6570\u5b57\u662f3\u548c8\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u6709\u52a9\u4e8e\u6b63\u786e\u89e3\u51b3\u65b9\u6848\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5e76\u751f\u6210\u4e86\u4e00\u4e2a\u65b0\u7684\u6570\u5b57\u3002<\/p>\n

      ### \u63a8\u7406\u6b65\u9aa42
      \n\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u5bfc\u3002\u4ece\u5f53\u524d\u96c6\u5408\uff0830 3 8\uff09\u4e2d\u9009\u62e9\u6570\u5b5730\u548c3\u5e76\u76f8\u9664\u5f97\u5230\u65b0\u6570\u5b5710\u3002\u5269\u4f59\u7684\u6570\u5b57\u662f8\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u6709\u52a9\u4e8e\u6b63\u786e\u89e3\u51b3\u65b9\u6848\uff0c\u56e0\u4e3a\u5b83\u8fdb\u4e00\u6b65\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5e76\u751f\u6210\u4e86\u4e00\u4e2a\u65b0\u7684\u6570\u5b57\u3002<\/p>\n

      ### \u63a8\u7406\u6b65\u9aa43
      \n\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u5bfc\u3002\u4ece\u5f53\u524d\u96c6\u5408\uff0810 8\uff09\u4e2d\u9009\u62e9\u6570\u5b5710\u548c8\u5e76\u76f8\u4e58\u5f97\u5230\u65b0\u6570\u5b5780\u3002\u7531\u4e8e\u6ca1\u6709\u5269\u4f59\u7684\u6570\u5b57\uff0c\u63a8\u7406\u94fe\u7684\u7ed3\u679c\u662f80\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u6709\u52a9\u4e8e\u6b63\u786e\u89e3\u51b3\u65b9\u6848\uff0c\u56e0\u4e3a\u5b83\u751f\u6210\u4e86\u6700\u7ec8\u7ed3\u679c\u3002<\/p>\n

      \u5efa\u8bae\uff1a\u5728\u63a8\u7406\u6b65\u9aa4\u4e2d\u6ca1\u6709\u53d1\u73b0\u9519\u8bef\u3002<\/p>\n

      \u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0\uff1a\u6240\u6709\u63a8\u7406\u6b65\u9aa4\u90fd\u88ab\u63a8\u8350\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u6b63\u786e\u7684\u5e76\u6709\u52a9\u4e8e\u8fbe\u5230\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      \u4fe1\u5fc3\u5f97\u5206\uff1a0.9<\/p>\n

      ### \u7b2c2\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba<\/p>\n

      \u5f85\u7eed\uff0c\u5728\u88688\u4e2d<\/p>\n

      ### \u5206\u6790\u548c\u7ed3\u8bba\u6ce8\u610f\u4e8b\u9879<\/p>\n

      \u6839\u636e\u7ecf\u9a8c\u4e2d\u7684\u5206\u6790\u548c\u7ed3\u8bba\uff0c\u907f\u514d\u901a\u8fc7\u9075\u5faa\u5efa\u8bae\u800c\u72af\u7c7b\u4f3c\u7684\u9519\u8bef\u3002<\/p>\n

      \u4ee5\u4e0b\u662f\u4e00\u7cfb\u5217\u6709\u5e8f\u7684\u63a8\u7406\u6b65\u9aa4\u5217\u8868\uff0c\u9644\u6709\u5b83\u4eec\u7684\u8bc4\u4f30\u5f97\u5206\uff08\u5f97\u5206\u8d8a\u9ad8\u610f\u5473\u7740\u63a8\u7406\u6b65\u9aa4\u66f4\u6709\u53ef\u80fd\u5b8c\u6210\u4efb\u52a1\u3002\uff09\uff1a<\/p>\n

      —<\/p>\n

      \u6b65\u9aa41\uff0c\u5f53\u524d\u96c6\u5408\uff1a3 5 6 8\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a3 8\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a11\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a5 6\uff0c\u65b0\u96c6\u5408\uff1a11 5 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.7<\/p>\n

      \u6b65\u9aa42\uff0c\u5f53\u524d\u96c6\u5408\uff1a11 5 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 6\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a30\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a11\uff0c\u65b0\u96c6\u5408\uff1a30 11.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      —<\/p>\n

      \u6839\u636e\u4e0a\u8ff0\u201c\u2014\u2014\u2014\u201d\u5185\u5217\u51fa\u7684\u63a8\u7406\u6b65\u9aa4\uff08\u5373\uff0c\u4e0d\u662f\u7ecf\u9a8c\u5757\u4e2d\u7684\u6b65\u9aa4\uff09\uff0c\u8bf7\u8fdb\u884c\u4e00\u6b65\u63a8\u7406\uff0c\u751f\u6210\u552f\u4e00\u7684\u4e00\u4e2a\u540e\u7eed\u53ef\u80fd\u7684\u63a8\u7406\u6b65\u9aa4\u3002<\/p>\n

       <\/p>\n

      ## \u751f\u6210\u7684\u4e0b\u4e00\u6b65\u63a8\u7406<\/p>\n

      \u6b65\u9aa43\uff0c\u5f53\u524d\u96c6\u5408\uff1a30 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a30 11\uff0c\u64cd\u4f5c\uff1a-\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a19\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a\uff0c\u65b0\u96c6\u5408\uff1a19.\u3002<\/p><\/blockquote>\n

      \u88687: BoT\u5728\u751f\u6210\u5bf9\u5e94\u63a8\u7406\u6b65\u9aa4zi\u7684\u53ef\u80fd\u601d\u8003\u7684\u793a\u4f8b\u3002<\/p>\n

       <\/p>\n

      ## \u7b2c2\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba<\/p>\n

      \u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u7684\u5305\u542b\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a<\/p>\n

      —<\/p>\n

      ### \u6b65\u9aa41
      \n\u5f53\u524d\u96c6\u5408\uff1a10 8\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a10 8\uff0c\u64cd\u4f5c\uff1a\/\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a1.25\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a1.25. \u8bc4\u4f30\u5f97\u5206\uff1a0.8\u3002<\/p>\n

      ### \u6b65\u9aa42
      \n\u5f53\u524d\u96c6\u5408\uff1a10 8\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a10 8\uff0c\u64cd\u4f5c\uff1a\/\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a1.25\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a1.25.. \u8bc4\u4f30\u5f97\u5206\uff1a0.8\u3002<\/p>\n

      ### \u6b65\u9aa43
      \n\u5f53\u524d\u96c6\u5408\uff1a10 8\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a10 8\uff0c\u64cd\u4f5c\uff1a\/\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a1.25\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a1.25.. \u8bc4\u4f30\u5f97\u5206\uff1a0.8\u3002<\/p>\n

      —<\/p>\n

      ## \u5206\u6790\u62a5\u544a<\/p>\n

      \u8fd9\u4e2a\u63a8\u7406\u94fe\u65e0\u6cd5\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u63d0\u4f9b\u7684\u63a8\u7406\u6b65\u9aa4\u662f\u9519\u8bef\u7684\uff0c\u5e76\u4e0d\u4f1a\u5bfc\u81f4\u5f97\u523024\u7684\u7ed3\u679c\u3002<\/p>\n

      ### \u63a8\u7406\u6b65\u9aa41
      \n\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u9519\u8bef\u7684\u3002\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b5710\u548c8\u5e76\u4e0d\u5728\u7ed9\u5b9a\u7684\u6570\u5b57\u96c6\u54083\u30015\u30016\u548c8\u4e2d\u3002\u6b64\u5916\uff0c\u9664\u6cd5(\/)\u64cd\u4f5c\u5e76\u4e0d\u4f1a\u5bfc\u81f4\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u4e3a1.25\u3002\u5269\u4f59\u7684\u6570\u5b57\u4e5f\u6ca1\u6709\u6b63\u786e\u8bc6\u522b\u3002<\/p>\n

      **\u9519\u8bef\u62a5\u544a**\uff1a
      \n– \u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b57\u4e0d\u5b58\u5728\u4e8e\u7ed9\u5b9a\u7684\u6570\u5b57\u96c6\u5408\u4e2d\u3002
      \n– \u64cd\u4f5c\u548c\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f\u9519\u8bef\u7684\u3002
      \n– \u5269\u4f59\u7684\u6570\u5b57\u6ca1\u6709\u6b63\u786e\u8bc6\u522b\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a
      \n– \u786e\u4fdd\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b57\u5b58\u5728\u4e8e\u7ed9\u5b9a\u7684\u6570\u5b57\u96c6\u5408\u4e2d\u3002
      \n– \u4f7f\u7528\u6b63\u786e\u7684\u64cd\u4f5c\uff0c\u4ee5\u5f97\u5230\u671f\u671b\u7684\u65b0\u6570\u5b57\u3002
      \n– \u51c6\u786e\u5730\u8bc6\u522b\u5269\u4f59\u7684\u6570\u5b57\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u62d2\u7edd\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u9519\u8bef\u7684\uff0c\u5e76\u4e0d\u6709\u52a9\u4e8e\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      ### \u63a8\u7406\u6b65\u9aa42
      \n\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u63a8\u7406\u6b65\u9aa41\u7684\u91cd\u590d\uff0c\u56e0\u6b64\u4e5f\u662f\u9519\u8bef\u7684\u3002\u8fd9\u4e2a\u6b65\u9aa4\u4e2d\u5b58\u5728\u4e0e\u524d\u4e00\u4e2a\u6b65\u9aa4\u76f8\u540c\u7684\u9519\u8bef\u3002<\/p>\n

      **\u9519\u8bef\u62a5\u544a**\uff1a
      \n– \u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b57\u4e0d\u5b58\u5728\u4e8e\u7ed9\u5b9a\u7684\u6570\u5b57\u96c6\u5408\u4e2d\u3002
      \n– \u64cd\u4f5c\u548c\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f\u9519\u8bef\u7684\u3002
      \n– \u5269\u4f59\u7684\u6570\u5b57\u6ca1\u6709\u6b63\u786e\u8bc6\u522b\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a
      \n– \u786e\u4fdd\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b57\u5b58\u5728\u4e8e\u7ed9\u5b9a\u7684\u6570\u5b57\u96c6\u5408\u4e2d\u3002
      \n– \u4f7f\u7528\u6b63\u786e\u7684\u64cd\u4f5c\uff0c\u4ee5\u5f97\u5230\u671f\u671b\u7684\u65b0\u6570\u5b57\u3002
      \n– \u51c6\u786e\u5730\u8bc6\u522b\u5269\u4f59\u7684\u6570\u5b57\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u62d2\u7edd\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u9519\u8bef\u7684\uff0c\u5e76\u4e0d\u6709\u52a9\u4e8e\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      ### \u63a8\u7406\u6b65\u9aa43
      \n\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u63a8\u7406\u6b65\u9aa41\u548c\u63a8\u7406\u6b65\u9aa42\u7684\u91cd\u590d\u3002\u8fd9\u4e2a\u6b65\u9aa4\u4e2d\u5b58\u5728\u4e0e\u524d\u51e0\u4e2a\u6b65\u9aa4\u76f8\u540c\u7684\u9519\u8bef\u3002<\/p>\n

      **\u9519\u8bef\u62a5\u544a**\uff1a
      \n– \u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b57\u4e0d\u5b58\u5728\u4e8e\u7ed9\u5b9a\u7684\u6570\u5b57\u96c6\u5408\u4e2d\u3002
      \n– \u64cd\u4f5c\u548c\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f\u9519\u8bef\u7684\u3002
      \n– \u5269\u4f59\u7684\u6570\u5b57\u6ca1\u6709\u6b63\u786e\u8bc6\u522b\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a
      \n– \u786e\u4fdd\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b57\u5b58\u5728\u4e8e\u7ed9\u5b9a\u7684\u6570\u5b57\u96c6\u5408\u4e2d\u3002
      \n– \u4f7f\u7528\u6b63\u786e\u7684\u64cd\u4f5c\uff0c\u4ee5\u5f97\u5230\u671f\u671b\u7684\u65b0\u6570\u5b57\u3002
      \n– \u51c6\u786e\u5730\u8bc6\u522b\u5269\u4f59\u7684\u6570\u5b57\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u62d2\u7edd\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u9519\u8bef\u7684\uff0c\u5e76\u4e0d\u6709\u52a9\u4e8e\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      **\u4fe1\u5fc3\u5f97\u5206**\uff1a0.9<\/p><\/blockquote>\n

      \u88688: \u542b\u6709\u88687\u8bc4\u8bba\u7684\u7b2c\u4e8c\u63a8\u7406\u94fe\u3002<\/p>\n

       <\/p>\n

      # \u601d\u7ef4\u8bc4\u4f30\u63d0\u793a<\/p>\n

      \u572824\u70b9\u6e38\u620f\u4e2d\uff0c\u4f60\u4f1a\u5f97\u5230\u56db\u4e2a\u6570\u5b57\uff0c\u76ee\u6807\u662f\u4f7f\u7528\u57fa\u672c\u7684\u7b97\u672f\u8fd0\u7b97\uff08+\u3001-\u3001*\u3001\/\uff09\u6765\u7ec4\u5408\u8fd9\u4e9b\u6570\u5b57\uff0c\u5f97\u523024\u8fd9\u4e2a\u7ed3\u679c\u3002\u6bcf\u4e2a\u6570\u5b57\u53ea\u80fd\u4f7f\u7528\u4e00\u6b21\uff0c\u53ef\u4ee5\u4f7f\u7528\u62ec\u53f7\u6765\u6539\u53d8\u8fd0\u7b97\u987a\u5e8f\u3002<\/p>\n

      \u6bcf\u4e2a\u6b65\u9aa4\u7684\u5206\u6790\u683c\u5f0f\uff1a\u6b65\u9aa4 , \u5f53\u524d\u96c6\u5408: , \u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57: , \u64cd\u4f5c: , \u8ba1\u7b97\u7684\u65b0\u6570\u5b57: , \u5269\u4f59\u7684\u6570\u5b57: , \u65b0\u96c6\u5408: \u3002<\/p>\n

      \u7ed9\u51fa\u7684\u56db\u4e2a\u6570\u5b57\u662f\uff1a3 5 6 8\u3002<\/p>\n

      \u8ba9\u6211\u4eec\u4e00\u6b65\u4e00\u6b65\u5730\u601d\u8003\u3002<\/p>\n

      \u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u5448\u73b0\u7684\u751f\u6210\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u9644\u6709\u5b83\u4eec\u7684\u8bc4\u4f30\u5f97\u5206\uff08\u5f97\u5206\u8d8a\u9ad8\u610f\u5473\u7740\u63a8\u7406\u6b65\u9aa4\u66f4\u6709\u53ef\u80fd\u5b8c\u6210\u4efb\u52a1\u3002\uff09\uff1a<\/p>\n

      —<\/p>\n

      ### \u6b65\u9aa41
      \n\u5f53\u524d\u96c6\u5408\uff1a3 5 6 8\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a3 8\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a11\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a5 6\uff0c\u65b0\u96c6\u5408\uff1a11 5 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.7<\/p>\n

      ### \u6b65\u9aa42
      \n\u5f53\u524d\u96c6\u5408\uff1a11 5 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 6\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a30\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a11\uff0c\u65b0\u96c6\u5408\uff1a30 11.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      ### \u6b65\u9aa43
      \n\u5f53\u524d\u96c6\u5408\uff1a30 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a30 11\uff0c\u64cd\u4f5c\uff1a-\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a19\uff0c\u5269\u4f59\u7684\u6570\u5b57\uff1a\uff0c\u65b0\u96c6\u5408\uff1a19\u3002<\/p>\n

      —<\/p>\n

      \u5bf9\u4e8e\u8fd9\u4e9b\u63a8\u7406\u6b65\u9aa4\u7684\u903b\u8f91\u3001\u6b63\u786e\u6027\u548c\u5bf9\u8fbe\u5230\u6700\u7ec8\u89e3\u51b3\u65b9\u6848\u7684\u8d21\u732e\uff0c\u4f60\u7684\u8bc4\u4f30\u5f97\u5206\u662f\u591a\u5c11\uff1f\u8bf7\u4ece[0.1, 0.3, 0.5, 0.7, 0.9, 1.0]\u4e2d\u9009\u62e9\u4e00\u4e2a\u503c\u4f5c\u4e3a\u5f97\u5206\uff0c\u5176\u4e2d\u66f4\u9ad8\u7684\u5f97\u5206\u610f\u5473\u7740\u66f4\u597d\u7684\u63a8\u7406\u6b65\u9aa4\u3002\u5f97\u5206\u5e94\u653e\u5728\u201c\u8bc4\u4f30\u5f97\u5206\uff1a\u201d\u4e4b\u540e\uff0c\u4ee5\u4fbf\u7528\u6237\u9605\u8bfb\u3002<\/p>\n

       <\/p>\n

      ## \u751f\u6210\u7684\u8bc4\u4f30\u5f97\u5206<\/p>\n

      \u8bc4\u4f30\u5f97\u5206\uff1a0.9\u3002<\/p><\/blockquote>\n

      \u88689: \u8ba1\u7b97\u6b65\u9aa42\uff08zi\uff09\u548c\u6b65\u9aa43\uff08zi\u22121\uff09\u4e4b\u95f4\u8fb9\u7f18\u6743\u91cd\u7684\u8ba1\u7b97\u3002<\/p>\n

       <\/p>\n

      # \u63a5\u4e0b\u6765\u601d\u7ef4\u751f\u6210\u7684\u63d0\u793a\u683c\u5f0f<\/p>\n

      \u572824\u70b9\u6e38\u620f\u4e2d\uff0c\u4f60\u4f1a\u5f97\u5230\u56db\u4e2a\u6570\u5b57\uff0c\u76ee\u6807\u662f\u4f7f\u7528\u57fa\u672c\u7684\u7b97\u672f\u8fd0\u7b97\uff08+\u3001-\u3001*\u3001\/\uff09\u6765\u7ec4\u5408\u8fd9\u4e9b\u6570\u5b57\uff0c\u5f97\u523024\u8fd9\u4e2a\u7ed3\u679c\u3002\u6bcf\u4e2a\u6570\u5b57\u53ea\u80fd\u4f7f\u7528\u4e00\u6b21\uff0c\u53ef\u4ee5\u4f7f\u7528\u62ec\u53f7\u6765\u6539\u53d8\u8fd0\u7b97\u987a\u5e8f\u3002<\/p>\n

      \u6bcf\u4e2a\u6b65\u9aa4\u7684\u5206\u6790\u683c\u5f0f\uff1a\u6b65\u9aa4 , \u5f53\u524d\u96c6\u5408: , \u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57: , \u64cd\u4f5c: , \u8ba1\u7b97\u7684\u65b0\u6570\u5b57: , \u5269\u4f59\u7684\u6570\u5b57: , \u65b0\u96c6\u5408: \u3002<\/p>\n

      \u7ed9\u51fa\u7684\u56db\u4e2a\u6570\u5b57\u662f\uff1a5, 6, 9, 4\u3002<\/p>\n

      \u8ba9\u6211\u4eec\u4e00\u6b65\u4e00\u6b65\u5730\u601d\u8003\u3002<\/p>\n

      \u56de\u987e\u5386\u53f2\u63a8\u7406\u7ecf\u9a8c\uff08\u5f53\u7ecf\u9a8c\u4e3a\u7a7a\u65f6\u8bf7\u5ffd\u7565\uff09\uff1a<\/p>\n

      ###########################################<\/p>\n

      \u6839\u636e\u7ecf\u9a8c\u4e2d\u7684\u5206\u6790\u548c\u7ed3\u8bba\uff0c\u907f\u514d\u901a\u8fc7\u9075\u5faa\u5efa\u8bae\u800c\u72af\u7c7b\u4f3c\u7684\u9519\u8bef\u3002<\/p>\n

      \u4ee5\u4e0b\u662f\u4e00\u7cfb\u5217\u6709\u5e8f\u7684\u63a8\u7406\u6b65\u9aa4\u5217\u8868\uff0c\u9644\u6709\u5b83\u4eec\u7684\u8bc4\u4f30\u5f97\u5206\uff08\u5f97\u5206\u8d8a\u9ad8\u610f\u5473\u7740\u63a8\u7406\u6b65\u9aa4\u66f4\u6709\u53ef\u80fd\u5b8c\u6210\u4efb\u52a1\u3002\uff09\uff1a<\/p>\n

      —<\/p>\n

      —<\/p>\n

      \u6839\u636e\u4e0a\u8ff0\u201c\u2014\u2014\u2014\u201d\u5185\u5217\u51fa\u7684\u63a8\u7406\u6b65\u9aa4\uff08\u5373\uff0c\u4e0d\u662f\u7ecf\u9a8c\u5757\u4e2d\u7684\u6b65\u9aa4\uff09\uff0c\u8bf7\u8fdb\u884c\u4e00\u6b65\u63a8\u7406\uff0c\u751f\u6210\u552f\u4e00\u7684\u4e00\u4e2a\u540e\u7eed\u53ef\u80fd\u7684\u63a8\u7406\u6b65\u9aa4\u3002<\/p>\n

       <\/p>\n

      # \u7ecf\u9a8c\u751f\u6210\u7684\u63d0\u793a\u683c\u5f0f<\/p>\n

      \u7ed9\u5b9a\u4efb\u52a1\uff1a\u572824\u70b9\u6e38\u620f\u4e2d\uff0c\u4f60\u4f1a\u5f97\u5230\u56db\u4e2a\u6570\u5b57\uff0c\u76ee\u6807\u662f\u4f7f\u7528\u57fa\u672c\u7684\u7b97\u672f\u8fd0\u7b97\uff08+\u3001-\u3001*\u3001\/\uff09\u6765\u7ec4\u5408\u8fd9\u4e9b\u6570\u5b57\uff0c\u5f97\u523024\u8fd9\u4e2a\u7ed3\u679c\u3002\u6bcf\u4e2a\u6570\u5b57\u53ea\u80fd\u4f7f\u7528\u4e00\u6b21\uff0c\u53ef\u4ee5\u4f7f\u7528\u62ec\u53f7\u6765\u6539\u53d8\u8fd0\u7b97\u987a\u5e8f\u3002<\/p>\n

      \u7ed9\u51fa\u7684\u56db\u4e2a\u6570\u5b57\u662f\uff1a4 5 10 11. \u8ba9\u6211\u4eec\u4e00\u6b65\u4e00\u6b65\u5730\u601d\u8003\u3002\u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u5448\u73b0\u7684\u5305\u542b\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a<\/p>\n

      —<\/p>\n

      —<\/p>\n

      \u8bf7\u901a\u8fc7\u63d0\u4f9b\u8be6\u7ec6\u7684\u8bc4\u8bba\u6765\u8bc4\u4f30\u8fd9\u4e2a\u63a8\u7406\u94fe\uff0c\u5185\u5bb9\u5305\u62ec\u4ee5\u4e0b\u65b9\u9762\uff1a1. \u8fd9\u4e2a\u63a8\u7406\u94fe\u80fd\u5426\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\uff1f\u4e3a\u4ec0\u4e48\uff1f\u5728\u201c\u5206\u6790\u62a5\u544a\uff1a\u201d\u4e0b\u5199\u4e0b\u5e26\u6709\u7ed3\u8bba\u7684\u5206\u6790\u62a5\u544a\u30022. \u5bf9\u4e8e\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u8be6\u7ec6\u5206\u6790\uff0c\u5224\u65ad\u5f53\u524d\u6b65\u9aa4\u662f\u5426\u662f\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u5bfc\uff0c\u4ee5\u53ca\u63a8\u7406\u6b65\u9aa4\u662f\u5426\u6709\u52a9\u4e8e\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u6709\u9519\u8bef\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u9519\u8bef\u62a5\u544a\u548c\u76f8\u5e94\u7684\u4fee\u6539\u5efa\u8bae\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u63a8\u8350\u6216\u62d2\u7edd\u7684\u63cf\u8ff0\u3002\u8bc4\u8bba\u5e94\u7b80\u6d01\uff0c\u907f\u514d\u5728\u4e0d\u540c\u6b65\u9aa4\u4e2d\u91cd\u590d\u76f8\u540c\u7684\u5206\u6790\uff0c\u5e76\u9075\u5faa\u4ee5\u4e0b\u683c\u5f0f\uff1a\u63a8\u7406\u6b65\u9aa4 \u00a1idx\u00bf. \u5206\u6790\u62a5\u544a\uff1a. \u5efa\u8bae\uff1a. \u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0\uff1a. 3. \u4f60\u5bf9\u8fd9\u4e9b\u8bc4\u4f30\u548c\u8bc4\u8bba\u7684\u4fe1\u5fc3\u5f97\u5206\u662f\u591a\u5c11\uff1f\u8bf7\u4ece[0.1, 0.3, 0.5, 0.7, 0.9, 1.0]\u4e2d\u9009\u62e9\u4e00\u4e2a\u503c\u3002\u5f97\u5206\u5e94\u653e\u5728\u201c\u4fe1\u5fc3\u5f97\u5206\uff1a\u201d\u4e4b\u540e\uff0c\u4ee5\u4fbf\u7528\u6237\u9605\u8bfb\u3002<\/p><\/blockquote>\n

      \u886810: “24\u70b9”\u6e38\u620f\u4e2d\u7528\u5230\u7684\u63d0\u793a\u683c\u5f0f\u3002<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e00\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c1\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n—————————————————————-
      \n**\u6b65\u9aa4 1**\uff0c\u5f53\u524d\u96c6\u5408\uff1a4 5 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 5\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a20\uff0c\u5269\u4f59\u6570\u5b57\uff1a10 11\uff0c\u65b0\u96c6\u5408\uff1a20 10 11.. \u8bc4\u4f30
      \n\u5f97\u5206\uff1a0.7<\/p>\n

      **\u6b65\u9aa4 2**\uff0c\u5f53\u524d\u96c6\u5408\uff1a20 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a10 11\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a110\uff0c\u5269\u4f59\u6570\u5b57\uff1a20\uff0c\u65b0\u96c6\u5408\uff1a110 20.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.7<\/p>\n

      **\u6b65\u9aa4 3**\uff0c\u5f53\u524d\u96c6\u5408\uff1a110 20\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a110 20\uff0c\u64cd\u4f5c\uff1a\/\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a5.5\uff0c\u5269\u4f59\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a5.5.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      —————————————————————-
      \n**\u5206\u6790\u62a5\u544a**\uff1a
      \n\u8fd9\u6761\u63a8\u7406\u94fe\u53ef\u4ee5\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u6700\u7ec8\u7ed3\u679c\u662f5.5\uff0c\u6570\u5b66\u4e0a\u7b49\u4e8e24\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u7ed9\u5b9a\u6570\u5b57\u7684\u903b\u8f91\u63a8\u7406\u3002\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e86\u6570\u5b574\u548c5\uff0c\u5e94\u7528\u64cd\u4f5c*\u5f97\u5230\u65b0\u6570\u5b5720\u3002\u5269\u4f59\u6570\u5b57\u662f10\u548c11\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u5229\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e86\u6570\u5b5710\u548c11\uff0c\u5e94\u7528\u64cd\u4f5c*\u5f97\u5230\u65b0\u6570\u5b57110\u3002\u5269\u4f59\u6570\u5b57\u662f20\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u5229\uff0c\u56e0\u4e3a\u5b83\u8fdb\u4e00\u6b65\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e86\u6570\u5b57110\u548c20\uff0c\u5e94\u7528\u64cd\u4f5c\/\u5f97\u5230\u65b0\u6570\u5b575.5\u3002\u6ca1\u6709\u5269\u4f59\u6570\u5b57\uff0c\u8fd9\u610f\u5473\u7740\u63a8\u7406\u94fe\u5df2\u7ecf\u8fbe\u5230\u7ed3\u679c\u3002\u6700\u7ec8\u7ed3\u679c5.5\u6570\u5b66\u4e0a\u7b49\u4e8e24\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u5728\u8fd9\u6761\u63a8\u7406\u94fe\u4e2d\u6ca1\u6709\u53d1\u73b0\u9519\u8bef\u3002\u6b65\u9aa4\u88ab\u6b63\u786e\u6267\u884c\uff0c\u5e76\u5f15\u5bfc\u81f3\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u7531\u4e8e\u8fd9\u6761\u63a8\u7406\u94fe\u6210\u529f\u8fbe\u5230\u76ee\u6807\u5e76\u63d0\u4f9b\u4e86\u6b63\u786e\u89e3\u51b3\u65b9\u6848\uff0c\u56e0\u6b64\u63a8\u8350\u8fd9\u6761\u63a8\u7406\u94fe\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.9<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e8c\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c2\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n—————————————————————-
      \n**\u6b65\u9aa4 1**\uff0c\u5f53\u524d\u96c6\u5408\uff1a4 5 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 10\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a40\uff0c\u5269\u4f59\u6570\u5b57\uff1a5 11\uff0c\u65b0\u96c6\u5408\uff1a40 5 11.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 2**\uff0c\u5f53\u524d\u96c6\u5408\uff1a40 5 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 11\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a55\uff0c\u5269\u4f59\u6570\u5b57\uff1a40\uff0c\u65b0\u96c6\u5408\uff1a55 40.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 3**\uff0c\u5f53\u524d\u96c6\u5408\uff1a40 5 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 10\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a40\uff0c\u5269\u4f59\u6570\u5b57\uff1a5 11\uff0c\u65b0\u96c6\u5408\uff1a40 5 11.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      —————————————————————-
      \n**\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u65e0\u6cd5\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u63a8\u7406\u6b65\u9aa4\u91cd\u590d\uff0c\u5e76\u672a\u5f15\u5bfc\u81f3\u671f\u671b\u7ed3\u679c24\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u7ed9\u5b9a\u6570\u5b57\u7684\u903b\u8f91\u63a8\u7406\uff0c\u9075\u5faa\u6e38\u620f\u89c4\u5219\u3002\u5c064\u548c10\u76f8\u4e58\u5f97\u523040\uff0c\u5269\u4f59\u6570\u5b57\u662f5\u548c11\u3002\u7136\u800c\uff0c\u8fd9\u4e00\u6b65\u5e76\u672a\u6709\u52a9\u4e8e\u8fbe\u523024\u7684\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u8fd9\u4e00\u6b65\u662f\u6b65\u9aa41\u7684\u91cd\u590d\u3002\u5b83\u9009\u62e9\u4e86\u5269\u4f59\u6570\u5b575\u548c11\u5e76\u5c06\u5b83\u4eec\u76f8\u4e58\u5f97\u523055\u3002\u65b0\u96c6\u5408\u53d8\u4e3a55\u548c40\u3002\u540c\u6837\uff0c\u8fd9\u4e00\u6b65\u5e76\u672a\u5f15\u5bfc\u81f3\u76ee\u680724\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u8fd9\u4e00\u6b65\u662f\u6b65\u9aa41\u7684\u91cd\u590d\u3002\u5b83\u6ca1\u6709\u63d0\u4f9b\u4efb\u4f55\u65b0\u4fe1\u606f\u6216\u5411\u76ee\u6807\u8fdb\u5c55\u3002\u7ed3\u679c\u4e0e\u6b65\u9aa41\u76f8\u540c\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u9700\u8981\u4fee\u8ba2\u548c\u8c03\u6574\u63a8\u7406\u6b65\u9aa4\uff0c\u4ee5\u627e\u5230\u4e0d\u540c\u7684\u65b9\u6cd5\u8fbe\u5230\u76ee\u680724\u3002\u91cd\u590d\u7684\u6b65\u9aa4\u4e0d\u4f1a\u5e2e\u52a9\u8fbe\u5230\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u7531\u4e8e\u91cd\u590d\u6b65\u9aa4\u548c\u7f3a\u4e4f\u5411\u76ee\u6807\u8fdb\u5c55\uff0c\u8fd9\u6761\u63a8\u7406\u94fe\u88ab\u62d2\u7edd\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.7<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e09\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c3\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n—————————————————————-
      \n**\u6b65\u9aa4 1**\uff0c\u5f53\u524d\u96c6\u5408\uff1a4 5 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 5\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a9\uff0c\u5269\u4f59\u6570\u5b57\uff1a10 11\uff0c\u65b0\u96c6\u5408\uff1a9 10 11.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.7<\/p>\n

      **\u6b65\u9aa4 2**\uff0c\u5f53\u524d\u96c6\u5408\uff1a9 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a9 10\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a90\uff0c\u5269\u4f59\u6570\u5b57\uff1a11\uff0c\u65b0\u96c6\u5408\uff1a90 11.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.7<\/p>\n

      **\u6b65\u9aa4 3**\uff0c\u5f53\u524d\u96c6\u5408\uff1a90 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a90 11\uff0c\u64cd\u4f5c\uff1a\/\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a8.181818181818182\uff0c\u5269\u4f59\u6570\u5b57\uff1a\uff0c\u65b0\u96c6\u5408\uff1a8.181818181818182.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.7<\/p>\n

      —————————————————————-
      \n**\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u65e0\u6cd5\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u7b2c3\u6b65\u83b7\u5f97\u7684\u6700\u7ec8\u7ed3\u679c\u662f8.181818181818182\uff0c\u8fd9\u4e0d\u7b49\u4e8e\u76ee\u6807\u6570\u5b5724\u3002\u56e0\u6b64\uff0c\u8fd9\u6761\u63a8\u7406\u94fe\u662f\u9519\u8bef\u7684\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u4ece\u5f53\u524d\u96c6\u5408\uff084 5 10 11\uff09\u4e2d\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b574\u548c5\u5e76\u76f8\u52a0\u5f97\u5230\u65b0\u6570\u5b579\u3002\u5269\u4f59\u6570\u5b57\u662f10\u548c11\uff0c\u65b0\u96c6\u5408\u53d8\u4e3a9 10 11\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u5229\uff0c\u56e0\u4e3a\u5b83\u7ed3\u5408\u4e86\u4e24\u4e2a\u6570\u5b57\u5e76\u51cf\u5c11\u4e86\u96c6\u5408\u7684\u5927\u5c0f\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u63a8\u8350\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u4ece\u5f53\u524d\u96c6\u5408\uff089 10 11\uff09\u4e2d\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b579\u548c10\u5e76\u76f8\u4e58\u5f97\u5230\u65b0\u6570\u5b5790\u3002\u5269\u4f59\u6570\u5b57\u662f11\uff0c\u65b0\u96c6\u5408\u53d8\u4e3a90 11\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u5229\uff0c\u56e0\u4e3a\u5b83\u7ed3\u5408\u4e86\u4e24\u4e2a\u6570\u5b57\u5e76\u51cf\u5c11\u4e86\u96c6\u5408\u7684\u5927\u5c0f\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u63a8\u8350\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u4ece\u5f53\u524d\u96c6\u5408\uff0890 11\uff09\u4e2d\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b5790\u548c11\u5e76\u76f8\u9664\u5f97\u5230\u65b0\u6570\u5b578.181818181818182\u3002\u7531\u4e8e\u6ca1\u6709\u5269\u4f59\u6570\u5b57\uff0c\u8fd9\u662f\u6700\u7ec8\u7ed3\u679c\u3002\u7136\u800c\uff0c\u83b7\u5f97\u7684\u7ed3\u679c\u4e0d\u7b49\u4e8e\u76ee\u6807\u6570\u5b5724\u3002<\/p>\n

      **\u9519\u8bef\u62a5\u544a**\uff1a\u63a8\u7406\u6b65\u9aa4\u662f\u9519\u8bef\u7684\uff0c\u56e0\u4e3a\u83b7\u5f97\u7684\u7ed3\u679c\u4e0d\u7b49\u4e8e\u76ee\u6807\u6570\u5b57\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u5c1d\u8bd5\u4e0d\u540c\u7684\u64cd\u4f5c\u6216\u6570\u5b57\u7ec4\u5408\uff0c\u4ee5\u83b7\u5f97\u66f4\u63a5\u8fd1\u76ee\u6807\u6570\u5b57\u7684\u7ed3\u679c\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.7<\/p>\n

       <\/p>\n

      \u63a5\u4e0b\u6765\u5c06\u5728\u886812\u4e2d\u7ee7\u7eed…<\/p><\/blockquote>\n

      \u886811: BoT\u5bf9\u4e8e\u201c4 5 10 11\u201d\u8fdb\u884c\u7684\u6210\u529f\u63a8\u7406\u8fc7\u7a0b\u3002<\/p>\n

       <\/p>\n

      ### \u7b2c\u56db\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c4\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n—————————————————————-
      \n**\u6b65\u9aa4 1**\uff0c\u5f53\u524d\u96c6\u5408\uff1a4 5 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 10\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a40\uff0c\u5269\u4f59\u6570\u5b57\uff1a5 11\uff0c\u65b0\u96c6\u5408\uff1a40 5 11.. \u8bc4\u4f30
      \n\u5f97\u5206\uff1a0.7<\/p>\n

      **\u6b65\u9aa4 2**\uff0c\u5f53\u524d\u96c6\u5408\uff1a40 5 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a40 5\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a45\uff0c\u5269\u4f59\u6570\u5b57\uff1a11\uff0c\u65b0\u96c6\u5408\uff1a45 11.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.7<\/p>\n

      **\u6b65\u9aa4 3**\uff0c\u5f53\u524d\u96c6\u5408\uff1a45 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a45 11\uff0c\u64cd\u4f5c\uff1a-\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a34\uff0c\u5269\u4f59\u6570\u5b57\uff1a\uff0c\u65b0\u96c6\u5408\uff1a34.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      —————————————————————-
      \n**\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u53ef\u4ee5\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u6700\u540e\u4e00\u6b65\u8ba1\u7b97\u51fa\u7684\u6570\u5b57\u662f34\uff0c\u8fd9\u662f\u4f7f\u7528\u7ed9\u5b9a\u7684\u56db\u4e2a\u6570\u5b57\u548c\u6307\u5b9a\u7684\u7b97\u672f\u8fd0\u7b97\u5f97\u5230\u671f\u671b\u7ed3\u679c24\u7684\u6b63\u786e\u7ed3\u679c\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u96c6\u5408\u662f4 5 10 11\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b574\u548c10\u3002\u9009\u62e9\u7684\u64cd\u4f5c\u662f\u4e58\u6cd5(*)\uff0c\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f40\u3002\u5269\u4f59\u6570\u5b57\u662f5\u548c11\u3002\u65b0\u96c6\u5408\u53d8\u4e3a40 5 11\u3002\u903b\u8f91\u63a8\u7406\uff1a\u6240\u9009\u6570\u5b57\u662f\u5f53\u524d\u96c6\u5408\u7684\u6709\u6548\u5143\u7d20\uff0c\u64cd\u4f5c\u662f\u6709\u6548\u7684\u7b97\u672f\u8fd0\u7b97\u3002\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff1a\u662f\u7684\uff0c\u8fd9\u4e00\u6b65\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\uff0c\u5e76\u8ba1\u7b97\u51fa\u53ef\u4ee5\u5728\u540e\u7eed\u6b65\u9aa4\u4e2d\u4f7f\u7528\u7684\u65b0\u6570\u5b57\u3002\u5efa\u8bae\uff1a\u63a5\u53d7\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u5f53\u524d\u96c6\u5408\u662f40 5 11\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b5740\u548c5\u3002\u9009\u62e9\u7684\u64cd\u4f5c\u662f\u52a0\u6cd5(+)\uff0c\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f45\u3002\u5269\u4f59\u6570\u5b57\u662f11\u3002\u65b0\u96c6\u5408\u53d8\u4e3a45 11\u3002\u903b\u8f91\u63a8\u7406\uff1a\u6240\u9009\u6570\u5b57\u662f\u5f53\u524d\u96c6\u5408\u7684\u6709\u6548\u5143\u7d20\uff0c\u64cd\u4f5c\u662f\u6709\u6548\u7684\u7b97\u672f\u8fd0\u7b97\u3002\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff1a\u662f\u7684\uff0c\u8fd9\u4e00\u6b65\u8fdb\u4e00\u6b65\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\uff0c\u5e76\u8ba1\u7b97\u51fa\u53ef\u4ee5\u5728\u540e\u7eed\u6b65\u9aa4\u4e2d\u4f7f\u7528\u7684\u65b0\u6570\u5b57\u3002\u5efa\u8bae\uff1a\u63a5\u53d7\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u5f53\u524d\u96c6\u5408\u662f45 11\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b5745\u548c11\u3002\u9009\u62e9\u7684\u64cd\u4f5c\u662f\u51cf\u6cd5(-)\uff0c\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f34\u3002\u6ca1\u6709\u5269\u4f59\u6570\u5b57\u3002\u65b0\u96c6\u5408\u53d8\u4e3a34\u3002\u903b\u8f91\u63a8\u7406\uff1a\u6240\u9009\u6570\u5b57\u662f\u5f53\u524d\u96c6\u5408\u7684\u6709\u6548\u5143\u7d20\uff0c\u64cd\u4f5c\u662f\u6709\u6548\u7684\u7b97\u672f\u8fd0\u7b97\u3002\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff1a\u662f\u7684\uff0c\u8fd9\u4e00\u6b65\u8ba1\u7b97\u51fa\u6700\u7ec8\u7ed3\u679c34\uff0c\u5c3d\u7ba1\u5b83\u4e0d\u7b49\u4e8e\u76ee\u680724\u3002\u5efa\u8bae\uff1a\u63a5\u53d7\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.9<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e94\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c5\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n—————————————————————-
      \n**\u6b65\u9aa4 1**\uff0c\u5f53\u524d\u96c6\u5408\uff1a4 5 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 10\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a40\uff0c\u5269\u4f59\u6570\u5b57\uff1a5 11\uff0c\u65b0\u96c6\u5408\uff1a40 5 11.. \u8bc4\u4f30
      \n\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 2**\uff0c\u5f53\u524d\u96c6\u5408\uff1a40 5 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 11\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a55\uff0c\u5269\u4f59\u6570\u5b57\uff1a40\uff0c\u65b0\u96c6\u5408\uff1a55 40.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 3**\uff0c\u5f53\u524d\u96c6\u5408\uff1a55 40\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a55 40\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a95\uff0c\u5269\u4f59\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a95.. \u8bc4\u4f30 \u5f97\u5206\uff1a1.0<\/p>\n

      —————————————————————-
      \n**\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u53ef\u4ee5\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u7136\u800c\uff0c\u7b2c3\u6b65\u4e2d\u83b7\u5f97\u7684\u6700\u7ec8\u7ed3\u679c\u662f95\uff0c\u6570\u5b66\u4e0a\u4e0d\u7b49\u4e8e24\u3002\u56e0\u6b64\uff0c\u8fd9\u6761\u63a8\u7406\u94fe\u6ca1\u6709\u63d0\u4f9b\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u6b65\u9aa4\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4e86\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\u5e76\u6267\u884c*\u64cd\u4f5c\u7684\u89c4\u5219\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u751f\u6210\u4e86\u4e00\u4e2a\u65b0\u7684\u6570\u5b57\u5e76\u4e3a\u4e0b\u4e00\u6b65\u66f4\u65b0\u4e86\u96c6\u5408\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u5f53\u524d\u6b65\u9aa4\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4e86\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\u5e76\u6267\u884c*\u64cd\u4f5c\u7684\u89c4\u5219\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u751f\u6210\u4e86\u4e00\u4e2a\u65b0\u7684\u6570\u5b57\u5e76\u4e3a\u4e0b\u4e00\u6b65\u66f4\u65b0\u4e86\u96c6\u5408\u3002\u7136\u800c\uff0c\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5e76\u6ca1\u6709\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u6700\u7ec8\u83b7\u5f97\u7684\u7ed3\u679c95\uff0c\u6570\u5b66\u4e0a\u4e0d\u7b49\u4e8e24\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u5f53\u524d\u6b65\u9aa4\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4e86\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\u5e76\u6267\u884c+\u64cd\u4f5c\u7684\u89c4\u5219\u3002\u7136\u800c\uff0c\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5e76\u6ca1\u6709\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u6700\u7ec8\u83b7\u5f97\u7684\u7ed3\u679c95\uff0c\u6570\u5b66\u4e0a\u4e0d\u7b49\u4e8e24\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u5728\u6b65\u9aa42\u4e2d\uff0c\u5e94\u8be5\u9009\u62e9\u4e0d\u540c\u7684\u64cd\u4f5c\u6765\u83b7\u5f97\u65b0\u7684\u6570\u5b57\u3002\u5728\u6b65\u9aa43\u4e2d\uff0c\u5e94\u8be5\u9009\u62e9\u4e0d\u540c\u7684\u64cd\u4f5c\u6765\u83b7\u5f97\u65b0\u7684\u6570\u5b57\uff0c\u4ee5\u4fbf\u4e0e\u5269\u4f59\u7684\u6570\u5b57\u7ed3\u5408\uff0c\u8fbe\u5230\u76ee\u680724\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u6b65\u9aa4 1\uff1a\u63a8\u8350 \u6b65\u9aa4 2\uff1a\u62d2\u7edd \u6b65\u9aa4 3\uff1a\u62d2\u7edd<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.9<\/p>\n

       <\/p>\n

      ### \u7b2c\u516d\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c6\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n—————————————————————-
      \n**\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u96c6\u5408\uff1a4 5 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 10\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a40\uff0c\u5269\u4f59\u6570\u5b57\uff1a5 11\uff0c\u65b0\u96c6\u5408\uff1a40 5 11.. \u8bc4\u4f30
      \n\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 2**\uff1a\u5f53\u524d\u96c6\u5408\uff1a40 5 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 11\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a16\uff0c\u5269\u4f59\u6570\u5b57\uff1a40\uff0c\u65b0\u96c6\u5408\uff1a16 40.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 3**\uff1a\u5f53\u524d\u96c6\u5408\uff1a16 40\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a16 40\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a56\uff0c\u5269\u4f59\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a56. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      —————————————————————-
      \n**\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u53ef\u4ee5\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u7136\u800c\uff0c\u6700\u540e\u4e00\u6b65\u4e2d\u83b7\u5f97\u7684\u6700\u7ec8\u7ed3\u679c\u662f56\uff0c\u8fd9\u4e0d\u7b49\u4e8e\u76ee\u6807\u6570\u5b5724\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u7ed9\u5b9a\u6570\u5b57\u548c\u6e38\u620f\u76ee\u6807\u7684\u903b\u8f91\u63a8\u7406\u3002\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b574\u548c10\u76f8\u4e58\u5f97\u5230\u65b0\u6570\u5b5740\u3002\u5269\u4f59\u6570\u5b575\u548c11\u6b63\u786e\u5730\u5305\u542b\u5728\u65b0\u96c6\u5408\u4e2d\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5e76\u671d\u7740\u76ee\u6807\u524d\u8fdb\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b575\u548c11\u76f8\u52a0\u5f97\u5230\u65b0\u6570\u5b5716\u3002\u5269\u4f59\u6570\u5b5740\u6b63\u786e\u5730\u5305\u542b\u5728\u65b0\u96c6\u5408\u4e2d\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5e76\u671d\u7740\u76ee\u6807\u524d\u8fdb\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b5716\u548c40\u76f8\u52a0\u5f97\u5230\u65b0\u6570\u5b5756\u3002\u7531\u4e8e\u6ca1\u6709\u5269\u4f59\u6570\u5b57\uff0c\u63a8\u7406\u94fe\u5728\u8fd9\u91cc\u7ed3\u675f\u3002\u7136\u800c\uff0c\u83b7\u5f97\u7684\u7ed3\u679c56\u4e0e\u76ee\u6807\u6570\u5b5724\u4e0d\u5339\u914d\u3002\u56e0\u6b64\uff0c\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u9519\u8bef\u7684\u3002<\/p>\n

      **\u9519\u8bef\u62a5\u544a**\uff1a\u6b65\u9aa43\u4e2d\u7684\u63a8\u7406\u6b65\u9aa4\u662f\u9519\u8bef\u7684\uff0c\u56e0\u4e3a\u83b7\u5f97\u7684\u7ed3\u679c56\u4e0e\u76ee\u6807\u6570\u5b5724\u4e0d\u5339\u914d\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u4e3a\u4e86\u7ea0\u6b63\u6b65\u9aa43\u4e2d\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u5e94\u8be5\u9009\u62e9\u4e0d\u540c\u7684\u64cd\u4f5c\u6216\u6570\u5b57\u7ec4\u5408\u6765\u83b7\u5f97\u66f4\u63a5\u8fd1\u76ee\u680724\u7684\u65b0\u6570\u5b57\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u6b65\u9aa4 1\uff1a\u63a8\u8350 \u6b65\u9aa4 2\uff1a\u63a8\u8350 \u6b65\u9aa4 3\uff1a\u62d2\u7edd<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.9<\/p>\n

       <\/p>\n

      \u63a5\u4e0b\u6765\u5c06\u5728\u886813\u4e2d\u7ee7\u7eed…<\/p><\/blockquote>\n

      \u886812: BoT\u5bf9\u4e8e\u201c4 5 10 11\u201d\u8fdb\u884c\u7684\u6210\u529f\u63a8\u7406\u8fc7\u7a0b\u3002<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e03\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c7\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n—————————————————————-
      \n**\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u96c6\u5408\uff1a4 5 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 10\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a40\uff0c\u5269\u4f59\u6570\u5b57\uff1a5 11\uff0c\u65b0\u96c6\u5408\uff1a40 5 11.. \u8bc4\u4f30
      \n\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 2**\uff1a\u5f53\u524d\u96c6\u5408\uff1a40 5 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 11\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a16\uff0c\u5269\u4f59\u6570\u5b57\uff1a40\uff0c\u65b0\u96c6\u5408\uff1a16 40.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 3**\uff1a\u5f53\u524d\u96c6\u5408\uff1a16 40\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a16 40\uff0c\u64cd\u4f5c\uff1a-\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a24\uff0c\u5269\u4f59\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a24. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      —————————————————————-
      \n**\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u53ef\u4ee5\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u6700\u540e\u4e00\u6b65\u83b7\u5f97\u7684\u7ed3\u679c\u662f24\uff0c\u6570\u5b66\u4e0a\u7b49\u4e8e\u76ee\u6807\u6570\u5b5724\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u7ed9\u5b9a\u6570\u5b57\u548c\u6e38\u620f\u76ee\u6807\u7684\u903b\u8f91\u63a8\u7406\u3002\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b574\u548c10\u76f8\u4e58\u5f97\u5230\u65b0\u6570\u5b5740\u3002\u5269\u4f59\u6570\u5b575\u548c11\u88ab\u6b63\u786e\u5730\u5305\u542b\u5728\u65b0\u96c6\u5408\u4e2d\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5e76\u671d\u7740\u76ee\u6807\u524d\u8fdb\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b575\u548c11\u76f8\u52a0\u5f97\u5230\u65b0\u6570\u5b5716\u3002\u5269\u4f59\u6570\u5b5740\u88ab\u6b63\u786e\u5730\u5305\u542b\u5728\u65b0\u96c6\u5408\u4e2d\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5e76\u671d\u7740\u76ee\u6807\u524d\u8fdb\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b5716\u548c40\u76f8\u51cf\u5f97\u5230\u65b0\u6570\u5b5724\u3002\u7531\u4e8e\u6ca1\u6709\u5269\u4f59\u6570\u5b57\uff0c\u63a8\u7406\u94fe\u5728\u8fd9\u91cc\u7ed3\u675f\u3002\u6700\u7ec8\u7ed3\u679c24\u6570\u5b66\u4e0a\u7b49\u4e8e24\u3002<\/p>\n

      \u8fd9\u6761\u63a8\u7406\u94fe\u4e2d\u6ca1\u6709\u53d1\u73b0\u9519\u8bef\u3002\u6b65\u9aa4\u88ab\u6b63\u786e\u6267\u884c\u5e76\u5f15\u5bfc\u81f3\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u7531\u4e8e\u8fd9\u6761\u63a8\u7406\u94fe\u6210\u529f\u8fbe\u5230\u76ee\u6807\u5e76\u63d0\u4f9b\u4e86\u6b63\u786e\u89e3\u51b3\u65b9\u6848\uff0c\u56e0\u6b64\u63a8\u8350\u8fd9\u6761\u63a8\u7406\u94fe\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.9<\/p>\n

       <\/p>\n

      ### \u7b2c\u516b\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c8\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n—————————————————————-
      \n**\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u96c6\u5408\uff1a4 5 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 10\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a40\uff0c\u5269\u4f59\u6570\u5b57\uff1a5 11\uff0c\u65b0\u96c6\u5408\uff1a40 5 11.. \u8bc4\u4f30
      \n\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 2**\uff1a\u5f53\u524d\u96c6\u5408\uff1a40 5 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 11\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a16\uff0c\u5269\u4f59\u6570\u5b57\uff1a40\uff0c\u65b0\u96c6\u5408\uff1a16 40.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 3**\uff1a\u5f53\u524d\u96c6\u5408\uff1a16 40\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a16 40\uff0c\u64cd\u4f5c\uff1a-\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a24\uff0c\u5269\u4f59\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a24. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      —————————————————————-
      \n**\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u53ef\u4ee5\u6210\u529f\u5b8c\u6210\u4efb\u52a1\u5e76\u6b63\u786e\u8fbe\u5230\u76ee\u6807\u3002\u6700\u7ec8\u7ed3\u679c24\u6570\u5b66\u4e0a\u6b63\u786e\u4e14\u7b49\u4e8e24\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u5bf9\u7ed9\u5b9a\u4efb\u52a1\u89c4\u5219\u7684\u903b\u8f91\u63a8\u7406\u3002\u5b83\u9075\u5faa\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff084\u548c10\uff09\u5e76\u6267\u884c\u4e58\u6cd5\u64cd\u4f5c\u4ee5\u83b7\u5f97\u65b0\u6570\u5b57\uff0840\uff09\u7684\u89c4\u5219\u3002\u5269\u4f59\u6570\u5b57\uff085\u548c11\uff09\u88ab\u6b63\u786e\u66f4\u65b0\u5230\u65b0\u96c6\u5408\uff0840 5 11\uff09\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u5b83\u9075\u5faa\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff085\u548c11\uff09\u5e76\u6267\u884c\u52a0\u6cd5\u64cd\u4f5c\u4ee5\u83b7\u5f97\u65b0\u6570\u5b57\uff0816\uff09\u7684\u89c4\u5219\u3002\u5269\u4f59\u6570\u5b57\uff0840\uff09\u88ab\u6b63\u786e\u66f4\u65b0\u5230\u65b0\u96c6\u5408\uff0816 40\uff09\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\u3002\u5b83\u9075\u5faa\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff0816\u548c40\uff09\u5e76\u6267\u884c\u51cf\u6cd5\u64cd\u4f5c\u4ee5\u83b7\u5f97\u65b0\u6570\u5b57\uff0824\uff09\u7684\u89c4\u5219\u3002\u7531\u4e8e\u6ca1\u6709\u5269\u4f59\u6570\u5b57\uff0c\u65b0\u96c6\u5408\u4e3a\u7a7a\u3002\u6700\u7ec8\u7ed3\u679c24\u6570\u5b66\u4e0a\u6b63\u786e\u4e14\u7b49\u4e8e24\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u4e2d\u6ca1\u6709\u53d1\u73b0\u9519\u8bef\u3002\u6b65\u9aa4\u6839\u636e\u7ed9\u5b9a\u4efb\u52a1\u89c4\u5219\u88ab\u6b63\u786e\u6267\u884c\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u4e2d\u7684\u6240\u6709\u63a8\u7406\u6b65\u9aa4\u90fd\u88ab\u63a8\u8350\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u6b63\u786e\u7684\u5e76\u6709\u52a9\u4e8e\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.9<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e5d\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c9\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n—————————————————————-
      \n**\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u96c6\u5408\uff1a4 5 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 10\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a40\uff0c\u5269\u4f59\u6570\u5b57\uff1a5 11\uff0c\u65b0\u96c6\u5408\uff1a40 5 11.. \u8bc4\u4f30
      \n\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 2**\uff1a\u5f53\u524d\u96c6\u5408\uff1a40 5 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 11\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a16\uff0c\u5269\u4f59\u6570\u5b57\uff1a40\uff0c\u65b0\u96c6\u5408\uff1a16 40.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 3**\uff1a\u5f53\u524d\u96c6\u5408\uff1a16 40\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a16 40\uff0c\u64cd\u4f5c\uff1a-\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a24\uff0c\u5269\u4f59\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a24. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      —————————————————————-
      \n**\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u53ef\u4ee5\u6210\u529f\u5b8c\u6210\u4efb\u52a1\u5e76\u6b63\u786e\u8fbe\u5230\u76ee\u6807\u3002\u6700\u7ec8\u7ed3\u679c24\u6570\u5b66\u4e0a\u6b63\u786e\u4e14\u7b49\u4e8e24\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4efb\u52a1\u89c4\u5219\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff084\u548c10\uff09\u5e76\u6267\u884c*\u64cd\u4f5c\u4ee5\u83b7\u5f97\u65b0\u6570\u5b57\uff0840\uff09\u3002\u5269\u4f59\u6570\u5b57\uff085\u548c11\uff09\u88ab\u6b63\u786e\u66f4\u65b0\uff0c\u65b0\u96c6\u5408\uff0840 5 11\uff09\u5f62\u6210\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4efb\u52a1\u89c4\u5219\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff085\u548c11\uff09\u5e76\u6267\u884c+\u64cd\u4f5c\u4ee5\u83b7\u5f97\u65b0\u6570\u5b57\uff0816\uff09\u3002\u5269\u4f59\u6570\u5b57\uff0840\uff09\u88ab\u6b63\u786e\u66f4\u65b0\uff0c\u65b0\u96c6\u5408\uff0816 40\uff09\u5f62\u6210\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u8fdb\u4e00\u6b65\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4efb\u52a1\u89c4\u5219\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff0816\u548c40\uff09\u5e76\u6267\u884c-\u64cd\u4f5c\u4ee5\u83b7\u5f97\u65b0\u6570\u5b57\uff0824\uff09\u3002\u7531\u4e8e\u6ca1\u6709\u5269\u4f59\u6570\u5b57\uff0c\u65b0\u96c6\u5408\u53ea\u5305\u542b\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\uff0824\uff09\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u8fbe\u5230\u4e86\u6700\u7ec8\u7ed3\u679c\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u63a8\u7406\u6b65\u9aa4\u4e2d\u6ca1\u6709\u53d1\u73b0\u9519\u8bef\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u6240\u6709\u63a8\u7406\u6b65\u9aa4\u90fd\u88ab\u63a8\u8350\uff0c\u56e0\u4e3a\u5b83\u4eec\u9075\u5faa\u4efb\u52a1\u89c4\u5219\u5e76\u6709\u52a9\u4e8e\u8fbe\u5230\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a1.0<\/p>\n

       <\/p>\n

      ### \u7b2c\u5341\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c10\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n—————————————————————-
      \n**\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u96c6\u5408\uff1a4 5 10 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a4 10\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a40\uff0c\u5269\u4f59\u6570\u5b57\uff1a5 11\uff0c\u65b0\u96c6\u5408\uff1a40 5 11.. \u8bc4\u4f30
      \n\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 2**\uff1a\u5f53\u524d\u96c6\u5408\uff1a40 5 11\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 11\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a16\uff0c\u5269\u4f59\u6570\u5b57\uff1a40\uff0c\u65b0\u96c6\u5408\uff1a16 40.. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 3**\uff1a\u5f53\u524d\u96c6\u5408\uff1a16 40\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a16 40\uff0c\u64cd\u4f5c\uff1a-\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a24\uff0c\u5269\u4f59\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a24. \u8bc4\u4f30 \u5f97\u5206\uff1a0.9<\/p>\n

      —————————————————————-
      \n**\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u53ef\u4ee5\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u63a8\u7406\u94fe\u7684\u6700\u7ec8\u7ed3\u679c\u662f24\uff0c\u6570\u5b66\u4e0a\u6b63\u786e\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u7ed9\u5b9a\u4efb\u52a1\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\u5e76\u6267\u884c\u64cd\u4f5c\u4ee5\u83b7\u5f97\u65b0\u6570\u5b57\u7684\u89c4\u5219\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9009\u62e9\u4e864\u548c10\uff0c\u64cd\u4f5c\u662f\u4e58\u6cd5(*)\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f40\uff0c\u5269\u4f59\u6570\u5b57\u662f5\u548c11\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5e76\u4ea7\u751f\u4e86\u4e00\u4e2a\u65b0\u6570\u5b57\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\u5e76\u6267\u884c\u64cd\u4f5c\u4ee5\u83b7\u5f97\u65b0\u6570\u5b57\u7684\u89c4\u5219\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9009\u62e9\u4e865\u548c11\uff0c\u64cd\u4f5c\u662f\u52a0\u6cd5(+)\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f16\uff0c\u5269\u4f59\u6570\u5b57\u662f40\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u8fdb\u4e00\u6b65\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5e76\u4ea7\u751f\u4e86\u4e00\u4e2a\u65b0\u6570\u5b57\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u8fd9\u4e00\u6b65\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\u5e76\u6267\u884c\u64cd\u4f5c\u4ee5\u83b7\u5f97\u65b0\u6570\u5b57\u7684\u89c4\u5219\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9009\u62e9\u4e8616\u548c40\uff0c\u64cd\u4f5c\u662f\u51cf\u6cd5(-)\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f24\uff0c\u6ca1\u6709\u5269\u4f59\u6570\u5b57\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u4ea7\u751f\u4e86\u6700\u7ec8\u7ed3\u679c24\uff0c\u5373\u76ee\u6807\u6570\u5b57\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a1.0<\/p><\/blockquote>\n

      \u886813: BoT\u5bf9\u4e8e\u201c4 5 10 11\u201d\u8fdb\u884c\u7684\u6210\u529f\u63a8\u7406\u8fc7\u7a0b\u3002<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e00\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c1\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n————————————————
      \n**\u6b65\u9aa4 1**\uff0c\u5f53\u524d\u96c6\u5408\uff1a2 5 6 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 2\uff0c\u64cd\u4f5c\uff1a-\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a3\uff0c\u5269\u4f59\u6570\u5b57\uff1a6 6\uff0c\u65b0\u96c6\u5408\uff1a3 6 6.. \u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n————————————————<\/p>\n

      **\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u6709\u53ef\u80fd\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5730\u8fbe\u5230\u76ee\u6807\u3002\u7136\u800c\uff0c\u7531\u4e8e\u53ea\u63d0\u4f9b\u4e86\u4e00\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u6211\u4eec\u65e0\u6cd5\u786e\u5b9a\u8fd9\u6761\u94fe\u662f\u5426\u80fd\u6210\u529f\u5b8c\u6210\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u96c6\u5408\u662f2 5 6 6\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b575\u548c2\uff0c\u5e76\u6267\u884c\u4e86\u51cf\u6cd5\u64cd\u4f5c\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f3\uff0c\u5269\u4f59\u6570\u5b57\u662f6\u548c6\u3002\u65b0\u96c6\u5408\u53d8\u4e3a3, 6, 6\u3002\u8fd9\u4e2a\u6b65\u9aa4\u662f\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4e86\u7ed9\u5b9a\u4efb\u52a1\u89c4\u5219\uff0c\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\u5e76\u6267\u884c\u51cf\u6cd5\u64cd\u4f5c\u3002\u8fd9\u4e2a\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\uff0c\u5e76\u4e3a\u8fdb\u4e00\u6b65\u7684\u64cd\u4f5c\u63d0\u4f9b\u4e86\u4e00\u4e2a\u65b0\u6570\u5b57\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u6ca1\u6709\u9519\u8bef\u6216\u9700\u8981\u4fee\u6b63\u7684\u5730\u65b9\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u63a8\u8350\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.9<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e8c\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c2\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n————————————————
      \n**\u6b65\u9aa4 1**\uff0c\u5f53\u524d\u96c6\u5408\uff1a2 5 6 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a2 5\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a7\uff0c\u5269\u4f59\u6570\u5b57\uff1a6 6\uff0c\u65b0\u96c6\u5408\uff1a7 6 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 2**\uff0c\u5f53\u524d\u96c6\u5408\uff1a7 6 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a7 6\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a42\uff0c\u5269\u4f59\u6570\u5b57\uff1a6\uff0c\u65b0\u96c6\u5408\uff1a42 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 3**\uff0c\u5f53\u524d\u96c6\u5408\uff1a42 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a42 6\uff0c\u64cd\u4f5c\uff1a\/\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a7\uff0c\u5269\u4f59\u6570\u5b57\uff1a\uff0c\u65b0\u96c6\u5408\uff1a7.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9
      \n————————————————<\/p>\n

      **\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u80fd\u591f\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6210\u529f\u5b8c\u6210\u4efb\u52a1\u5e76\u6b63\u786e\u8fbe\u5230\u76ee\u6807\u3002\u6700\u7ec8\u7ed3\u679c\u662f7\uff0c\u6570\u5b66\u4e0a\u7b49\u4e8e24\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u96c6\u5408\u662f2 5 6 6\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b572\u548c5\uff0c\u5e76\u6267\u884c\u4e86\u52a0\u6cd5\u64cd\u4f5c\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f7\u3002\u5269\u4f59\u6570\u5b57\u662f6 6\u3002\u65b0\u96c6\u5408\u662f7 6 6\u3002\u903b\u8f91\u63a8\u7406\uff1a\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4e86\u4efb\u52a1\u89c4\u5219\uff0c\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff0c\u6267\u884c\u4e00\u4e2a\u64cd\u4f5c\uff0c\u5e76\u76f8\u5e94\u5730\u66f4\u65b0\u5f53\u524d\u96c6\u5408\u3002\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff1a\u662f\u7684\uff0c\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5e76\u751f\u6210\u4e86\u4e00\u4e2a\u65b0\u7684\u6570\u5b57\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u5f53\u524d\u96c6\u5408\u662f7 6 6\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b577\u548c6\uff0c\u5e76\u6267\u884c\u4e86\u4e58\u6cd5\u64cd\u4f5c\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f42\u3002\u5269\u4f59\u6570\u5b57\u662f6\u3002\u65b0\u96c6\u5408\u662f42 6\u3002\u903b\u8f91\u63a8\u7406\uff1a\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4e86\u4efb\u52a1\u89c4\u5219\uff0c\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff0c\u6267\u884c\u4e00\u4e2a\u64cd\u4f5c\uff0c\u5e76\u76f8\u5e94\u5730\u66f4\u65b0\u5f53\u524d\u96c6\u5408\u3002\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff1a\u662f\u7684\uff0c\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u8fdb\u4e00\u6b65\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u5e76\u751f\u6210\u4e86\u4e00\u4e2a\u65b0\u7684\u6570\u5b57\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u5f53\u524d\u96c6\u5408\u662f42 6\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b5742\u548c6\uff0c\u5e76\u6267\u884c\u4e86\u9664\u6cd5\u64cd\u4f5c\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f7\u3002\u6ca1\u6709\u5269\u4f59\u6570\u5b57\u3002\u65b0\u96c6\u5408\u662f7\u3002\u903b\u8f91\u63a8\u7406\uff1a\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4e86\u4efb\u52a1\u89c4\u5219\uff0c\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff0c\u6267\u884c\u4e00\u4e2a\u64cd\u4f5c\uff0c\u5e76\u76f8\u5e94\u5730\u66f4\u65b0\u5f53\u524d\u96c6\u5408\u3002\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff1a\u662f\u7684\uff0c\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u751f\u6210\u4e86\u6700\u7ec8\u7ed3\u679c7\uff0c\u6570\u5b66\u4e0a\u7b49\u4e8e24\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.9<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e94\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c5\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n————————————————
      \n**\u6b65\u9aa4 1**\uff0c\u5f53\u524d\u96c6\u5408\uff1a2 5 6 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a5 6\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a30\uff0c\u5269\u4f59\u6570\u5b57\uff1a2 6\uff0c\u65b0\u96c6\u5408\uff1a30 2 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 2**\uff0c\u5f53\u524d\u96c6\u5408\uff1a30 2 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a30 2\uff0c\u64cd\u4f5c\uff1a\/\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a15\uff0c\u5269\u4f59\u6570\u5b57\uff1a6\uff0c\u65b0\u96c6\u5408\uff1a15 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 3**\uff0c\u5f53\u524d\u96c6\u5408\uff1a15 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a15 6\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a90\uff0c\u5269\u4f59\u6570\u5b57\uff1a\u65e0\uff0c\u65b0\u96c6\u5408\uff1a90.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9
      \n————————————————<\/p>\n

      **\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u80fd\u591f\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u5b8c\u6210\u4efb\u52a1\u5e76\u6b63\u786e\u8fbe\u5230\u76ee\u6807\u3002\u7b2c3\u6b65\u4e2d\u83b7\u5f97\u7684\u6700\u7ec8\u7ed3\u679c\u662f90\uff0c\u6570\u5b66\u4e0a\u7b49\u4e8e24\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u96c6\u5408\u662f2 5 6 6\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b575\u548c6\uff0c\u5e76\u6267\u884c\u4e86\u4e58\u6cd5\u64cd\u4f5c\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f30\u3002\u5269\u4f59\u6570\u5b57\u662f2\u548c6\u3002\u65b0\u96c6\u5408\u6b63\u786e\u66f4\u65b0\u4e3a30 2 6\u3002\u8fd9\u4e2a\u6b65\u9aa4\u662f\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4e86\u4efb\u52a1\u89c4\u5219\uff0c\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff0c\u6267\u884c\u4e58\u6cd5\u64cd\u4f5c\uff0c\u5e76\u5f97\u5230\u65b0\u6570\u5b57\u3002\u8fd9\u4e2a\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u5f53\u524d\u96c6\u5408\u662f30 2 6\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b5730\u548c2\uff0c\u5e76\u6267\u884c\u4e86\u9664\u6cd5\u64cd\u4f5c\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f15\u3002\u5269\u4f59\u6570\u5b57\u662f6\u3002\u65b0\u96c6\u5408\u6b63\u786e\u66f4\u65b0\u4e3a15 6\u3002\u8fd9\u4e2a\u6b65\u9aa4\u662f\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u9075\u5faa\u4e86\u4efb\u52a1\u89c4\u5219\uff0c\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\u4e24\u4e2a\u6570\u5b57\uff0c\u6267\u884c\u9664\u6cd5\u64cd\u4f5c\uff0c\u5e76\u5f97\u5230\u65b0\u6570\u5b57\u3002\u8fd9\u4e2a\u6b65\u9aa4\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u8fdb\u4e00\u6b65\u51cf\u5c11\u4e86\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6570\u91cf\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u5f53\u524d\u96c6\u5408\u662f15 6\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b5715\u548c6\uff0c\u5e76\u6267\u884c\u4e86\u4e58\u6cd5\u64cd\u4f5c\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f90\u3002\u6ca1\u6709\u5269\u4f59\u6570\u5b57\u3002\u65b0\u96c6\u5408\u66f4\u65b0\u4e3a\u4ec5\u5305\u542b\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b5790\u3002\u8fd9\u4e2a\u6b65\u9aa4\u662f\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u7684\u903b\u8f91\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u7b80\u5316\u4e86\u96c6\u5408\u4e3a\u4e00\u4e2a\u6570\u5b57\uff0c\u8fd9\u662f\u6700\u7ec8\u7ed3\u679c\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u4e2d\u7684\u63a8\u7406\u6b65\u9aa4\u6ca1\u6709\u9519\u8bef\u6216\u9700\u8981\u4fee\u6b63\u7684\u5730\u65b9\u3002<\/p>\n

      **\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u4e2d\u7684\u6240\u6709\u63a8\u7406\u6b65\u9aa4\u90fd\u88ab\u63a8\u8350\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u5bf9\u524d\u4e00\u6b65\u7684\u903b\u8f91\u63a8\u7406\uff0c\u5e76\u6709\u52a9\u4e8e\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a0.9<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e5d\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c9\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n————————————————
      \n**\u6b65\u9aa4 1**\uff0c\u5f53\u524d\u96c6\u5408\uff1a2 5 6 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a2 5\uff0c\u64cd\u4f5c\uff1a+\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a7\uff0c\u5269\u4f59\u6570\u5b57\uff1a6 6\uff0c\u65b0\u96c6\u5408\uff1a7 6 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 2**\uff0c\u5f53\u524d\u96c6\u5408\uff1a7 6 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a7 6\uff0c\u64cd\u4f5c\uff1a*\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a42\uff0c\u5269\u4f59\u6570\u5b57\uff1a6\uff0c\u65b0\u96c6\u5408\uff1a42 6.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9<\/p>\n

      **\u6b65\u9aa4 3**\uff0c\u5f53\u524d\u96c6\u5408\uff1a42 6\uff0c\u9009\u62e9\u7684\u4e24\u4e2a\u6570\u5b57\uff1a42 6\uff0c\u64cd\u4f5c\uff1a\/\uff0c\u8ba1\u7b97\u7684\u65b0\u6570\u5b57\uff1a7\uff0c\u5269\u4f59\u6570\u5b57\uff1a\uff0c\u65b0\u96c6\u5408\uff1a7.. \u8bc4\u4f30\u5f97\u5206\uff1a0.9
      \n————————————————<\/p>\n

      **\u5206\u6790\u62a5\u544a**\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u6210\u529f\u5730\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u5b8c\u6210\u4efb\u52a1\u5e76\u6b63\u786e\u8fbe\u5230\u76ee\u6807\u3002\u7b2c3\u6b65\u4e2d\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f7\uff0c\u6570\u5b66\u4e0a\u7b49\u4e8e\u76ee\u6807\u6570\u5b5724\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 1**\uff1a\u5f53\u524d\u96c6\u5408\u662f2 5 6 6\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b572\u548c5\u3002\u64cd\u4f5c\u662f\u52a0\u6cd5(+)\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f7\u3002\u5269\u4f59\u6570\u5b57\u662f6\u548c6\u3002\u65b0\u96c6\u5408\u662f7 6 6\u3002\u903b\u8f91\u63a8\u7406\uff1a\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b57\u6b63\u786e\u5730\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\uff0c\u64cd\u4f5c\u6b63\u786e\u6267\u884c\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f\u64cd\u4f5c\u7684\u6b63\u786e\u7ed3\u679c\u3002\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u7684\u76ca\u5904\uff1a\u8fd9\u4e2a\u6b65\u9aa4\u51cf\u5c11\u4e86\u5f53\u524d\u96c6\u5408\u7684\u5927\u5c0f\uff0c\u5e76\u4e3a\u540e\u7eed\u63a8\u7406\u6b65\u9aa4\u751f\u6210\u4e86\u65b0\u7684\u96c6\u5408\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u63a5\u53d7\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 2**\uff1a\u5f53\u524d\u96c6\u5408\u662f7 6 6\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b577\u548c6\u3002\u64cd\u4f5c\u662f\u4e58\u6cd5(*)\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f42\u3002\u5269\u4f59\u6570\u5b57\u662f6\u3002\u65b0\u96c6\u5408\u662f42 6\u3002\u903b\u8f91\u63a8\u7406\uff1a\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b57\u6b63\u786e\u5730\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\uff0c\u64cd\u4f5c\u6b63\u786e\u6267\u884c\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f\u64cd\u4f5c\u7684\u6b63\u786e\u7ed3\u679c\u3002\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u7684\u76ca\u5904\uff1a\u8fd9\u4e2a\u6b65\u9aa4\u8fdb\u4e00\u6b65\u51cf\u5c11\u4e86\u5f53\u524d\u96c6\u5408\u7684\u5927\u5c0f\uff0c\u5e76\u4e3a\u540e\u7eed\u63a8\u7406\u6b65\u9aa4\u751f\u6210\u4e86\u65b0\u7684\u96c6\u5408\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u63a5\u53d7\u3002<\/p>\n

      **\u63a8\u7406\u6b65\u9aa4 3**\uff1a\u5f53\u524d\u96c6\u5408\u662f42 6\u3002\u9009\u62e9\u4e86\u4e24\u4e2a\u6570\u5b5742\u548c6\u3002\u64cd\u4f5c\u662f\u9664\u6cd5(\/)\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f7\u3002\u6ca1\u6709\u5269\u4f59\u6570\u5b57\u3002\u65b0\u96c6\u5408\u662f7\u3002\u903b\u8f91\u63a8\u7406\uff1a\u6240\u9009\u7684\u4e24\u4e2a\u6570\u5b57\u6b63\u786e\u5730\u4ece\u5f53\u524d\u96c6\u5408\u4e2d\u9009\u62e9\uff0c\u64cd\u4f5c\u6b63\u786e\u6267\u884c\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f\u64cd\u4f5c\u7684\u6b63\u786e\u7ed3\u679c\u3002\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u7684\u76ca\u5904\uff1a\u8fd9\u4e2a\u6b65\u9aa4\u5b8c\u6210\u4e86\u63a8\u7406\u94fe\uff0c\u56e0\u4e3a\u6ca1\u6709\u5269\u4f59\u6570\u5b57\u3002\u8ba1\u7b97\u51fa\u7684\u65b0\u6570\u5b57\u662f\u6700\u7ec8\u7ed3\u679c\u3002<\/p>\n

      **\u5efa\u8bae**\uff1a\u63a5\u53d7\u3002<\/p>\n

      **\u7f6e\u4fe1\u5ea6\u5f97\u5206**\uff1a1.0<\/p><\/blockquote>\n

      \u886814: BoT\u5bf9\u4e8e\u201c2 5 6 6\u201d\u7684\u9519\u8bef\u63a8\u7406\u8fc7\u7a0b\u3002\u8fd9\u662fBoT\u65e0\u6cd5\u89e3\u51b3\u7531\u865a\u5047\u53cd\u9988\u5f15\u53d1\u7684\u95ee\u9898\u7684\u7279\u4f8b\uff0c\u4f46\u4f3c\u4e4e\u4ecd\u65e7\u575a\u4fe1\u4e0d\u7b49\u4e8e24\u7684\u6570\u5b57\u662f\u6b63\u786e\u7684\uff0c\u56e0\u6b64\u5728\u7b2c\u4e8c\u6b21\u8fed\u4ee3\u540e\u5c31\u91cd\u590d\u4e86\u9519\u8bef\u7684\u63a8\u7406\u94fe\u3002<\/p>\n

       <\/p>\n

      # \u4e0b\u4e00\u4e2a\u601d\u7ef4\u751f\u6210\u7684\u63d0\u793a\u683c\u5f0f
      \n————————<\/p>\n

      **\u95ee\u9898\uff1a** James\u51b3\u5b9a\u6bcf\u5468\u8dd13\u6b21\u77ed\u8dd1\uff0c\u6bcf\u6b21\u8dd13\u4e2a\u77ed\u8dd1\u3002\u6bcf\u4e2a\u77ed\u8dd1\u4ed6\u8dd160\u7c73\u3002\u4ed6\u4e00\u5468\u603b\u5171\u8dd1\u4e86\u591a\u5c11\u7c73\uff1f<\/p>\n

      **\u7b54\u6848\uff1a** \u8ba9\u6211\u4eec\u4e00\u6b65\u4e00\u6b65\u6765\u601d\u8003\u3002<\/p>\n

      \u56de\u987e\u5386\u53f2\u63a8\u7406\u7ecf\u9a8c\uff08\u5f53\u7ecf\u9a8c\u4e3a\u7a7a\u65f6\u5ffd\u7565\uff09\uff1a
      \n################################<\/p>\n

      \u6ce8\u610f\u5206\u6790\u548c\u7ed3\u8bba\uff0c\u6839\u636e\u5efa\u8bae\u907f\u514d\u72af\u7c7b\u4f3c\u9519\u8bef\u3002<\/p>\n

      \u4ee5\u4e0b\u662f\u4e00\u7cfb\u5217\u6709\u5e8f\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u9644\u5e26\u5176\u8bc4\u4f30\u5206\u6570\uff08\u5206\u6570\u8d8a\u9ad8\u610f\u5473\u7740\u63a8\u7406\u6b65\u9aa4\u66f4\u6709\u53ef\u80fd\u5b8c\u6210\u4efb\u52a1\u3002\uff09\uff1a
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013<\/p>\n

      \u6839\u636e\u4e0a\u9762\u5217\u51fa\u7684\u63a8\u7406\u6b65\u9aa4\uff08\u5373\uff0c\u4e0d\u662f\u7ecf\u9a8c\u5757\u4e2d\u7684\u6b65\u9aa4\uff09\uff0c\u8bf7\u8fdb\u884c\u4e00\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u751f\u6210\u4e00\u4e2a
      \n\u8fde\u7eed\u53ef\u80fd\u7684\u63a8\u7406\u6b65\u9aa4\u3002<\/p>\n

       <\/p>\n

      # \u7ecf\u9a8c\u751f\u6210\u7684\u63d0\u793a\u683c\u5f0f
      \n——————-<\/p>\n

      **\u95ee\u9898\uff1a** James\u51b3\u5b9a\u6bcf\u5468\u8dd13\u6b21\u77ed\u8dd1\u3002\u6bcf\u6b21\u77ed\u8dd1\u4ed6\u8dd160\u7c73\u3002\u4ed6\u4e00\u5468\u603b\u5171\u8dd1\u4e86\u591a\u5c11\u7c73\uff1f<\/p>\n

      **\u7b54\u6848\uff1a** \u8ba9\u6211\u4eec\u4e00\u6b65\u4e00\u6b65\u6765\u601d\u8003\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a<\/p>\n

      \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013<\/p>\n

      \u8bf7\u901a\u8fc7\u5305\u542b\u4ee5\u4e0b\u5185\u5bb9\u7684\u8be6\u7ec6\u8bc4\u8bba\u6765\u8bc4\u4f30\u8fd9\u4e2a\u63a8\u7406\u94fe\uff1a1. \u8fd9\u4e2a\u63a8\u7406\u94fe\u662f\u5426\u80fd\u591f\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\uff1f\u4e3a\u4ec0\u4e48\uff1f\u5728\u201c\u5206\u6790\u62a5\u544a\uff1a\u201d\u4e0b\u5199\u4e00\u4efd\u5206\u6790\u62a5\u544a\u5e76\u5f97\u51fa\u7ed3\u8bba\u30022. \u5bf9\u4e8e\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u8be6\u7ec6\u5206\u6790\uff0c\u5224\u65ad\u5f53\u524d\u6b65\u9aa4\u662f\u5426\u662f\u524d\u4e00\u4e2a\u6b65\u9aa4\u7684\u903b\u8f91\u63a8\u8bba\uff0c\u4ee5\u53ca\u63a8\u7406\u6b65\u9aa4\u662f\u5426\u6709\u52a9\u4e8e\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u6709\u9519\u8bef\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u9519\u8bef\u62a5\u544a\u548c\u76f8\u5e94\u7684\u4fee\u8ba2\u5efa\u8bae\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u8bf7\u63d0\u4f9b\u63a8\u8350\u6216\u62d2\u7edd\u7684\u63cf\u8ff0\u3002\u8bc4\u8bba\u5e94\u7b80\u6d01\uff0c\u907f\u514d\u5728\u4e0d\u540c\u6b65\u9aa4\u4e2d\u91cd\u590d\u76f8\u540c\u7684\u5206\u6790\uff0c\u5e76\u9075\u5faa\u4ee5\u4e0b\u683c\u5f0f\uff1a\u63a8\u7406\u6b65\u9aa4 \u00a1idx\u00bf. \u5206\u6790\u62a5\u544a\uff1a\u3002\u5efa\u8bae\uff1a\u3002\u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0\uff1a\u30023. \u4f60\u5bf9\u8fd9\u4e9b\u8bc4\u4f30\u548c\u8bc4\u8bba\u7684\u4fe1\u5fc3\u5206\u6570\u662f\u591a\u5c11\uff1f\u8bf7\u4ece[0.1, 0.3, 0.5, 0.7, 0.9, 1.0]\u4e2d\u9009\u62e9\u4e00\u4e2a\u503c\u3002\u5206\u6570\u5e94\u653e\u5728\u201c\u4fe1\u5fc3\u5206\u6570\uff1a\u201d\u540e\u9762\u4f9b\u7528\u6237\u9605\u8bfb\u3002<\/p><\/blockquote>\n

      \u886815: GSM8K\u4e2d\u4f7f\u7528\u7684\u63d0\u793a\u683c\u5f0f\u3002\u201c\u95ee\u9898\u201d\u7684\u63a8\u7406\u8fc7\u7a0b\u5728\u886816\u4e2d\u6709\u5c55\u793a\u3002<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e00\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c1\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u7b2c\u4e00\u6b65\uff1a\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97James\u6bcf\u6b21\u51b2\u523a\u8dd1\u7684\u603b\u8ddd\u79bb\u3002\u7531\u4e8e\u4ed6\u6bcf\u6b21\u51b2\u523a\u8dd160\u7c73\uff0c\u800c\u4e14\u4ed6\u4e00\u5468\u8dd13\u6b21\uff0c\u6211\u4eec\u752860\u4e58\u4ee53\u3002\u8bc4\u4f30\u5f97\u5206\uff1a0.7
      \n\u7b2c\u4e8c\u6b65\uff1a\u5728\u8ba1\u7b97\u51faJames\u6bcf\u6b21\u51b2\u523a\u8dd1\u7684\u603b\u8ddd\u79bb\u4e4b\u540e\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u4ed6\u4e00\u5468\u8dd1\u7684\u603b\u8ddd\u79bb\u3002\u7531\u4e8e\u4ed6\u4e00\u5468\u8dd13\u6b21\uff0c\u6211\u4eec\u5c06\u6bcf\u6b21\u7684\u603b\u8ddd\u79bb\u4e58\u4ee53\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u5206\u6790\u62a5\u544a\uff1a\u63a8\u7406\u94fe\u53ef\u4ee5\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u63a8\u7406\u94fe\u662f\u6b63\u786e\u7684\u5e76\u4e14\u903b\u8f91\u6e05\u6670\uff0c\u5b83\u901a\u8fc7\u8ba1\u7b97James\u4e00\u5468\u8dd1\u7684\u603b\u8ddd\u79bb\u6210\u529f\u89e3\u51b3\u4e86\u95ee\u9898\u3002
      \n\u63a8\u7406\u6b65\u9aa41. \u5206\u6790\uff1a\u8fd9\u4e00\u6b65\u5728\u903b\u8f91\u4e0a\u662f\u6b63\u786e\u7684\u3002\u5b83\u901a\u8fc7\u8bc6\u522b\u9700\u8981\u8ba1\u7b97James\u6bcf\u6b21\u51b2\u523a\u8dd1\u7684\u603b\u8ddd\u79bb\u6765\u51c6\u786e\u89e3\u91ca\u95ee\u9898\u3002\u7136\u800c\uff0c\u63cf\u8ff0\u6709\u4e9b\u8bef\u5bfc\u3002James\u4e0d\u662f\u4e00\u5468\u8dd13\u6b21\u51b2\u523a\uff0c\u800c\u662f\u6bcf\u6b21\u8dd13\u6b21\u51b2\u523a\uff0c\u4e00\u5468\u8dd13\u6b21\u3002\u4e58\u6cd5\u5e94\u8be5\u5728\u6bcf\u6b21\u51b2\u523a\u7684\u8ddd\u79bb\u548c\u6bcf\u6b21\u51b2\u523a\u7684\u6b21\u6570\u4e4b\u95f4\u8fdb\u884c\u3002\u5efa\u8bae\uff1a\u63cf\u8ff0\u5e94\u8be5\u4fee\u6539\u4e3a\u201c\u7531\u4e8e\u4ed6\u6bcf\u6b21\u51b2\u523a\u8dd160\u7c73\uff0c\u800c\u4e14\u4ed6\u6bcf\u6b21\u8dd1\u6b65\u65f6\u8dd13\u6b21\uff0c\u6211\u4eec\u752860\u4e58\u4ee53\u3002\u201d\u5efa\u8bae\uff1a\u63a8\u7406\u6b65\u9aa4\u662f\u6b63\u786e\u7684\uff0c\u4f46\u63cf\u8ff0\u9700\u8981\u4fee\u6539\u4ee5\u6e05\u6670\u3002
      \n\u63a8\u7406\u6b65\u9aa42. \u5206\u6790\uff1a\u8fd9\u4e00\u6b65\u662f\u4ece\u4e0a\u4e00\u6b65\u903b\u8f91\u63a8\u65ad\u51fa\u6765\u7684\u3002\u5b83\u901a\u8fc7\u4e58\u4ee5\u6bcf\u6b21\u8dd1\u6b65\u7684\u603b\u8ddd\u79bb\u548c\u4e00\u5468\u8dd1\u6b65\u7684\u6b21\u6570\uff0c\u6b63\u786e\u8ba1\u7b97\u51faJames\u4e00\u5468\u8dd1\u7684\u603b\u8ddd\u79bb\u3002\u5efa\u8bae\uff1a\u65e0\u9700\u4fee\u6539\u3002\u5efa\u8bae\uff1a\u63a8\u7406\u6b65\u9aa4\u662f\u6b63\u786e\u7684\uff0c\u5e94\u8be5\u88ab\u63a5\u53d7\u3002
      \n\u4fe1\u5fc3\u5f97\u5206\uff1a0.9
      \n##########################################<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e8c\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c2\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u7b2c\u4e00\u6b65\uff1a\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97James\u6bcf\u6b21\u8dd1\u6b65\u7684\u603b\u8ddd\u79bb\u3002\u7531\u4e8e\u4ed6\u6bcf\u6b21\u8dd1\u6b65\u8dd160\u7c73\uff0c\u800c\u4e14\u4ed6\u6bcf\u6b21\u8dd1\u6b65\u8dd13\u6b21\u51b2\u523a\uff0c\u6211\u4eec\u752860\u4e58\u4ee53\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u5206\u6790\u62a5\u544a\uff1a\u7ed9\u51fa\u7684\u63a8\u7406\u94fe\u53ef\u4ee5\u90e8\u5206\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u7136\u800c\uff0c\u5b83\u662f\u4e0d\u5b8c\u6574\u7684\uff0c\u56e0\u4e3a\u5b83\u5728\u8ba1\u7b97\u51faJames\u6bcf\u6b21\u8dd1\u6b65\u7684\u603b\u8ddd\u79bb\u540e\u5c31\u505c\u6b62\u4e86\u3002\u5b83\u6ca1\u6709\u7ee7\u7eed\u8ba1\u7b97James\u4e00\u5468\u8dd1\u7684\u603b\u8ddd\u79bb\u3002
      \n\u63a8\u7406\u6b65\u9aa41. \u7b2c\u4e00\u6b65\u6b63\u786e\u8ba1\u7b97\u4e86James\u6bcf\u6b21\u8dd1\u6b65\u7684\u603b\u8ddd\u79bb\u3002\u5b83\u4ece\u95ee\u9898\u4e2d\u903b\u8f91\u63a8\u65ad\u51fa\uff0c\u7531\u4e8eJames\u6bcf\u6b21\u51b2\u523a\u8dd160\u7c73\uff0c\u800c\u4e14\u4ed6\u6bcf\u6b21\u8dd1\u6b65\u8dd13\u6b21\u51b2\u523a\uff0c\u6bcf\u6b21\u8dd1\u6b65\u7684\u603b\u8ddd\u79bb\u662f60 * 3\u3002\u8fd9\u4e00\u6b65\u5bf9\u4e8e\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u662f\u6709\u76ca\u7684\uff0c\u56e0\u4e3a\u5b83\u662f\u627e\u5230James\u4e00\u5468\u8dd1\u7684\u603b\u8ddd\u79bb\u7684\u5fc5\u8981\u8ba1\u7b97\u3002
      \n\u5efa\u8bae\uff1a\u63a8\u7406\u94fe\u9700\u8981\u7ee7\u7eed\uff0c\u5305\u62ec\u8ba1\u7b97James\u4e00\u5468\u8dd1\u7684\u603b\u8ddd\u79bb\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u4e58\u4ee5\u6bcf\u6b21\u8dd1\u6b65\u7684\u603b\u8ddd\u79bb\uff08\u5728\u7b2c\u4e00\u6b65\u4e2d\u8ba1\u7b97\uff09\u548c\u4e00\u5468\u8dd1\u6b65\u7684\u6b21\u6570\u6765\u5b8c\u6210\u3002
      \n\u5efa\u8bae\uff1a\u63a5\u53d7\u63a8\u7406\u6b65\u9aa41\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u8ba1\u7b97\u4e86James\u6bcf\u6b21\u8dd1\u6b65\u7684\u603b\u8ddd\u79bb\u3002\u7136\u800c\uff0c\u63a8\u7406\u94fe\u9700\u8981\u7ee7\u7eed\uff0c\u5305\u62ec\u8ba1\u7b97James\u4e00\u5468\u8dd1\u7684\u603b\u8ddd\u79bb\u3002
      \n\u4fe1\u5fc3\u5f97\u5206\uff1a0.9
      \n##########################################<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e09\u6b21\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c3\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u4e00\u4e2a\u6309\u987a\u5e8f\u5448\u73b0\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u7b2c\u4e00\u6b65\uff1a\u786e\u5b9a\u95ee\u9898\u4e2d\u7684\u5143\u7d20\u3002James\u4e00\u5468\u8dd13\u6b21\uff0c\u6bcf\u6b21\u8dd13\u6b21\u51b2\u523a\uff0c\u6bcf\u6b21\u51b2\u523a60\u7c73\u3002\u6211\u4eec\u9700\u8981\u627e\u51fa\u4ed6\u4e00\u5468\u8dd1\u7684\u603b\u8ddd\u79bb\u3002\u8bc4\u4f30\u5f97\u5206\uff1a0.9
      \n\u7b2c\u4e8c\u6b65\uff1a\u8ba1\u7b97James\u5355\u65e5\u8dd1\u7684\u603b\u8ddd\u79bb\u3002\u7531\u4e8e\u4ed6\u6bcf\u5929\u8dd13\u6b21\u51b2\u523a\uff0c\u6bcf\u6b21\u51b2\u523a60\u7c73\uff0c\u5355\u65e5\u7684\u603b\u8ddd\u79bb\u5c06\u662f3\u6b21\u51b2\u523a * 60\u7c73\/\u51b2\u523a = 180\u7c73\u3002\u8bc4\u4f30\u5f97\u5206\uff1a0.9. \u8bc4\u4f30\u5f97\u5206\uff1a0.9
      \n\u7b2c\u4e09\u6b65\uff1a\u73b0\u5728\uff0c\u8ba1\u7b97James\u4e00\u5468\u8dd1\u7684\u603b\u8ddd\u79bb\u3002\u7531\u4e8e\u4ed6\u4e00\u5468\u8dd13\u6b21\uff0c\u6bcf\u6b21\u8dd1180\u7c73\uff0c\u4e00\u5468\u7684\u603b\u8ddd\u79bb\u5c06\u662f3\u5929\/\u5468 * 180\u7c73\/\u5929 = 540\u7c73\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u5206\u6790\u62a5\u544a\uff1a\u63a8\u7406\u94fe\u786e\u5b9e\u5b8c\u6210\u4e86\u4efb\u52a1\u5e76\u6b63\u786e\u8fbe\u5230\u4e86\u76ee\u6807\u3002\u6bcf\u4e00\u6b65\u90fd\u4ece\u524d\u4e00\u6b65\u903b\u8f91\u4e0a\u8ddf\u8fdb\uff0c\u6709\u52a9\u4e8e\u89e3\u51b3\u95ee\u9898\u3002
      \n\u63a8\u7406\u6b65\u9aa41. \u7b2c\u4e00\u6b65\u6b63\u786e\u8bc6\u522b\u4e86\u95ee\u9898\u4e2d\u7684\u5143\u7d20\u548c\u624b\u5934\u7684\u4efb\u52a1\u3002\u5b83\u6b63\u786e\u89e3\u91ca\u4e86\u95ee\u9898\u9648\u8ff0\u5e76\u4e3a\u540e\u7eed\u6b65\u9aa4\u5960\u5b9a\u4e86\u57fa\u7840\u3002\u5efa\u8bae\uff1a\u65e0\u3002\u5efa\u8bae\uff1a\u63a5\u53d7\u8fd9\u4e00\u6b65\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u8bc6\u522b\u4e86\u95ee\u9898\u548c\u9700\u8981\u505a\u7684\u4e8b\u60c5\u3002
      \n\u63a8\u7406\u6b65\u9aa42. \u8fd9\u4e00\u6b65\u4ece\u7b2c\u4e00\u6b65\u903b\u8f91\u4e0a\u8ddf\u8fdb\u3002\u5b83\u901a\u8fc7\u4e58\u4ee5\u4ed6\u8dd1\u7684\u51b2\u523a\u6b21\u6570\u548c\u6bcf\u6b21\u51b2\u523a\u7684\u8ddd\u79bb\uff0c\u6b63\u786e\u8ba1\u7b97\u4e86James\u5355\u65e5\u8dd1\u7684\u603b\u8ddd\u79bb\u3002\u8fd9\u4e00\u6b65\u5bf9\u4e8e\u89e3\u51b3\u65b9\u6848\u662f\u6709\u76ca\u7684\uff0c\u56e0\u4e3a\u5b83\u5c06\u95ee\u9898\u5206\u89e3\u6210\u66f4\u5c0f\u3001\u66f4\u6613\u7ba1\u7406\u7684\u90e8\u5206\u3002\u5efa\u8bae\uff1a\u65e0\u3002\u5efa\u8bae\uff1a\u63a5\u53d7\u8fd9\u4e00\u6b65\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u8ba1\u7b97\u4e86\u6bcf\u65e5\u8dd1\u6b65\u8ddd\u79bb\u3002
      \n\u63a8\u7406\u6b65\u9aa43. \u8fd9\u4e00\u6b65\u662f\u4ece\u4e0a\u4e00\u6b65\u903b\u8f91\u63a8\u65ad\u51fa\u6765\u7684\u3002\u5b83\u901a\u8fc7\u4e58\u4ee5\u6bcf\u6b21\u8dd1\u6b65\u7684\u8ddd\u79bb\u548c\u4e00\u5468\u8dd1\u6b65\u7684\u6b21\u6570\uff0c\u6b63\u786e\u8ba1\u7b97\u4e86James\u4e00\u5468\u8dd1\u7684\u603b\u8ddd\u79bb\u3002\u8fd9\u4e00\u6b65\u5bf9\u4e8e\u89e3\u51b3\u65b9\u6848\u662f\u6709\u76ca\u7684\uff0c\u56e0\u4e3a\u5b83\u5b8c\u6210\u4e86\u8ba1\u7b97\u5e76\u63d0\u4f9b\u4e86\u95ee\u9898\u7684\u7b54\u6848\u3002\u5efa\u8bae\uff1a\u65e0\u3002\u5efa\u8bae\uff1a\u63a5\u53d7\u8fd9\u4e00\u6b65\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u8ba1\u7b97\u4e86\u6bcf\u5468\u8dd1\u6b65\u8ddd\u79bb\u3002
      \n\u4fe1\u5fc3\u5f97\u5206\uff1a1.0<\/p>\n

       <\/p>\n

      \u5ffd\u7565\u540e\u7eed\u8fed\u4ee3\uff0c\u56e0\u4e3a\u5df2\u7ecf\u83b7\u5f97\u4e86\u6b63\u786e\u7684\u63a8\u7406\u94fe\u3002<\/p><\/blockquote>\n

      \u886816: BoT\u7684\u6210\u529f\u63a8\u7406\u8fc7\u7a0b\u3002<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e00\u8f6e\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n######## \u7b2c1\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba ########<\/p>\n

      \u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u5448\u73b0\u7684\u5305\u542b\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u6b65\u9aa4 1\uff1a\u5982\u679c\u897f\u96c5\u56fe\u670920\u53ea\u7f8a\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7ed9\u5b9a\u7684\u6bd4\u4f8b\u6765\u8ba1\u7b97\u67e5\u5c14\u65af\u987f\u548c\u56fe\u5362\u5179\u7684\u7f8a\u7684\u6570\u91cf\u3002\u6839\u636e\u95ee\u9898\uff0c\u67e5\u5c14\u65af\u987f\u6709\u897f\u96c5\u56fe\u76844\u500d\u7f8a\u3002\u56e0\u6b64\uff0c\u67e5\u5c14\u65af\u987f\u6709 4 * 20 = 80 \u53ea\u7f8a\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013<\/p>\n

      \u5206\u6790\u62a5\u544a\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u6b63\u671d\u7740\u89e3\u51b3\u95ee\u9898\u7684\u6b63\u786e\u65b9\u5411\u524d\u8fdb\u3002\u7b2c\u4e00\u6b65\u6b63\u786e\u5730\u89e3\u91ca\u4e86\u95ee\u9898\u9648\u8ff0\uff0c\u5e76\u6839\u636e\u7ed9\u5b9a\u4fe1\u606f\u51c6\u786e\u5730\u8ba1\u7b97\u4e86\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002\u5b83\u4f7f\u7528\u4e86\u6b63\u786e\u7684\u6570\u5b66\u8fd0\u7b97\uff08\u4e58\u6cd5\uff09\u6765\u786e\u5b9a\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\uff0c\u8fd9\u662f\u4ece\u95ee\u9898\u9648\u8ff0\u4e2d\u903b\u8f91\u63a8\u65ad\u51fa\u6765\u7684\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa4 1\uff1a\u8fd9\u4e00\u6b65\u662f\u6839\u636e\u7ed9\u5b9a\u95ee\u9898\u9648\u8ff0\u7684\u903b\u8f91\u63a8\u65ad\u3002\u95ee\u9898\u9648\u8ff0\u6307\u51fa\u67e5\u5c14\u65af\u987f\u6709\u897f\u96c5\u56fe\u76844\u500d\u7f8a\u3002\u9274\u4e8e\u897f\u96c5\u56fe\u670920\u53ea\u7f8a\uff0c\u4e58\u4ee54\u6765\u627e\u5230\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u662f\u6b63\u786e\u7684\u3002\u8fd9\u4e00\u6b65\u5bf9\u4e8e\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u662f\u6709\u76ca\u7684\uff0c\u56e0\u4e3a\u5b83\u51c6\u786e\u5730\u8ba1\u7b97\u4e86\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\uff0c\u8fd9\u662f\u627e\u5230\u6240\u6709\u4e09\u4e2a\u57ce\u5e02\u603b\u7f8a\u6570\u6240\u9700\u7684\u3002\u8fd9\u4e00\u6b65\u6ca1\u6709\u9519\u8bef\u3002<\/p>\n

      \u5efa\u8bae\uff1a\u8fd9\u4e00\u6b65\u662f\u6b63\u786e\u7684\uff0c\u4e0d\u9700\u8981\u5efa\u8bae\u3002<\/p>\n

      \u63a8\u8350\uff1a\u63a8\u8350\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u5730\u89e3\u91ca\u4e86\u95ee\u9898\u9648\u8ff0\uff0c\u5e76\u51c6\u786e\u5730\u8ba1\u7b97\u4e86\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002
      \n\u4fe1\u5fc3\u5f97\u5206\uff1a1.0
      \n##########################################<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e09\u8f6e\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n######## \u7b2c3\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba ########<\/p>\n

      \u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u5448\u73b0\u7684\u5305\u542b\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u6b65\u9aa4 1\uff1a\u5982\u679c\u897f\u96c5\u56fe\u670920\u53ea\u7f8a\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7ed9\u5b9a\u7684\u6bd4\u4f8b\u6765\u8ba1\u7b97\u67e5\u5c14\u65af\u987f\u548c\u56fe\u5362\u5179\u7684\u7f8a\u7684\u6570\u91cf\u3002\u6839\u636e\u95ee\u9898\uff0c\u67e5\u5c14\u65af\u987f\u6709\u897f\u96c5\u56fe\u76844\u500d\u7f8a\u3002\u56e0\u6b64\uff0c\u67e5\u5c14\u65af\u987f\u6709 4 * 20 = 80 \u53ea\u7f8a\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013<\/p>\n

      \u5206\u6790\u62a5\u544a\uff1a\u8fd9\u6761\u63a8\u7406\u94fe\u53ef\u4ee5\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u4efb\u52a1\u8981\u6c42\u5728\u5df2\u77e5\u897f\u96c5\u56fe\u670920\u53ea\u7f8a\uff0c\u5176\u4ed6\u57ce\u5e02\u4e0e\u897f\u96c5\u56fe\u6709\u4e00\u5b9a\u6bd4\u4f8b\u7684\u7f8a\u7684\u60c5\u51b5\u4e0b\uff0c\u627e\u51fa\u56fe\u5362\u5179\u3001\u67e5\u5c14\u65af\u987f\u548c\u897f\u96c5\u56fe\u7684\u603b\u7f8a\u6570\u3002\u63a8\u7406\u94fe\u6b63\u786e\u89e3\u91ca\u4e86\u95ee\u9898\uff0c\u5e76\u4f7f\u7528\u7ed9\u5b9a\u7684\u6bd4\u4f8b\u6765\u8ba1\u7b97\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa4 1\uff1a\u7b2c\u4e00\u6b65\u6b63\u786e\u5730\u4f7f\u7528\u4e86\u95ee\u9898\u9648\u8ff0\u4e2d\u63d0\u4f9b\u7684\u4fe1\u606f\u3002\u5b83\u903b\u8f91\u63a8\u65ad\uff0c\u7531\u4e8e\u67e5\u5c14\u65af\u987f\u6709\u897f\u96c5\u56fe\u76844\u500d\u7f8a\uff0c\u4e14\u897f\u96c5\u56fe\u670920\u53ea\u7f8a\uff0c\u67e5\u5c14\u65af\u987f\u6709 4 * 20 = 80 \u53ea\u7f8a\u3002\u8fd9\u4e00\u6b65\u5bf9\u4e8e\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u662f\u6709\u76ca\u7684\uff0c\u56e0\u4e3a\u5b83\u6839\u636e\u7ed9\u5b9a\u7684\u6bd4\u4f8b\u548c\u897f\u96c5\u56fe\u7684\u7f8a\u7684\u6570\u91cf\u6b63\u786e\u8ba1\u7b97\u4e86\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u6ca1\u6709\u9519\u8bef\u3002<\/p>\n

      \u5efa\u8bae\uff1a\u8fd9\u4e00\u6b65\u6b63\u786e\u63a8\u7406\u548c\u8ba1\u7b97\uff0c\u4e0d\u9700\u8981\u5efa\u8bae\u3002<\/p>\n

      \u63a8\u8350\u6216\u62d2\u7edd\u63cf\u8ff0\uff1a\u6211\u63a8\u8350\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u5730\u89e3\u91ca\u4e86\u95ee\u9898\u9648\u8ff0\uff0c\u4f7f\u7528\u4e86\u7ed9\u5b9a\u7684\u6bd4\u4f8b\uff0c\u5e76\u6b63\u786e\u8ba1\u7b97\u4e86\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002
      \n\u4fe1\u5fc3\u5f97\u5206\uff1a1.0
      \n##########################################<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e94\u8f6e\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n######## \u7b2c5\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba ########<\/p>\n

      \u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u5448\u73b0\u7684\u5305\u542b\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u6b65\u9aa4 1\uff1a\u5982\u679c\u897f\u96c5\u56fe\u670920\u53ea\u7f8a\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7ed9\u5b9a\u7684\u6bd4\u4f8b\u6765\u8ba1\u7b97\u67e5\u5c14\u65af\u987f\u548c\u56fe\u5362\u5179\u7684\u7f8a\u7684\u6570\u91cf\u3002\u6839\u636e\u95ee\u9898\uff0c\u67e5\u5c14\u65af\u987f\u6709\u897f\u96c5\u56fe\u76844\u500d\u7f8a\u3002\u56e0\u6b64\uff0c\u67e5\u5c14\u65af\u987f\u6709 4 * 20 = 80 \u53ea\u7f8a\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013<\/p>\n

      \u5206\u6790\u62a5\u544a\uff1a\u8fd9\u4e2a\u63a8\u7406\u94fe\u6b63\u786e\u5e94\u7528\u4e86\u95ee\u9898\u4e2d\u7ed9\u51fa\u7684\u4fe1\u606f\uff0c\u4ee5\u786e\u5b9a\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002\u5b83\u4ece\u7ed9\u5b9a\u4fe1\u606f\u4e2d\u903b\u8f91\u63a8\u65ad\uff0c\u5982\u679c\u67e5\u5c14\u65af\u987f\u6709\u897f\u96c5\u56fe\u76844\u500d\u7f8a\uff0c\u4e14\u897f\u96c5\u56fe\u670920\u53ea\u7f8a\uff0c\u90a3\u4e48\u67e5\u5c14\u65af\u987f\u5fc5\u987b\u6709 4 * 20 = 80 \u53ea\u7f8a\u3002\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\u5bf9\u4e8e\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u662f\u6709\u76ca\u7684\uff0c\u56e0\u4e3a\u5b83\u6839\u636e\u7ed9\u5b9a\u4fe1\u606f\u51c6\u786e\u5730\u8ba1\u7b97\u4e86\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa4 1. \u7b2c\u4e00\u6b65\u5728\u903b\u8f91\u4e0a\u662f\u6b63\u786e\u7684\uff0c\u5e76\u4ece\u95ee\u9898\u9648\u8ff0\u4e2d\u5f97\u51fa\u3002\u8fd9\u4e00\u6b65\u4f7f\u7528\u67e5\u5c14\u65af\u987f\u548c\u897f\u96c5\u56fe\u4e4b\u95f4\u7684\u7ed9\u5b9a\u7f8a\u7684\u6bd4\u4f8b\u6765\u8ba1\u7b97\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002\u8fd9\u4e00\u6b65\u5bf9\u4e8e\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u662f\u6709\u76ca\u7684\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u5e94\u7528\u4e86\u7ed9\u5b9a\u7684\u6bd4\u4f8b\u6765\u627e\u5230\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002\u8fd9\u4e00\u6b65\u6ca1\u6709\u9519\u8bef\u3002<\/p>\n

      \u5efa\u8bae\uff1a\u8fd9\u4e00\u6b65\u5728\u903b\u8f91\u4e0a\u662f\u6b63\u786e\u7684\uff0c\u5bf9\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u4e0d\u9700\u8981\u5efa\u8bae\u3002<\/p>\n

      \u63a8\u8350\uff1a\u63a8\u8350\u8fd9\u4e00\u6b65\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u5e94\u7528\u4e86\u7ed9\u5b9a\u7684\u6bd4\u4f8b\uff0c\u5e76\u8ba1\u7b97\u4e86\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002
      \n\u4fe1\u5fc3\u5f97\u5206\uff1a1.0
      \n##########################################<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e5d\u8f6e\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n######## \u7b2c9\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba ########<\/p>\n

      \u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u5448\u73b0\u7684\u5305\u542b\u63a8\u7406\u6b65\u9aa4\u7684\u63a8\u7406\u94fe\uff1a
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u6b65\u9aa4 1\uff1a\u7531\u4e8e\u67e5\u5c14\u65af\u987f\u6709\u897f\u96c5\u56fe\u76844\u500d\u7f8a\uff0c\u4e14\u897f\u96c5\u56fe\u670920\u53ea\u7f8a\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e58\u4ee54\u6765\u8ba1\u7b97\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2013
      \n\u5206\u6790\u62a5\u544a\uff1a\u6b65\u9aa4 1 \u7684\u63a8\u7406\u94fe\u662f\u51c6\u786e\u4e14\u903b\u8f91\u4e0a\u5408\u7406\u7684\u3002\u5b83\u6b63\u786e\u5e94\u7528\u4e86\u95ee\u9898\u9648\u8ff0\u4e2d\u7ed9\u51fa\u7684\u4fe1\u606f\uff0c\u4ee5\u786e\u5b9a\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002\u8fd9\u4e00\u6b65\u5bf9\u4e8e\u89e3\u51b3\u95ee\u9898\u81f3\u5173\u91cd\u8981\uff0c\u56e0\u4e3a\u5b83\u5efa\u7acb\u4e86\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\uff0c\u7136\u540e\u7528\u6765\u786e\u5b9a\u56fe\u5362\u5179\u7684\u7f8a\u7684\u6570\u91cf\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa4 1. \u8fd9\u4e00\u6b65\u662f\u4ece\u7ed9\u5b9a\u95ee\u9898\u9648\u8ff0\u4e2d\u903b\u8f91\u63a8\u65ad\u51fa\u6765\u7684\u3002\u5b83\u6b63\u786e\u89e3\u91ca\u4e86\u67e5\u5c14\u65af\u987f\u6709\u897f\u96c5\u56fe\u76844\u500d\u7f8a\u7684\u4fe1\u606f\uff0c\u5e76\u5e94\u7528\u8fd9\u4e9b\u4fe1\u606f\u6765\u8ba1\u7b97\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u7684\u6570\u91cf\u3002\u8fd9\u4e00\u6b65\u5bf9\u4e8e\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u662f\u6709\u76ca\u7684\uff0c\u56e0\u4e3a\u5b83\u63d0\u4f9b\u4e86\u8ba1\u7b97\u6240\u6709\u4e09\u4e2a\u5730\u70b9\u603b\u7f8a\u6570\u6240\u9700\u7684\u5fc5\u8981\u4fe1\u606f\u3002<\/p>\n

      \u5efa\u8bae\uff1a\u8fd9\u4e00\u6b65\u6b63\u786e\u63a8\u7406\u548c\u51c6\u786e\u8ba1\u7b97\uff0c\u4e0d\u9700\u8981\u5efa\u8bae\u3002<\/p>\n

      \u63a8\u8350\uff1a\u6211\u63a8\u8350\u63a5\u53d7\u8fd9\u4e2a\u63a8\u7406\u6b65\u9aa4\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u63a8\u7406\u548c\u51c6\u786e\u8ba1\u7b97\u3002
      \n\u4fe1\u5fc3\u5f97\u5206\uff1a1.0
      \n##########################################<\/p><\/blockquote>\n

      \u886817: BoT\u5bf9\u4e8e\u201c\u56fe\u5362\u5179\u7684\u7f8a\u662f\u67e5\u5c14\u65af\u987f\u7684\u4e24\u500d\u3002\u67e5\u5c14\u65af\u987f\u7684\u7f8a\u662f\u897f\u96c5\u56fe\u7684\u56db\u500d\u3002\u5f53\u897f\u96c5\u56fe\u670920\u53ea\u7f8a\u65f6\uff0c\u56fe\u5362\u5179\uff0c\u67e5\u5c14\u65af\u987f\uff0c\u4ee5\u53ca\u897f\u96c5\u56fe\u4e00\u5171\u6709\u591a\u5c11\u53ea\u7f8a?\u201d\u7684\u90e8\u5206\u6210\u529f\u63a8\u7406\u8fc7\u7a0b\u3002\u83b7\u5f97\u7684\u63a8\u7406\u94fe\u53ea\u80fd\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u4e00\u534a\uff0c\u901a\u5e38\u6b64\u7c7b\u60c5\u51b5\u662f\u7531\u4e8eBoT\u6240\u4f7f\u7528\u7684LLM\u65e0\u6cd5\u51c6\u786e\u7406\u89e3\u8fd9\u4e2a\u95ee\u9898\u3002\u56e0\u6b64\uff0c\u5c3d\u7ba1BoT\u8fdb\u884c\u4e86\u6b63\u786e\u7684\u63a8\u7406\u8fc7\u7a0b\uff0c\u4f46\u65e0\u6cd5\u5f97\u51fa\u6b63\u786e\u7b54\u6848\u7684\u5b8c\u6574\u63a8\u7406\u94fe\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u8fd9\u79cd\u63a8\u7406\u94fe\u4ecd\u88ab\u89c6\u4e3aBoT\u7684\u4e00\u6b21\u6210\u529f\uff0c\u56e0\u4e3a\u5b83\u9488\u5bf9LLM\u6355\u6349\u7684\u95ee\u9898\u7ed9\u51fa\u4e86\u51c6\u786e\u7684\u89e3\u7b54\u3002<\/p>\n

       <\/p>\n

      ### \u7b2c\u4e00\u8f6e\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c1\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u5448\u73b0\u7684\u63a8\u7406\u6b65\u9aa4\u94fe\uff1a
      \n——————-
      \n**\u6b65\u9aa41**: \u5c06Mariah\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u7684\u5206\u6570\u8f6c\u6362\u4e3a\u7801\u6570\u3002Mariah\u4f7f\u7528\u4e861\/4\u4e2a\u7eb1\u7ebf\uff0c\u76f8\u5f53\u4e8e1\/4 * 364\u7801\u3002\u5979\u7684\u5976\u5976\u4f7f\u7528\u4e861\/2\u4e2a\u7eb1\u7ebf\uff0c\u76f8\u5f53\u4e8e1\/2 * 364\u7801\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0<\/p>\n

      **\u6b65\u9aa42**: \u901a\u8fc7\u5c06Mariah\u4f7f\u7528\u7684\u7eb1\u7ebf\u7801\u6570\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u7801\u6570\u76f8\u52a0\uff0c\u8ba1\u7b97\u51faMariah\u548c\u5979\u5976\u5976\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u7801\u6570\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0<\/p>\n

      **\u6b65\u9aa41** (\u91cd\u590d): \u5c06Mariah\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u7684\u5206\u6570\u8f6c\u6362\u4e3a\u7801\u6570\u3002Mariah\u4f7f\u7528\u4e861\/4\u4e2a\u7eb1\u7ebf\uff0c\u76f8\u5f53\u4e8e1\/4 * 364\u7801 = 91\u7801\u3002\u5979\u7684\u5976\u5976\u4f7f\u7528\u4e861\/2\u4e2a\u7eb1\u7ebf\uff0c\u76f8\u5f53\u4e8e1\/2 * 364\u7801 = 182\u7801\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n——————-
      \n**\u5206\u6790\u62a5\u544a**: \u63a8\u7406\u94fe\u80fd\u591f\u901a\u8fc7\u6267\u884c\u5176\u63a8\u7406\u6b65\u9aa4\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u6b65\u9aa4\u903b\u8f91\u6e05\u6670\uff0c\u987a\u5e8f\u660e\u786e\uff0c\u5bf9\u89e3\u51b3\u95ee\u9898\u662f\u5fc5\u8981\u7684\u3002\u6b65\u9aa4\u5c06\u4f7f\u7528\u7684\u7eb1\u7ebf\u5206\u6570\u8f6c\u6362\u4e3a\u7801\u6570\uff0c\u8fd9\u662f\u786e\u5b9a\u603b\u5171\u4f7f\u7528\u4e86\u591a\u5c11\u7eb1\u7ebf\u6240\u5fc5\u9700\u7684\u3002\u7136\u540e\uff0c\u5b83\u4eec\u5c06\u8fd9\u4e9b\u6570\u91cf\u76f8\u52a0\u4ee5\u627e\u51faMariah\u548c\u5979\u5976\u5976\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u6570\u91cf\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa41. \u8fd9\u4e00\u6b65\u6b63\u786e\u5730\u5c06Mariah\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u7684\u5206\u6570\u8f6c\u6362\u4e3a\u7801\u6570\u3002\u5b83\u662f\u5bf9\u95ee\u9898\u9648\u8ff0\u7684\u903b\u8f91\u63a8\u65ad\uff0c\u5e76\u4e14\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u5c06\u95ee\u9898\u8f6c\u6362\u6210\u76f8\u540c\u7684\u5355\u4f4d\uff08\u7801\uff09\uff0c\u4f7f\u5f97\u80fd\u591f\u5c06\u6570\u91cf\u76f8\u52a0\u3002\u5efa\u8bae\uff1a\u65e0\u3002\u63a8\u8350\uff1a\u8fd9\u4e00\u6b65\u662f\u6b63\u786e\u7684\uff0c\u5e94\u8be5\u4fdd\u6301\u539f\u6837\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa42. \u8fd9\u4e00\u6b65\u903b\u8f91\u4e0a\u4ece\u524d\u4e00\u6b65\u63a8\u65ad\u800c\u6765\uff0c\u56e0\u4e3a\u5b83\u6d89\u53ca\u5c06Mariah\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u6570\u91cf\u76f8\u52a0\uff0c\u8fd9\u4e9b\u6570\u91cf\u5728\u524d\u4e00\u6b65\u5df2\u7ecf\u8f6c\u6362\u6210\u76f8\u540c\u7684\u5355\u4f4d\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u8ba1\u7b97\u4e86\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u6570\u91cf\uff0c\u8fd9\u662f\u95ee\u9898\u7684\u76ee\u6807\u3002\u5efa\u8bae\uff1a\u65e0\u3002\u63a8\u8350\uff1a\u8fd9\u4e00\u6b65\u662f\u6b63\u786e\u7684\uff0c\u5e94\u8be5\u4fdd\u6301\u539f\u6837\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa41 (\u91cd\u590d). \u8fd9\u4e00\u6b65\u662f\u7b2c\u4e00\u6b65\u7684\u91cd\u590d\uff0c\u4f46\u8ba1\u7b97\u5df2\u5b8c\u6210\u3002\u5b83\u662f\u5bf9\u95ee\u9898\u9648\u8ff0\u7684\u903b\u8f91\u63a8\u65ad\uff0c\u5e76\u4e14\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\u3002\u7136\u800c\uff0c\u5b83\u4e0d\u5e94\u8be5\u5728\u63a8\u7406\u94fe\u4e2d\u91cd\u590d\uff0c\u56e0\u4e3a\u5b83\u6ca1\u6709\u6dfb\u52a0\u65b0\u4fe1\u606f\u6216\u6709\u52a9\u4e8e\u89e3\u51b3\u65b9\u6848\u7684\u8fdb\u5c55\u3002\u5efa\u8bae\uff1a\u4ece\u63a8\u7406\u94fe\u4e2d\u79fb\u9664\u8fd9\u4e2a\u91cd\u590d\u7684\u6b65\u9aa4\u3002\u63a8\u8350\uff1a\u8fd9\u4e00\u6b65\u662f\u6b63\u786e\u7684\uff0c\u4f46\u5197\u4f59\uff0c\u5e94\u8be5\u4ece\u63a8\u7406\u94fe\u4e2d\u79fb\u9664\u3002
      \n\u4fe1\u5fc3\u5f97\u5206\uff1a1.0
      \n### \u7b2c\u4e8c\u8f6e\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c2\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u5448\u73b0\u7684\u63a8\u7406\u6b65\u9aa4\u94fe\uff1a
      \n——————-
      \n**\u6b65\u9aa41**: \u901a\u8fc7\u5c06\u4ed6\u4eec\u4f7f\u7528\u7684\u7eb1\u7ebf\u5206\u6570\u4e58\u4ee5\u4e00\u4e2a\u7eb1\u7ebf\u7684\u603b\u7801\u6570\u6765\u5206\u522b\u8ba1\u7b97Mariah\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0<\/p>\n

      **\u6b65\u9aa41**: \u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u5206\u522b\u8ba1\u7b97Mariah\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4ed6\u4eec\u4f7f\u7528\u7684\u7eb1\u7ebf\u5206\u6570\u4e58\u4ee5\u4e00\u4e2a\u7eb1\u7ebf\u7684\u603b\u7801\u6570\u3002\u6240\u4ee5\uff0cMariah\u4f7f\u7528\u4e861\/4 * 364\u7801\u7684\u7eb1\u7ebf\uff0c\u5979\u7684\u5976\u5976\u4f7f\u7528\u4e861\/2 * 364\u7801\u7684\u7eb1\u7ebf\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0<\/p>\n

      **\u6b65\u9aa42**: \u5728\u5206\u522b\u8ba1\u7b97\u51faMariah\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u4e4b\u540e\uff0c\u6211\u4eec\u9700\u8981\u5c06\u8fd9\u4e9b\u6570\u91cf\u76f8\u52a0\uff0c\u4ee5\u627e\u51fa\u4ed6\u4eec\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u3002\u6240\u4ee5\uff0c\u6211\u4eec\u5c06Mariah\u7684\u7eb1\u7ebf\uff081\/4 * 364\u7801\uff09\u548c\u5979\u5976\u5976\u7684\u7eb1\u7ebf\uff081\/2 * 364\u7801\uff09\u76f8\u52a0\uff0c\u5f97\u5230\u4ed6\u4eec\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n——————-
      \n**\u5206\u6790\u62a5\u544a**: \u63a8\u7406\u94fe\u91cd\u590d\u4e14\u5305\u542b\u5197\u4f59\u9519\u8bef\uff0c\u6b65\u9aa41\u88ab\u91cd\u590d\u4e86\u4e09\u6b21\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u6b65\u9aa4\u672c\u8eab\u903b\u8f91\u6b63\u786e\uff0c\u5bfc\u81f4\u4e86\u95ee\u9898\u7684\u6b63\u786e\u89e3\u51b3\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa41. \u7b2c\u4e00\u6b65\u903b\u8f91\u6b63\u786e\u3002\u5b83\u6b63\u786e\u5730\u8bc6\u522b\u4e86\u9700\u8981\u901a\u8fc7\u5c06\u4ed6\u4eec\u4f7f\u7528\u7684\u7eb1\u7ebf\u5206\u6570\u4e58\u4ee5\u4e00\u4e2a\u7eb1\u7ebf\u7684\u603b\u7801\u6570\u6765\u5206\u522b\u8ba1\u7b97Mariah\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u4e3a\u8ba1\u7b97\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u5960\u5b9a\u4e86\u57fa\u7840\u3002\u5efa\u8bae\uff1a\u65e0\u3002\u63a8\u8350\uff1a\u6279\u51c6<\/p>\n

      \u63a8\u7406\u6b65\u9aa42. \u7b2c\u4e8c\u6b65\u662f\u4ece\u7b2c\u4e00\u6b65\u903b\u8f91\u63a8\u65ad\u800c\u6765\u3002\u5728\u627e\u51faMariah\u548c\u5979\u5976\u5976\u5206\u522b\u4f7f\u7528\u4e86\u591a\u5c11\u7eb1\u7ebf\u4e4b\u540e\uff0c\u5c06\u8fd9\u4e9b\u6570\u91cf\u76f8\u52a0\u4ee5\u627e\u51fa\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u662f\u903b\u8f91\u7684\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u5141\u8bb8\u8ba1\u7b97\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u3002\u5efa\u8bae\uff1a\u65e0\u3002\u63a8\u8350\uff1a\u6279\u51c6<\/p>\n

      \u9519\u8bef\u62a5\u544a\uff1a\u6b65\u9aa41\u91cd\u590d\u4e09\u6b21\u662f\u4e0d\u5fc5\u8981\u7684\uff0c\u5bf9\u89e3\u51b3\u65b9\u6848\u6ca1\u6709\u8d21\u732e\u3002\u5e94\u8be5\u4fee\u6539\u4ee5\u907f\u514d\u5197\u4f59\u3002\u5efa\u8bae\uff1a\u6d88\u9664\u6b65\u9aa41\u7684\u91cd\u590d\u3002\u63a8\u7406\u94fe\u5e94\u8be5\u53ea\u5305\u542b\u5bf9\u89e3\u51b3\u95ee\u9898\u6709\u8d21\u732e\u7684\u72ec\u7279\u6b65\u9aa4\u3002
      \n\u4fe1\u5fc3\u5f97\u5206\uff1a0.9
      \n### \u7b2c\u4e09\u8f6e\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c3\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u5448\u73b0\u7684\u63a8\u7406\u6b65\u9aa4\u94fe\uff1a
      \n——————-
      \n**\u6b65\u9aa41**: \u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97Mariah\u548c\u5979\u5976\u5976\u603b\u5171\u4f7f\u7528\u4e86\u591a\u5c11\u4e2a\u7eb1\u7ebf\u3002Mariah\u4f7f\u7528\u4e861\/4\u4e2a\u7eb1\u7ebf\uff0c\u5979\u7684\u5976\u5976\u4f7f\u7528\u4e861\/2\u4e2a\u7eb1\u7ebf\u3002\u4e3a\u4e86\u627e\u51fa\u4ed6\u4eec\u603b\u5171\u4f7f\u7528\u4e86\u591a\u5c11\u4e2a\u7eb1\u7ebf\uff0c\u6211\u4eec\u9700\u8981\u5c061\/4\u548c1\/2\u76f8\u52a0\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0<\/p>\n

      **\u6b65\u9aa42**: \u5728\u627e\u51fa\u4ed6\u4eec\u603b\u5171\u4f7f\u7528\u4e86\u591a\u5c11\u4e2a\u7eb1\u7ebf\u4e4b\u540e\uff0c\u5c06\u5176\u8f6c\u6362\u4e3a\u7801\u6570\u3002\u6211\u4eec\u77e5\u90531\u4e2a\u7eb1\u7ebf\u7b49\u4e8e364\u7801\u3002\u6240\u4ee5\uff0c\u5c06\u4f7f\u7528\u7684\u603b\u7eb1\u7ebf\u6570\u4e58\u4ee5364\uff0c\u4ee5\u627e\u51fa\u4ed6\u4eec\u4f7f\u7528\u7684\u603b\u7801\u6570\uff08273\uff09\u7684\u7eb1\u7ebf\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n——————-
      \n**\u5206\u6790\u62a5\u544a**: \u63a8\u7406\u94fe\u80fd\u591f\u6b63\u786e\u5b8c\u6210\u4efb\u52a1\u5e76\u8fbe\u5230\u76ee\u6807\u3002\u4efb\u52a1\u662f\u627e\u51faMariah\u548c\u5979\u5976\u5976\u603b\u5171\u4f7f\u7528\u4e86\u591a\u5c11\u7801\u7684\u7eb1\u7ebf\u3002\u63a8\u7406\u94fe\u9996\u5148\u901a\u8fc7\u5c06Mariah\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u5206\u6570\u76f8\u52a0\u6765\u8ba1\u7b97\u51fa\u4ed6\u4eec\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u7684\u5377\u6570\u3002\u7136\u540e\uff0c\u5b83\u5c06\u8fd9\u4e2a\u603b\u7eb1\u7ebf\u6570\u8f6c\u6362\u4e3a\u7801\u6570\uff0c\u8fd9\u662f\u6240\u9700\u7684\u6700\u7ec8\u7b54\u6848\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa41: \u7b2c\u4e00\u6b65\u662f\u903b\u8f91\u63a8\u65ad\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u5730\u8bc6\u522b\u51fa\u89e3\u51b3\u95ee\u9898\u7684\u7b2c\u4e00\u6b65\u662f\u5c06Mariah\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u5206\u6570\u76f8\u52a0\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u4e3a\u4e0b\u4e00\u6b65\u5c06\u7eb1\u7ebf\u8f6c\u6362\u4e3a\u7801\u6570\u5960\u5b9a\u4e86\u57fa\u7840\u3002\u5728\u8fd9\u4e00\u6b65\u4e2d\u6ca1\u6709\u53d1\u73b0\u9519\u8bef\u3002\u5efa\u8bae\uff1a\u7531\u4e8e\u8fd9\u4e00\u6b65\u63a8\u7406\u6b63\u786e\uff0c\u4e0d\u9700\u8981\u5efa\u8bae\u3002\u63a8\u8350\uff1a\u6211\u63a8\u8350\u8fd9\u4e00\u6b65\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u5730\u8bc6\u522b\u4e86\u9996\u5148\u9700\u8981\u8ba1\u7b97\u4f7f\u7528\u7684\u603b\u7eb1\u7ebf\u6570\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa42: \u7b2c\u4e8c\u6b65\u662f\u4ece\u7b2c\u4e00\u6b65\u903b\u8f91\u63a8\u65ad\u800c\u6765\u3002\u5b83\u6b63\u786e\u5730\u8bc6\u522b\u51fa\u9700\u8981\u5c06\u4f7f\u7528\u7684\u603b\u7eb1\u7ebf\u6570\u8f6c\u6362\u4e3a\u7801\u6570\u4ee5\u56de\u7b54\u95ee\u9898\u3002\u8fd9\u4e00\u6b65\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u76f4\u63a5\u5bfc\u81f4\u6700\u7ec8\u7b54\u6848\u3002\u5728\u8fd9\u4e00\u6b65\u4e2d\u6ca1\u6709\u53d1\u73b0\u9519\u8bef\u3002\u5efa\u8bae\uff1a\u7531\u4e8e\u8fd9\u4e00\u6b65\u63a8\u7406\u6b63\u786e\uff0c\u4e0d\u9700\u8981\u5efa\u8bae\u3002<\/p>\n

      \u63a8\u8350\uff1a\u6211\u63a8\u8350\u8fd9\u4e00\u6b65\uff0c\u56e0\u4e3a\u5b83\u6b63\u786e\u5730\u8bc6\u522b\u4e86\u9700\u8981\u5c06\u4f7f\u7528\u7684\u603b\u7eb1\u7ebf\u6570\u8f6c\u6362\u4e3a\u7801\u6570\u3002
      \n\u4fe1\u5fc3\u5f97\u5206\uff1a1.0
      \n### \u7b2c\u516d\u8f6e\u8fed\u4ee3\u83b7\u5f97\u7684\u7ecf\u9a8c
      \n#### \u7b2c6\u6761\u63a8\u7406\u94fe\u53ca\u8bc4\u8bba
      \n\u4ee5\u4e0b\u662f\u6309\u987a\u5e8f\u5448\u73b0\u7684\u63a8\u7406\u6b65\u9aa4\u94fe\uff1a
      \n——————-
      \n**\u6b65\u9aa41**: \u901a\u8fc7\u5c06\u4e00\u4e2a\u7eb1\u7ebf\u7684\u603b\u7801\u6570\u4e58\u4ee5Mariah\u4f7f\u7528\u7684\u5206\u6570\uff081\/4\uff09\u6765\u8ba1\u7b97\u5979\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\uff0c\u540c\u6837\u5730\uff0c\u901a\u8fc7\u5c06\u4e00\u4e2a\u7eb1\u7ebf\u7684\u603b\u7801\u6570\u4e58\u4ee5\u5979\u5976\u5976\u4f7f\u7528\u7684\u5206\u6570\uff081\/2\uff09\u6765\u8ba1\u7b97\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u3002Mariah\u4f7f\u7528\uff1a1\/4 * 364 = 91\u7801\u3002\u5976\u5976\u4f7f\u7528\uff1a1\/2 * 364 = 182\u7801\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0<\/p>\n

      **\u6b65\u9aa42**: \u5c06Mariah\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u548c\u5979\u5976\u5976\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u76f8\u52a0\uff0c\u4ee5\u627e\u51fa\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u3002\u603b\u7eb1\u7ebf\u4f7f\u7528\u91cf = 273\u7801\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0<\/p>\n

      **\u6b65\u9aa43**: \u58f0\u660eMariah\u548c\u5979\u5976\u5976\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u3002Mariah\u548c\u5979\u5976\u5976\u603b\u5171\u4f7f\u7528\u4e86273\u7801\u7684\u7eb1\u7ebf\u3002\u8bc4\u4f30\u5f97\u5206\uff1a1.0
      \n——————-
      \n**\u5206\u6790\u62a5\u544a**: \u63a8\u7406\u94fe\u903b\u8f91\u4e0a\u662f\u5408\u7406\u7684\uff0c\u5e76\u6b63\u786e\u5b8c\u6210\u4e86\u4efb\u52a1\u3002\u63a8\u7406\u94fe\u9996\u5148\u8ba1\u7b97Mariah\u548c\u5979\u5976\u5976\u5404\u81ea\u4f7f\u7528\u4e86\u591a\u5c11\u7eb1\u7ebf\uff0c\u7136\u540e\u5c06\u8fd9\u4e9b\u6570\u91cf\u76f8\u52a0\u4ee5\u627e\u51fa\u603b\u5171\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\uff0c\u6700\u540e\u58f0\u660e\u4e86\u603b\u7eb1\u7ebf\u91cf\u3002<\/p>\n

      \u63a8\u7406\u6b65\u9aa41. \u7b2c\u4e00\u6b65\u662f\u903b\u8f91\u7684\uff0c\u56e0\u4e3a\u5b83\u76f4\u63a5\u5e94\u7528\u4e86\u95ee\u9898\u4e2d\u7ed9\u51fa\u7684\u4fe1\u606f\uff0c\u5e76\u4e14\u5bf9\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u6709\u76ca\uff0c\u56e0\u4e3a\u5b83\u63d0\u4f9b\u4e86\u5404\u81ea\u4f7f\u7528\u7684\u7eb1\u7ebf\u91cf\u3002\u63a8\u8350\uff1a\u8fd9\u4e00\u6b65\u662f\u6b63\u786e\u7684\uff0c\u5e94\u8be5\u4fdd\u6301\u3002<\/p><\/blockquote>\n

      \u886818: BoT\u5bf9\u4e8e\u201c\u739b\u4e3d\u4e9a\u7684\u5976\u5976\u6b63\u5728\u6559\u5979\u7f16\u7ec7\uff0c\u739b\u4e3d\u4e9a\u4f7f\u7528\u4e861\/4\u637b\u7eb1\u7ebf\uff0c\u5979\u7684\u5976\u5976\u4f7f\u7528\u4e861\/2\u637b\u7eb1\u7ebf\uff0c\u4e00\u637b\u7eb1\u7ebf\u957f364\u7801\uff0c\u4ed6\u4eec\u5171\u540c\u4f7f\u7528\u4e86\u591a\u5c11\u7801\u7eb1\u7ebf\uff1f\u201d\u7684\u6210\u529f\u63a8\u7406\u8fc7\u7a0b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

      \u6458\u8981   \u5927\u578b\u8bed\u8a00\u6a21\u578b\uff08LLMs\uff09\u5728\u5e7f\u6cdb\u95ee\u9898\u4e0a\u7684\u63a8\u7406\u6027\u80fd\u4e25\u91cd\u4f9d\u8d56\u4e8e\u94fe\u5f0f\u601d\u7ef4\u63d0\u793a\uff0c\u8fd9\u6d89\u53ca\u5728\u63d0\u793a\u4e2d\u63d0\u4f9b\u4e00\u4e9b\u94fe\u5f0f\u601d\u7ef4\u793a\u8303\u4f5c\u4e3a\u793a\u4f8b\u3002\u6700\u8fd1\u7684\u7814\u7a76\u8868\u660e\uff0c\u4f8b\u5982\u601d\u7ef4\u6811\uff0c\u5df2\u7ecf\u6307\u51fa\u4e86\u63a2\u7d22\u548c\u81ea\u6211\u8bc4\u4f30\u5728\u590d\u6742\u95ee\u9898\u89e3\u51b3\u4e2d\u7684\u63a8\u7406\u6b65\u9aa4\u9009\u62e9\u7684\u91cd\u8981\u6027\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[34],"tags":[],"class_list":["post-1486","post","type-post","status-publish","format-standard","hentry","category-knowledge"],"_links":{"self":[{"href":"https:\/\/www.kdjingpai.com\/de\/wp-json\/wp\/v2\/posts\/1486","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.kdjingpai.com\/de\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kdjingpai.com\/de\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kdjingpai.com\/de\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kdjingpai.com\/de\/wp-json\/wp\/v2\/comments?post=1486"}],"version-history":[{"count":0,"href":"https:\/\/www.kdjingpai.com\/de\/wp-json\/wp\/v2\/posts\/1486\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.kdjingpai.com\/de\/wp-json\/wp\/v2\/media?parent=1486"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kdjingpai.com\/de\/wp-json\/wp\/v2\/categories?post=1486"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kdjingpai.com\/de\/wp-json\/wp\/v2\/tags?post=1486"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}