{"id":88583,"date":"2026-08-01T12:56:29","date_gmt":"2026-08-01T04:56:29","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/88583.html"},"modified":"2026-08-01T12:56:29","modified_gmt":"2026-08-01T04:56:29","slug":"%e4%b8%87%e5%ad%97%e4%b9%a6%e7%b1%8d%e9%80%9f%e9%80%9a%e4%b9%8b%e3%80%8a%e7%ae%97%e6%b3%95%e8%ae%be%e8%ae%a1%e4%b8%8e%e5%88%86%e6%9e%90%e3%80%8b%e6%80%bb-%e9%87%8d%e7%82%b9%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/88583.html","title":{"rendered":"\u4e07\u5b57\u4e66\u7c4d\u901f\u901a\u4e4b\u300a\u7b97\u6cd5\u8bbe\u8ba1\u4e0e\u5206\u6790\u300b(\u603b) + \u91cd\u70b9\u7b97\u6cd5\u5206\u6587\u7ae0\u8be6\u89e3"},"content":{"rendered":"

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\n

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\n

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\n

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\n

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\n

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    \n
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      \n
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      \n

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        \n
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      • \u95ee\u9898\u5f52\u7ea6\u601d\u60f3：\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\u7684\u5b9a\u4e49\u3001\u4f20\u9012\u6027\u3001\u5f52\u7ea6\u94fe（SAT\u21923-SAT\u2192CLIQUE\u2192VERTEX-COVER\u2192HAM-CYCLE\u2192TSP）<\/li>\n
      • \u7ecf\u5178NPC\u95ee\u9898\u8be6\u89e3：\u54c8\u5bc6\u987f\u56de\u8def（\u66b4\u529b\/Held-Karp DP）\u3001TSP（\u5224\u5b9a\u7248NPC vs \u4f18\u5316\u7248NP-Hard）\u3001\u5b50\u96c6\u548c（\u5f31NPC\u7279\u6027\u4e0e\u4f2a\u591a\u9879\u5f0f\u7b97\u6cd5）<\/li>\n
      • \u6807\u51c6\u65b9\u6cd5\u8bba：\u8bc1\u660e\u4e00\u4e2a\u95ee\u9898\u5c5e\u4e8eNPC\u7684"\u4e24\u6b65\u6cd5"\u6a21\u677f（\u2208NP + \u5df2\u77e5NPC\u2264\u209a\u5b83），\u9644\u9876\u70b9\u8986\u76d6\u5b8c\u6574\u8bc1\u660e<\/li>\n
      • 7\u9053\u5e38\u89c1\u7b80\u7b54\/\u8bba\u8ff0\u9898\u7cbe\u8bb2（\u542b\u6807\u51c6\u7b54\u6848）<\/li>\n
      • P vs NP\u5343\u79a7\u5e74\u95ee\u9898\u3001\u91cf\u5b50\u8ba1\u7b97\u4e0eNP\u7684\u73b0\u5b9e\u610f\u4e49\u8ba8\u8bba<\/li>\n<\/ul>\n
        \n

        \u7b97\u6cd5\u8bbe\u8ba1\u4e0e\u5206\u6790：\u56de\u6eaf\u6cd5\u6df1\u5ea6\u89e3\u6790\u2014\u2014\u89e3\u7a7a\u95f4\u6811\u3001\u526a\u679d\u6280\u5de7\u4e0e\u7ecf\u5178\u95ee\u9898\u5b9e\u6218<\/h4>\n

        \u7bc7\u5e45：\u7ea612000\u5b57 \u00b7 12\u8282<\/p>\n

        \u6838\u5fc3\u4eae\u70b9：<\/p>\n

          \n
        • \u89e3\u7a7a\u95f4\u6811\u7684\u4e24\u79cd\u57fa\u672c\u7c7b\u578b：\u5b50\u96c6\u6811（\n

          O<\/p>\n

          (<\/p>\n

          2<\/p>\n

          n<\/p>\n

          )<\/p>\n

          O(2^n)<\/p>\n

          <\/span><\/span>O<\/span>(<\/span>2<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u4e8c\u53c9\u6811）\u4e0e\u6392\u5217\u6811（<\/p>\n

          O<\/p>\n

          (<\/p>\n

          n<\/p>\n

          !<\/p>\n

          )<\/p>\n

          O(n!)<\/p>\n

          <\/span><\/span>O<\/span>(<\/span>n<\/span>!)<\/span><\/span><\/span><\/span><\/span>\u591a\u53c9\u6811），\u9644\u5b8c\u6574\u56fe\u793a<\/li>\n

        • \u516d\u5927\u526a\u679d\u7b56\u7565\u8be6\u89e3：\u53ef\u884c\u6027\u526a\u679d\u3001\u5bf9\u79f0\u6027\u526a\u679d\u3001\u6392\u5e8f\u526a\u679d\u3001\u53bb\u91cd\u526a\u679d\u3001\u4e0a\u4e0b\u754c\u526a\u679d\u3001\u8bb0\u5fc6\u5316\u526a\u679d<\/li>\n
        • \u56db\u5927\u7ecf\u5178\u95ee\u9898\u5b9e\u6218（C++\/Python\u53cc\u8bed\u8a00）：\n
            \n
          • N\u7687\u540e：\u6392\u5217\u6811 + \u5217\/\u5bf9\u89d2\u7ebf\n

            O<\/p>\n

            (<\/p>\n

            1<\/p>\n

            )<\/p>\n

            O(1)<\/p>\n

            <\/span><\/span>O<\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span>\u68c0\u67e5（\u5b9e\u9645\u641c\u7d22\u22482057\u8282\u70b9 vs 8!=40320）<\/li>\n

          • \u5b50\u96c6\u548c：\u5b50\u96c6\u6811 + \u6392\u5e8f + \u540e\u7f00\u548c\u4e0a\u4e0b\u754c\u526a\u679d<\/li>\n
          • \u56fe\u7740\u8272：k\u53c9\u6811 + \u90bb\u63a5\u7ea6\u675f + MRV\u542f\u53d1\u5f0f<\/li>\n
          • \u5168\u6392\u5217：\u4ea4\u6362\u6cd5\/\u6807\u8bb0\u6cd5 + \u53bb\u91cd\u526a\u679d<\/li>\n<\/ul>\n<\/li>\n
          • \u901a\u7528\u6a21\u677f（Python\/C++）+ \u5de5\u7a0b\u5b9e\u8df5\u6ce8\u610f\u4e8b\u9879<\/li>\n
          • \u56de\u6eaf\u6cd5 vs DP \/ \u5206\u652f\u9650\u754c \/ \u8d2a\u5fc3 \u5168\u65b9\u4f4d\u5bf9\u6bd4\u8868<\/li>\n
          • 10\u9053LeetCode\u63a8\u8350\u7ec3\u4e60\u9898<\/li>\n<\/ul>\n
            \n

            \u7b97\u6cd5\u8bbe\u8ba1\u4e0e\u5206\u6790：\u5206\u6cbb\u6cd5\u5168\u9762\u8be6\u89e3\u2014\u2014\u4ece\u7406\u8bba\u5230\u5b9e\u6218<\/h4>\n

            \u7bc7\u5e45：\u7ea612000\u5b57 \u00b7 11\u8282<\/p>\n

            \u6838\u5fc3\u4eae\u70b9：<\/p>\n

              \n
            • \u5206\u6cbb\u6cd5\u6838\u5fc3\u4e09\u6b65（\u5206\u2192\u6cbb\u2192\u5408）\u7684\u9012\u5f52\u7ed3\u6784\u56fe\u4e0e\u9002\u7528\u6761\u4ef6<\/li>\n
            • \u4e3b\u5b9a\u7406（Master Theorem）\u4e09\u79cd\u60c5\u51b5\u7684\u5b8c\u6574\u63a8\u5bfc + \u9012\u5f52\u6811\u65b9\u6cd5<\/li>\n
            • \u56db\u5927\u7ecf\u5178\u7b97\u6cd5\u6df1\u5ea6\u5256\u6790：\n
                \n
              • \u5f52\u5e76\u6392\u5e8f：\u91cd\u5728"\u5408"（Merge），\u7a33\u5b9a\n

                O<\/p>\n

                (<\/p>\n

                n<\/p>\n

                log<\/p>\n

                \u2061<\/p>\n

                n<\/p>\n

                )<\/p>\n

                O(n\\\\log n)<\/p>\n

                <\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>log<\/span><\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u9002\u5408\u5916\u90e8\u6392\u5e8f<\/li>\n

              • \u5feb\u901f\u6392\u5e8f：\u91cd\u5728"\u5206"（Partition），\u968f\u673a\u5316\/\u4e09\u6570\u53d6\u4e2d\u907f\u514d\u6700\u574f\n

                O<\/p>\n

                (<\/p>\n

                n<\/p>\n

                2<\/p>\n

                )<\/p>\n

                O(n^2)<\/p>\n

                <\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/li>\n

              • \u6700\u8fd1\u70b9\u5bf9：\u6309x\u5750\u6807\u7b49\u5206 + \u5e26\u72b6\u533a\u57df（\u22647\u70b9\u5b9a\u7406），\n

                O<\/p>\n

                (<\/p>\n

                n<\/p>\n

                log<\/p>\n

                \u2061<\/p>\n

                n<\/p>\n

                )<\/p>\n

                O(n\\\\log n)<\/p>\n

                <\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>log<\/span><\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span><\/li>\n

              • \u6700\u5927\u5b50\u6570\u7ec4：\u4e09\u5206\u5408\u5e76（\u5de6\/\u53f3\/\u8de8\u8d8a\u4e2d\u70b9），\u5bf9\u6bd4Kadane \n

                O<\/p>\n

                (<\/p>\n

                n<\/p>\n

                )<\/p>\n

                O(n)<\/p>\n

                <\/span><\/span>O<\/span>(<\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n

              • \u5f52\u5e76 vs \u5feb\u6392 \u6838\u5fc3\u5bf9\u6bd4：\u65f6\u95f4\u7a33\u5b9a\u6027\u3001\u7a7a\u95f4\u3001\u7f13\u5b58\u6027\u80fd\u3001\u9002\u7528\u573a\u666f<\/li>\n
              • \u5206\u6cbb\u6cd5 vs DP \/ \u8d2a\u5fc3 \/ \u56de\u6eaf \u7684\u5224\u65ad\u51c6\u5219<\/li>\n
              • \u4f18\u5316\u6280\u5de7：\u5c0f\u95ee\u9898\u5207\u6362\u63d2\u5165\u6392\u5e8f\u3001\u5c3e\u9012\u5f52\u4f18\u5316\u3001\u5e76\u884c\u5316<\/li>\n
              • \u5b9e\u6218\u7ec3\u4e60：\u9006\u5e8f\u5bf9\u8ba1\u6570\u3001Karatsuba\u5927\u6574\u6570\u4e58\u6cd5\u3001\u68cb\u76d8\u8986\u76d6<\/li>\n<\/ul>\n
                \n

                \u7b97\u6cd5\u8bbe\u8ba1\u4e0e\u5206\u6790：\u5206\u652f\u9650\u754c\u6cd5\u8be6\u89e3\u2014\u2014\u4ece\u539f\u7406\u5230\u5b9e\u6218\u5168\u9762\u5256\u6790<\/h4>\n

                \u7bc7\u5e45：\u7ea612000\u5b57 \u00b7 12\u8282<\/p>\n

                \u6838\u5fc3\u4eae\u70b9：<\/p>\n

                  \n
                • \u5206\u652f\u9650\u754c\u6cd5\u4e09\u8981\u7d20（\u5206\u652f\/\u9650\u754c\/\u641c\u7d22）\u4e0e\u6d3b\u8282\u70b9\/\u6b7b\u8282\u70b9\/E-\u8282\u70b9\u6982\u5ff5<\/li>\n
                • \u4e24\u79cd\u641c\u7d22\u7b56\u7565\u5bf9\u6bd4：\u961f\u5217\u5f0fFIFO（BFS）vs \u4f18\u5148\u961f\u5217\u5f0fLC（\u6700\u4f73\u4f18\u5148），\u9644\u641c\u7d22\u8fc7\u7a0b\u56fe\u89e3<\/li>\n
                • \u9650\u754c\u51fd\u6570\u8bbe\u8ba1\u4e09\u5927\u65b9\u6cd5：\u8d2a\u5fc3\u677e\u5f1b（\u80cc\u5305）\u3001\u4ee3\u4ef7\u77e9\u9635\u5f52\u7ea6（TSP）\u3001\u7b80\u5355\u4f30\u8ba1<\/li>\n
                • \u5206\u652f\u9650\u754c\u6cd5 vs \u56de\u6eaf\u6cd5 \u5168\u65b9\u4f4d\u5bf9\u6bd4（\u641c\u7d22\u7b56\u7565\/\u76ee\u6807\/\u6570\u636e\u7ed3\u6784\/\u7a7a\u95f4\u590d\u6742\u5ea6\/\u9002\u7528\u95ee\u9898）<\/li>\n
                • \u4e24\u5927\u7ecf\u5178\u6848\u4f8b\u5b8c\u6574\u4ee3\u7801（C++）：\n
                    \n
                  • 0\/1\u80cc\u5305：\u5206\u6570\u80cc\u5305\u4e0a\u754c + \u4f18\u5148\u961f\u5217，\u9644\u624b\u5199\u6a21\u62df\u5168\u8fc7\u7a0b<\/li>\n
                  • TSP：\u884c\u5217\u5f52\u7ea6\u4e0b\u754c + \u5b50\u56de\u8def\u9632\u6b62 + \u4f18\u5148\u961f\u5217\u641c\u7d22<\/li>\n<\/ul>\n<\/li>\n
                  • \u526a\u679d\u4f18\u5316\u516d\u5927\u6280\u5de7：\u9650\u754c\u526a\u679d\u3001\u53ef\u884c\u6027\u526a\u679d\u3001\u5bf9\u79f0\u6027\u526a\u679d\u3001\u652f\u914d\u526a\u679d\u3001\u9884\u5904\u7406\u6392\u5e8f\u3001\u521d\u59cb\u89e3\u83b7\u53d6<\/li>\n
                  • \u9ad8\u9891\u8003\u70b9\u4e0e\u6613\u9519\u70b9\u603b\u7ed3 + \u624b\u5199\u6a21\u62df\u9898\u6a21\u677f<\/li>\n
                  • \u5de5\u7a0b\u5e94\u7528\u62d3\u5c55：\u6574\u6570\u89c4\u5212（CPLEX\/Gurobi）\u3001A*\u641c\u7d22\u3001\u5206\u652f\u5b9a\u4ef7\u5207\u5272\u6cd5<\/li>\n<\/ul>\n
                    \n

                    🗺\ufe0f \u7cfb\u5217\u77e5\u8bc6\u56fe\u8c31<\/h3>\n

                    \u300a\u7b97\u6cd5\u8bbe\u8ba1\u4e0e\u5206\u6790\u300b\u5168\u7cfb\u5217
                    \n\u2502
                    \n\u251c\u2500\u2500 📘 \u4e07\u5b57\u901f\u901a（\u5168\u4e6611\u7ae0\u6982\u89c8，\u7ea63\u4e07\u5b57）
                    \n\u2502 \u251c\u2500\u2500 （1）\u7b2c1~5\u7ae0：\u57fa\u7840\u7b97\u6cd5\u8bbe\u8ba1\u8303\u5f0f
                    \n\u2502 \u251c\u2500\u2500 （2）\u7b2c6~8\u7ae0：\u9ad8\u7ea7\u7b56\u7565\u4e0e\u8ba1\u7b97\u590d\u6742\u6027
                    \n\u2502 \u2514\u2500\u2500 （3）\u7b2c9~11\u7ae0：\u4e13\u9898\u4e0e\u524d\u6cbf
                    \n\u2502
                    \n\u2514\u2500\u2500 📗 \u4e13\u9898\u6df1\u5ea6\u89e3\u6790（6\u7bc7，\u6bcf\u7bc7\u7ea612000\u5b57）
                    \n \u251c\u2500\u2500 \u8d2a\u5fc3\u7b97\u6cd5 \u2500\u2500\u2500 \u4e24\u5927\u6761\u4ef6 + \u56db\u5927\u6848\u4f8b + \u6b63\u786e\u6027\u8bc1\u660e
                    \n \u251c\u2500\u2500 \u52a8\u6001\u89c4\u5212 \u2500\u2500\u2500 \u56db\u5927\u6a21\u578b + \u4e09\u5927\u5fc5\u8003 + \u4f18\u5316\u6280\u5de7
                    \n \u251c\u2500\u2500 NP\u5b8c\u5168\u7406\u8bba \u2500\u2500 \u56db\u7c7b\u95ee\u9898 + \u5f52\u7ea6\u65b9\u6cd5 + NPC\u8bc1\u660e
                    \n \u251c\u2500\u2500 \u56de\u6eaf\u6cd5 \u2500\u2500\u2500\u2500\u2500 \u89e3\u7a7a\u95f4\u6811 + \u516d\u5927\u526a\u679d + \u56db\u5927\u95ee\u9898
                    \n \u251c\u2500\u2500 \u5206\u6cbb\u6cd5 \u2500\u2500\u2500\u2500\u2500 \u4e3b\u5b9a\u7406 + \u56db\u5927\u7b97\u6cd5 + \u7b56\u7565\u5bf9\u6bd4
                    \n \u2514\u2500\u2500 \u5206\u652f\u9650\u754c\u6cd5 \u2500\u2500 \u641c\u7d22\u7b56\u7565 + \u9650\u754c\u8bbe\u8ba1 + \u4e24\u5927\u6848\u4f8b<\/p>\n

                    \n

                    📋 \u5efa\u8bae\u9605\u8bfb\u987a\u5e8f<\/h3>\n\n\u9636\u6bb5\u9605\u8bfb\u5185\u5bb9\u76ee\u6807<\/tr>\n\n\n\n\n\n
                    \u7b2c\u4e00\u904d<\/td>\n\u901f\u901a（1）（2）（3）<\/td>\n\u5efa\u7acb\u5168\u4e66\u77e5\u8bc6\u6846\u67b6，\u4e86\u89e3\u6bcf\u7ae0\u6838\u5fc3\u6982\u5ff5<\/td>\n<\/tr>\n
                    \u7b2c\u4e8c\u904d<\/td>\n\u5206\u6cbb\u6cd5 \u2192 \u8d2a\u5fc3 \u2192 \u52a8\u6001\u89c4\u5212<\/td>\n\u638c\u63e1\u4e09\u5927\u57fa\u7840\u7b97\u6cd5\u8bbe\u8ba1\u8303\u5f0f<\/td>\n<\/tr>\n
                    \u7b2c\u4e09\u904d<\/td>\n\u56de\u6eaf\u6cd5 \u2192 \u5206\u652f\u9650\u754c\u6cd5<\/td>\n\u638c\u63e1\u641c\u7d22\u7c7b\u7b97\u6cd5\u7684\u8bbe\u8ba1\u4e0e\u4f18\u5316<\/td>\n<\/tr>\n
                    \u7b2c\u56db\u904d<\/td>\nNP\u5b8c\u5168\u7406\u8bba<\/td>\n\u7406\u89e3\u8ba1\u7b97\u590d\u6742\u6027，\u5efa\u7acb\u7b97\u6cd5\u9009\u62e9\u7684\u7406\u8bba\u4f9d\u636e<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
                    \n

                    📝 \u4f5c\u8005：\u57f9\u98ce\u56fe\u5357\u4ee5\u661f\u6cb3\u63fd\u80dc<\/p>\n

                    📂 \u4e13\u680f：\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5Leetcode（\u76ee\u524d209\u7bc7）<\/p>\n

                    💡 \u5982\u679c\u89c9\u5f97\u6709\u5e2e\u52a9，\u6b22\u8fce \u70b9\u8d5e👍 \u6536\u85cf\u2b50 \u5173\u6ce8🔔 \u4e09\u8fde\u652f\u6301！\u6709\u95ee\u9898\u6b22\u8fce\u8bc4\u8bba\u533a\u4ea4\u6d41\u8ba8\u8bba~<\/p>\n","protected":false},"excerpt":{"rendered":"

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