{"id":215,"date":"2023-08-14T10:59:31","date_gmt":"2023-08-14T02:59:31","guid":{"rendered":"http:\/\/lingbo.online\/?p=215"},"modified":"2023-08-21T14:54:12","modified_gmt":"2023-08-21T06:54:12","slug":"branch_and_bound","status":"publish","type":"post","link":"https:\/\/lingbo.online\/index.php\/algorithm_learning\/branch_and_bound\/","title":{"rendered":"\u5206\u679d\u5b9a\u754c\u6cd5"},"content":{"rendered":"<h3>\u5b9a\u4e49<\/h3>\n<p>\u5206\u652f\u5b9a\u754c\u6cd5\u662f\u4e00\u79cd\u6c42\u89e3\u79bb\u6563\u6700\u4f18\u5316\u95ee\u9898\u7684\u8ba1\u7b97\u5206\u6790\u65b9\u6cd5\uff0c\u7531R.J\u8fbe\u91d1\u548c\u5170\u5fb7-\u591a\u4f0a\u572820\u4e16\u7eaa60\u5e74\u4ee3\u521d\u63d0\u51fa\u3002\u8fd9\u79cd\u65b9\u6cd5\u901a\u80c0\u4ec5\u9700\u8ba1\u7b97\u548c\u5206\u6790\u90e8\u5206\u5141\u8bb8\u89e3\uff0c\u5373\u53ef\u6c42\u5f97\u6700\u4f18\u89e3\u3002\u56e0\u6b64\u5728\u6c42\u89e3\u5206\u6d3e\u95ee\u9898\u548c\u6574\u6570\u89c4\u5212\u95ee\u9898\u65f6\u5e38\u7528\u6b64\u65b9\u6cd5\u3002\u8be5\u65b9\u6cd5\u540c\u6837\u53ef\u4ee5\u7528\u4e8e\u6df7\u5408\u6574\u6570\u89c4\u5212\u95ee\u9898\uff0c\u4ee5\u4e00\u822c\u7ebf\u6027\u89c4\u5212\u4e4b\u5355\u7eaf\u5f62\u6cd5\u89e3\u5f97\u6700\u4f18\u89e3\u540e\uff0c\u5c06\u975e\u6574\u6570\u4e4b\u51b3\u7b56\u53d8\u91cf\u5206\u5272\u4e3a\u6700\u63a5\u8fd1\u7684\u4e24\u4e2a\u6574\u6570\uff0c\u5206\u88c2\u6761\u4ef6\u52a0\u5165\u539f\u95ee\u9898\uff0c\u5f62\u6210\u4e24\u4e2a\u5b50\u95ee\u9898\uff08\u6216\u5206\u652f\uff09\u5206\u522b\u6c42\u89e3\uff0c\u5982\u6b64\u4fbf\u53ef\u6c42\u5f97\u76ee\u6807\u51fd\u6570\u7684\u4e0a\u754c\u6216\u4e0b\u754c\uff0c\u4ece\u4e2d\u5bfb\u5f97\u6700\u4f18\u89e3\u3002<\/p>\n<h3>\u57fa\u672c\u601d\u60f3<\/h3>\n<h4>\u7b97\u6cd5\u601d\u60f3<\/h4>\n<p>\u5206\u679d\u5b9a\u754c\u6cd5\u662f\u4e00\u4e2a\u7528\u9014\u5341\u5206\u5e7f\u6cdb\u7684\u7b97\u6cd5\uff0c\u8fd0\u7528\u8fd9\u79cd\u7b97\u6cd5\u7684\u6280\u5de7\u6027\u5f88\u5f3a\uff0c\u4e0d\u540c\u7c7b\u578b\u7684\u95ee\u9898\u89e3\u6cd5\u4e5f\u5404\u4e0d\u76f8\u540c\u3002\u5206\u652f\u5b9a\u754c\u6cd5\u7684\u57fa\u672c\u601d\u60f3\u662f\u5bf9\u6709\u7ea6\u675f\u6761\u4ef6\u7684\u6700\u4f18\u5316\u95ee\u9898\u7684\u6240\u6709\u53ef\u884c\u89e3\uff08\u6570\u76ee\u6709\u9650\uff09\u7a7a\u95f4\u8fdb\u884c\u641c\u7d22\u3002\u8be5\u7b97\u6cd5\u5728\u5177\u4f53\u6267\u884c\u65f6\uff0c\u628a\u5168\u90e8\u53ef\u884c\u7684\u89e3\u7a7a\u95f4\u4e0d\u65ad\u5206\u5272\u4e3a\u8d8a\u6765\u8d8a\u5c0f\u7684\u5b50\u96c6\uff08\u79f0\u4e3a\u5206\u652f\uff09\uff0c\u5e76\u4e3a\u6bcf\u4e2a\u5b50\u96c6\u5185\u7684\u89e3\u7684\u503c\u8ba1\u7b97\u4e00\u4e2a\u4e0b\u754c\u6216\u4e0a\u754c\uff08\u79f0\u4e3a\u5b9a\u754c\uff09\u3002\u5728\u6bcf\u6b21\u5206\u652f\u540e\uff0c\u5bf9\u51e1\u662f\u754c\u9650\u8d85\u51fa\u5df2\u77e5\u53ef\u884c\u89e3\u503c\u90a3\u4e9b\u5b50\u96c6\u4e0d\u518d\u505a\u8fdb\u4e00\u6b65\u5206\u652f\u3002\u8fd9\u6837\uff0c\u89e3\u7684\u8bb8\u591a\u5b50\u96c6\uff08\u5373\u641c\u7d22\u6811\u4e0a\u7684\u8bb8\u591a\u7ed3\u70b9\uff09\u5c31\u53ef\u4ee5\u4e0d\u4e88\u8003\u8651\u4e86\uff0c\u4ece\u800c\u7f29\u5c0f\u4e86\u641c\u7d22\u8303\u56f4\u3002\u8fd9\u4e00\u8fc7\u7a0b\u4e00\u76f4\u8fdb\u884c\u5230\u627e\u51fa\u53ef\u884c\u89e3\u4e3a\u6b62\uff0c\u8be5\u53ef\u884c\u89e3\u7684\u503c\u4e0d\u5927\u4e8e\u4efb\u4f55\u5b50\u96c6\u7684\u754c\u9650\u3002\u56e0\u6b64\u8fd9\u79cd\u7b97\u6cd5\u4e00\u822c\u53ef\u4ee5\u6c42\u5f97\u6700\u4f18\u89e3\u3002<br \/>\n\u5177\u4f53\u6765\u8bf4\uff0c\u6c42\u89e3\u4e00\u4e2a\u7ea6\u675f\u6761\u4ef6\u8f83\u591a\u7684\u95ee\u9898A,\u53ef\u4ee5\u6682\u7f13\u8003\u8651\u90e8\u5206\u6761\u4ef6\uff0c\u53d8\u6362\u6210\u95ee\u9898B,\u5148\u6c42B\u7684\u6700\u4f18\u89e3\u3002B\u7684\u6700\u4f18\u89e3\u4e00\u5b9a\u6bd4A\u7684\u597d\uff08\u6216\u76f8\u5f53\uff09\u3002\u518d\u5c06\u539f\u6765\u6682\u7f13\u8003\u8651\u7684\u90e8\u5206\u6761\u4ef6\u9010\u6b65\u63d2\u5165\u95ee\u9898B\u4e2d\uff0c\u5f97\u5230B\u7684\u82e5\u5e72\u5b50\u95ee\u9898\uff0c\u79f0\u4e3a\u5206\u679d\u3002\u6c42\u89e3\u8fd9\u4e9b\u5b50\u95ee\u9898\uff0c\u6dd8\u6c70\u8f83\u5dee\u7684\u89e3\uff0c\u76f4\u5230\u6240\u6709\u6682\u7f13\u8003\u8651\u7684\u90e8\u5206\u6761\u4ef6\u5168\u90e8\u63d2\u5165\u4e3a\u6b62\u3002\u8fd9\u65f6\u6c42\u5f97\u7684\u6700\u4f18\u89e3\u5c31\u662f\u95ee\u9898A\u7684\u6700\u4f18\u89e3\u3002<\/p>\n<h4>\u5206\u652f\u8282\u70b9\u7684\u9009\u62e9<\/h4>\n<p>\u5bf9\u641c\u7d22\u6811\u4e0a\u7684\u67d0\u4e9b\u70b9\u5fc5\u987b\u4f5c\u51fa\u5206\u679d\u51b3\u7b56\uff0c\u5373\u51e1\u662f\u754c\u9650\u5c0f\u4e8e\u8fc4\u4eca\u4e3a\u6b62\u6240\u6709\u53ef\u884c\u89e3\u6700\u5c0f\u4e0b\u754c\u7684\u4efb\u4f55\u5b50\u96c6\uff08\u8282\u70b9\uff09\uff0c\u90fd\u6709\u53ef\u80fd\u4f5c\u4e3a\u5206\u679d\u7684\u9009\u62e9\u5bf9\u8c61\uff08\u5bf9\u6c42\u6700\u5c0f\u503c\u95ee\u9898\u800c\u8a00\uff09\u3002\u600e\u6837\u9009\u62e9\u641c\u7d22\u6811\u4e0a\u7684\u8282\u70b9\u4f5c\u4e3a\u4e0b\u6b21\u5206\u679d\u7684\u8282\u70b9\u5462\uff1f\u6709\u4e24\u4e2a\u539f\u5219\uff1a<\/p>\n<ul>\n<li>\n<p>\u4ece\u6700\u5c0f\u4e0b\u754c\u5206\u679d\uff08\u961f\u5217\u5f0fFIFO\u5206\u679d\u9650\u754c\u6cd5\uff09\uff1a\u6bcf\u6b21\u7b97\u5b8c\u754c\u9650\u540e\uff0c\u628a\u641c\u7d22\u6811\u4e0a\u5f53\u524d\u6240\u6709\u53f6\u8282\u70b9\u7684\u754c\u9650\u8fdb\u884c\u6bd4\u8f83\u3002\u627e\u51fa\u9650\u754c\u6700\u5c0f\u7684\u8282\u70b9\uff0c\u6b64\u7ed3\u70b9\u5373\u4e3a\u4e0b\u6b21\u5206\u679d\u7684\u7ed3\u70b9\u3002<\/p>\n<ul>\n<li>\u4f18\u70b9\uff1a\u68c0\u67e5\u5b50\u95ee\u9898\u8f83\u5c11\uff0c\u80fd\u8f83\u5feb\u5730\u6c42\u5f97\u6700\u4f73\u89e3\uff1b<\/li>\n<li>\u7f3a\u70b9\uff1a\u8981\u5b58\u50a8\u5f88\u591a\u53f6\u8282\u70b9\u7684\u754c\u9650\u53ca\u5bf9\u5e94\u7684\u8017\u8d39\u77e9\u9635\uff0c\u82b1\u8d39\u5f88\u591a\u5185\u5b58\u7a7a\u95f4\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u4ece\u6700\u65b0\u4ea7\u751f\u7684\u6700\u5c0f\u4e0b\u754c\u5206\u679d\uff08\u4f18\u5148\u961f\u5217\u5f0f\u5206\u679d\u9650\u754c\u6cd5\uff09\uff1a\u4ece\u6700\u65b0\u4ea7\u751f\u7684\u5404\u5b50\u96c6\u4e2d\u9009\u62e9\u5177\u6709\u6700\u5c0f\u7684\u4e0b\u754c\u7684\u7ed3\u70b9\u8fdb\u884c\u5206\u679d\u3002<\/p>\n<ul>\n<li>\u4f18\u70b9\uff1a\u8282\u7701\u4e86\u7a7a\u95f4\uff1b<\/li>\n<li>\u7f3a\u70b9\uff1a\u9700\u8981\u8f83\u591a\u7684\u5206\u679d\u8fd0\u7b97\uff0c\u8017\u8d39\u7684\u65f6\u95f4\u8f83\u591a\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u8fd9\u4e24\u4e2a\u539f\u5219\u66f4\u8fdb\u4e00\u6b65\u8bf4\u660e\u4e86\uff0c\u5728\u7b97\u6cd5\u8bbe\u8ba1\u4e2d\u7684\u65f6\u7a7a\u8f6c\u6362\u6982\u5ff5\u3002\u5206\u679d\u5b9a\u754c\u6cd5\u5df2\u7ecf\u6210\u529f\u5730\u5e94\u7528\u4e8e\u6c42\u89e3\u6574\u6570\u89c4\u5212\u95ee\u9898\u3001\u751f\u4ea7\u8fdb\u5ea6\u8868\u95ee\u9898\u3001\u8d27\u90ce\u62c5\u95ee\u9898\u3001\u9009\u5740\u95ee\u9898\u3001\u80cc\u5305\u95ee\u9898\u4ee5\u53ca\u53ef\u884c\u89e3\u7684\u6570\u76ee\u4e3a\u6709\u9650\u7684\u8bb8\u591a\u5176\u5b83\u95ee\u9898\u3002\u5bf9\u4e8e\u4e0d\u540c\u7684\u95ee\u9898\uff0c\u5206\u679d\u4e0e\u754c\u9650\u7684\u6b65\u9aa4\u548c\u5185\u5bb9\u53ef\u80fd\u4e0d\u540c\uff0c\u4f46\u57fa\u672c\u539f\u7406\u662f\u4e00\u6837\u7684\u3002<\/p>\n<h3>\u89e3\u6cd5\u6b65\u9aa4<\/h3>\n<p>\u5206\u652f\u5b9a\u754c\u6cd5\u7684\u6b65\u9aa4\u5982\u4e0b\u6240\u8ff0\uff1a<\/p>\n<ol>\n<li>\n<p>\u5982\u679c\u95ee\u9898\u7684\u76ee\u6807\u4e3a\u6700\u5c0f\u5316\uff0c\u5219\u8bbe\u5b9a\u76ee\u524d\u6700\u4f18\u89e3\u7684\u503c<span class=\"katex-eq\" data-katex-display=\"false\">Z=\\infty<\/span>\uff1b<\/p>\n<\/li>\n<li>\n<p>\u6839\u636e\u5206\u679d\u6cd5\u5219\uff08Branching rule\uff09\uff0c\u4ece\u5c1a\u672a\u88ab\u6d1e\u6089\uff08Fathomed\uff09\u8282\u70b9\uff08\u5c40\u90e8\u89e3\uff09\u4e2d\u9009\u62e9\u4e00\u4e2a\u8282\u70b9\uff0c\u5e76\u5728\u6b64\u8282\u70b9\u7684\u4e0b\u4e00\u9636\u5c42\u4e2d\u5206\u4e3a\u51e0\u4e2a\u65b0\u7684\u8282\u70b9\uff1b<\/p>\n<\/li>\n<li>\n<p>\u8ba1\u7b97\u6bcf\u4e00\u4e2a\u65b0\u5206\u679d\u51fa\u6765\u8282\u70b9\u7684\u4e0b\u9650\u503c\uff08Lower bound\uff0cLB\uff09\uff1b<\/p>\n<\/li>\n<li>\n<p>\u5bf9\u6bcf\u4e00\u8282\u70b9\u8fdb\u884c\u6d1e\u6089\u6761\u4ef6\u6d4b\u8bd5\uff0c\u82e5\u8282\u70b9\u6ee1\u8db3\u4ee5\u4e0b\u4efb\u610f\u4e00\u4e2a\u6761\u4ef6\uff0c\u5219\u6b64\u8282\u70b9\u53ef\u6d1e\u6089\u800c\u4e0d\u518d\u88ab\u8003\u8651<\/p>\n<ul>\n<li>\u6b64\u8282\u70b9\u7684\u4e0b\u9650\u503c\u5927\u4e8e\u7b49\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">Z<\/span>\u503c\uff1b<\/li>\n<li>\u5df2\u627e\u5230\u5728\u6b64\u8282\u70b9\u4e2d\uff0c\u5177\u6700\u5c0f\u4e0b\u9650\u503c\u7684\u53ef\u884c\u89e3\uff1b\u82e5\u6b64\u6761\u4ef6\u6210\u7acb\uff0c\u5219\u9700\u6bd4\u8f83\u6b64\u53ef\u884c\u89e3\u4e0eZ\u503c\uff0c\u82e5\u524d\u8005\u8f83\u5c0f\uff0c\u5219\u9700\u66f4\u65b0Z\u503c\uff0c\u4ee5\u6b64\u4e3a\u53ef\u884c\u89e3\u7684\u503c\uff1b<\/li>\n<li>\u6b64\u8282\u70b9\u4e0d\u53ef\u80fd\u5305\u542b\u53ef\u884c\u89e3\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u5224\u65ad\u662f\u5426\u4ecd\u6709\u5c1a\u672a\u88ab\u6d1e\u6089\u7684\u8282\u70b9\uff0c\u5982\u679c\u6709\uff0c\u5219\u8fdb\u884c\u6b65\u9aa4\u4e8c\uff0c\u5982\u679c\u5df2\u65e0\u5c1a\u672a\u88ab\u6d1e\u6089\u7684\u8282\u70b9\uff0c\u5219\u6f14\u7b97\u505c\u6b62\uff0c\u5e76\u5f97\u5230\u6700\u4f18\u89e3<\/p>\n<\/li>\n<\/ol>\n<figure id=\"attachment_216\" aria-describedby=\"caption-attachment-216\" style=\"width: 1702px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/\u5206\u652f\u5b9a\u754c\u6cd5.jpg\" alt=\"\" width=\"1702\" height=\"542\" class=\"size-full wp-image-216\" srcset=\"http:\/\/youpaiyun.lingbo.online\/2023\/08\/\u5206\u652f\u5b9a\u754c\u6cd5.jpg 1702w, http:\/\/youpaiyun.lingbo.online\/2023\/08\/\u5206\u652f\u5b9a\u754c\u6cd5-300x96.jpg 300w, http:\/\/youpaiyun.lingbo.online\/2023\/08\/\u5206\u652f\u5b9a\u754c\u6cd5-1024x326.jpg 1024w, http:\/\/youpaiyun.lingbo.online\/2023\/08\/\u5206\u652f\u5b9a\u754c\u6cd5-768x245.jpg 768w, http:\/\/youpaiyun.lingbo.online\/2023\/08\/\u5206\u652f\u5b9a\u754c\u6cd5-1536x489.jpg 1536w\" sizes=\"auto, (max-width: 1702px) 100vw, 1702px\" \/><figcaption id=\"caption-attachment-216\" class=\"wp-caption-text\">\u5206\u679d\u5b9a\u754c\u7b97\u6cd5\u6d41\u7a0b<\/figcaption><\/figure>\n<h3>\u6848\u4f8b\u5206\u6790<\/h3>\n<p>\u6c42\u89e3\u4e0b\u9762\u7684\u6574\u6570\u89c4\u5212\u95ee\u9898\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/\u6848\u4f8b.jpg\" alt=\"\" \/><\/p>\n<p>\u89e3\uff1a\u9996\u5148\u4e0d\u8003\u8651\u6574\u6570\u6761\u4ef6\uff085\uff09\uff0c\u6c42\u89e3\u76f8\u5e94\u7684\u7ebf\u6027\u89c4\u5212\u95ee\u9898L\uff0c\u5f97\u5230\u6700\u4f18\u89e3\uff1a<\/p>\n<p>$$x_1=4.81,x_2=1.82,Z_0=356$$<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/g0206.jpg\" alt=\"\" \/><\/p>\n<p>\u8be5\u89e3\u4e0d\u662f\u6574\u6570\u89e3\u3002\u9009\u62e9\u5176\u4e2d\u4e00\u4e2a\u975e\u6574\u6570\u53d8\u91cf\uff0c\u5982<span class=\"katex-eq\" data-katex-display=\"false\">x_1=4.81<\/span>\uff0c\u5bf9\u95ee\u9898L\u5206\u522b\u589e\u52a0\u7ea6\u675f\u6761\u4ef6\uff1a<br \/>\n<span class=\"katex-eq\" data-katex-display=\"false\">x_1\\leq4,x_1\\geq5<\/span>\u5c06\u95ee\u9898L\u5206\u89e3\u4e3a\u4e24\u4e2a\u5b50\u95ee\u9898<span class=\"katex-eq\" data-katex-display=\"false\">L_1,L_2<\/span>\uff08\u5206\u679d\uff09\uff0c\u4e5f\u5c31\u662f\u53bb\u6389\u95ee\u9898L\u4e0d\u542b\u6574\u6570\u89e3\u7684\u4e00\u90e8\u5206\u53ef\u884c\u57df\uff0c\u5c06\u539f\u53ef\u884c\u57df<span class=\"katex-eq\" data-katex-display=\"false\">D<\/span>\u53d8\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">D_1,D_2<\/span>\u4e24\u4e2a\u90e8\u5206\uff0c\u5982\u56fe\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/g0207.jpg\" alt=\"\" \/><\/p>\n<p>\u56e0\u4e3a\u6ca1\u6709\u5f97\u5230\u6574\u6570\u89e3\uff0c\u6240\u4ee5\u5bf9<span class=\"katex-eq\" data-katex-display=\"false\">L_1<\/span>\u8fdb\u884c\u5206\u89e3\uff0c\u589e\u52a0\u7ea6\u675f<span class=\"katex-eq\" data-katex-display=\"false\">x_1\\leq2,x_1\\geq3<\/span>\u5c06<span class=\"katex-eq\" data-katex-display=\"false\">L_1<\/span>\u5206\u89e3\u4e3a\u95ee\u9898<span class=\"katex-eq\" data-katex-display=\"false\">L_3<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">L_4<\/span>\uff0c\u5e76\u4e14\u6c42\u5f97\u6700\u4f18\u89e3\u5982\u4e0b\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/g0208.jpg\" alt=\"\" \/><\/p>\n<p>\u95ee\u9898<span class=\"katex-eq\" data-katex-display=\"false\">L_3<\/span>\u7684\u89e3\u5df2\u7ecf\u662f\u6574\u6570\u89e3\uff0c\u5b83\u7684\u76ee\u6807\u503c<span class=\"katex-eq\" data-katex-display=\"false\">Z_3=340<\/span>,\u5927\u4e8e\u95ee\u9898<span class=\"katex-eq\" data-katex-display=\"false\">L_4<\/span>\u7684\u76ee\u6807\u503c\uff0c\u6240\u4ee5\u95ee\u9898<span class=\"katex-eq\" data-katex-display=\"false\">L_4<\/span>\u5df2\u7ecf\u65e0\u5fc5\u8981\u518d\u5206\u679d\u3002\u4f46\u7531\u4e8e\u95ee\u9898<span class=\"katex-eq\" data-katex-display=\"false\">L_2<\/span>\u7684\u76ee\u6807\u503c<span class=\"katex-eq\" data-katex-display=\"false\">Z_2<\/span>\u5927\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">Z_3<\/span>,\u5206\u89e3<span class=\"katex-eq\" data-katex-display=\"false\">L_2<\/span>\u8fd8\u6709\u53ef\u80fd\u4ea7\u751f\u66f4\u597d\u7684\u6574\u6570\u89e3\uff0c\u56e0\u6b64\u7ee7\u7eed\u5bf9<span class=\"katex-eq\" data-katex-display=\"false\">L_2<\/span>\u5206\u679d\u3002\u589e\u52a0\u7ea6\u675f<span class=\"katex-eq\" data-katex-display=\"false\">x_2\\leq1,x_2\\geq2<\/span>\u5c06<span class=\"katex-eq\" data-katex-display=\"false\">L_2<\/span>\u5206\u89e3\u6210\u95ee\u9898<span class=\"katex-eq\" data-katex-display=\"false\">L_5<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">L_6<\/span>\uff0c\u5e76\u6c42\u89e3\uff0c\u7ed3\u679c\u5982\u4e0b\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/g0209.jpg\" alt=\"\" \/><\/p>\n<p>\u95ee\u9898<span class=\"katex-eq\" data-katex-display=\"false\">L_5<\/span>\u7684<span class=\"katex-eq\" data-katex-display=\"false\"><\/span>Z_5=308<Z_3=340[\/latex]\uff0c\u6240\u4ee5\u4e0d\u5fc5\u5206\u89e3\u4e86\uff1b\u95ee\u9898[latex]L_6[\/latex]\u65e0\u53ef\u884c\u89e3\uff0c\u4e8e\u662f\u53ef\u4ee5\u65ad\u5b9a\u95ee\u9898[latex]L_3[\/latex]\u7684\u89e3\uff1a[latex]x_1=4.00,x_2=2.00[\/latex]\uff0c\u5373\u4e3a\u6700\u4f18\u6574\u6570\u89e3\u3002\n\u6574\u4e2a\u5206\u652f\u5b9a\u754c\u6cd5\u8fc7\u7a0b\u5982\u56fe\u6240\u793a\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/g0211.jpg\" alt=\"\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9a\u4e49 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&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[2,31],"tags":[18,10,17],"class_list":["post-215","post","type-post","status-publish","format-standard","hentry","category-algorithm_learning","category-operations","tag-18","tag-10","tag-17"],"_links":{"self":[{"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/posts\/215","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/comments?post=215"}],"version-history":[{"count":3,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/posts\/215\/revisions"}],"predecessor-version":[{"id":225,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/posts\/215\/revisions\/225"}],"wp:attachment":[{"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/media?parent=215"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/categories?post=215"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/tags?post=215"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}