{"id":101396,"date":"2026-09-06T19:09:05","date_gmt":"2026-09-06T11:09:05","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/101396.html"},"modified":"2026-09-06T19:09:05","modified_gmt":"2026-09-06T11:09:05","slug":"%e4%bb%8e%e4%b8%80%e9%81%93gesp%e4%ba%94%e7%ba%a7%e7%9c%9f%e9%a2%98%e5%87%ba%e5%8f%91%ef%bc%9a%e8%81%8a%e8%81%8a%e4%ba%8c%e5%88%86%e7%ad%94%e6%a1%88%e4%b8%8e%e8%b4%aa%e5%bf%83%e5%88%a4%e5%ae%9a","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/101396.html","title":{"rendered":"\u4ece\u4e00\u9053GESP\u4e94\u7ea7\u771f\u9898\u51fa\u53d1\uff1a\u804a\u804a\u4e8c\u5206\u7b54\u6848\u4e0e\u8d2a\u5fc3\u5224\u5b9a\u7684\u4f18\u96c5\u7ec4\u5408"},"content":{"rendered":"

\u9898\u6e90：\u6d1b\u8c37 P14917 [GESP202512 \u4e94\u7ea7] \u6570\u5b57\u79fb\u52a8 \u9898\u76ee\u94fe\u63a5<\/p>\n

1. \u80cc\u666f<\/h3>\n

\u5728\u7b97\u6cd5\u7ade\u8d5b\u4e2d，"\u6700\u5c0f\u5316\u6700\u5927\u503c"\u7c7b\u95ee\u9898\u6709\u7740\u6781\u5176\u7edf\u4e00\u7684\u89e3\u9898\u6846\u67b6\u2014\u2014\u4e8c\u5206\u7b54\u6848\u3002\u8fd9\u7c7b\u95ee\u9898\u7684\u5178\u578b\u7279\u5f81\u662f：\u6211\u4eec\u8981\u6c42\u4e00\u4e2a\u9608\u503c <\/p>\n

x<\/p>\n

x<\/p>\n

<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>，\u4f7f\u5f97\u6240\u6709\u4ee3\u4ef7\u4e0d\u8d85\u8fc7 <\/p>\n

x<\/p>\n

x<\/p>\n

<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u64cd\u4f5c\u80fd\u591f\u5b8c\u6210\u4efb\u52a1，\u4e14 <\/p>\n

x<\/p>\n

x<\/p>\n

<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u8d8a\u5c0f\u8d8a\u597d\u3002\u5982\u679c\u76f4\u63a5\u6c42\u89e3\u6700\u4f18 <\/p>\n

x<\/p>\n

x<\/p>\n

<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u5f88\u56f0\u96be，\u4f46\u5224\u65ad"\u7ed9\u5b9a <\/p>\n

x<\/p>\n

x<\/p>\n

<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u662f\u5426\u53ef\u884c"\u5374\u76f8\u5bf9\u5bb9\u6613，\u90a3\u4e48\u4e8c\u5206\u7b54\u6848\u5c31\u662f\u5929\u7136\u7684\u9009\u62e9\u3002<\/p>\n

\u672c\u9898\u6b63\u662f\u8fd9\u4e00\u601d\u60f3\u7684\u5b8c\u7f8e\u4f53\u73b0\u3002\u5e8f\u5217\u4e2d\u6bcf\u4e2a\u6570\u5b57\u6070\u597d\u51fa\u73b0\u4e24\u6b21，\u6bcf\u6b21\u53ef\u4ee5\u79fb\u52a8\u4e00\u4e2a\u6570\u5b57\u5230\u4efb\u610f\u4f4d\u7f6e，\u82b1\u8d39\u7b49\u4e8e\u6570\u5b57\u672c\u8eab\u3002\u6211\u4eec\u9700\u8981\u627e\u5230\u4e00\u4e2a\u6700\u5c0f\u7684 <\/p>\n

x<\/p>\n

x<\/p>\n

<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>，\u4f7f\u5f97\u53ea\u79fb\u52a8\u6570\u503c\u4e0d\u8d85\u8fc7 <\/p>\n

x<\/p>\n

x<\/p>\n

<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u6570\u5b57（\u5373\u6bcf\u6b21\u82b1\u8d39\u4e0d\u8d85\u8fc7 <\/p>\n

x<\/p>\n

x<\/p>\n

<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>），\u5c31\u80fd\u8ba9\u6240\u6709\u76f8\u540c\u6570\u5b57\u5728\u5e8f\u5217\u4e2d\u76f8\u90bb\u3002<\/p>\n

\u521d\u770b\u4e4b\u4e0b，\u8fd9\u4f3c\u4e4e\u662f\u4e00\u4e2a\u9700\u8981\u590d\u6742\u8d2a\u5fc3\u6216\u52a8\u6001\u89c4\u5212\u7684\u95ee\u9898\u3002\u4f46\u4e00\u65e6\u4f60\u628a"\u79fb\u52a8\u82b1\u8d39 <\/p>\n

\u2264<\/p>\n

x<\/p>\n

\\\\le x<\/p>\n

<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>"\u7406\u89e3\u4e3a"\u6570\u503c <\/p>\n

><\/p>\n

x<\/p>\n

> x<\/p>\n

<\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u6570\u5b57\u4e0d\u80fd\u79fb\u52a8，\u5fc5\u987b\u5f85\u5728\u539f\u5730"，\u95ee\u9898\u5c31\u53d8\u5f97\u5f02\u5e38\u6e05\u6670：\u4e0d\u53ef\u79fb\u52a8\u7684\u6570\u5b57\u5fc5\u987b\u5728\u539f\u59cb\u5e8f\u5217\u4e2d（\u5ffd\u7565\u53ef\u79fb\u52a8\u6570\u5b57\u540e）\u5df2\u7ecf\u6210\u5bf9\u76f8\u90bb\u3002<\/p>\n

\u672c\u9898\u5728 GESP \u4e94\u7ea7\u4e2d\u5b9a\u4f4d\u4e3a"\u666e\u53ca"\u96be\u5ea6，\u6838\u5fc3\u8003\u5bdf\u7684\u662f：<\/p>\n

  • \u5982\u4f55\u5c06"\u79fb\u52a8\u9650\u5236"\u8f6c\u5316\u4e3a"\u56fa\u5b9a\u5143\u7d20"\u7684\u6761\u4ef6；<\/li>\n
  • \u5982\u4f55\u8bbe\u8ba1\u9ad8\u6548\u7684\u8d2a\u5fc3\u5224\u5b9a\u51fd\u6570；<\/li>\n
  • \u5982\u4f55\u5229\u7528\u4e8c\u5206\u7b54\u6848\u5904\u7406"\u6700\u5c0f\u5316\u6700\u5927\u503c"\u7c7b\u95ee\u9898\u3002<\/li>\n

    \u672c\u6587\u5c06\u4ece"\u6b63\u5411\u601d\u8003\u79fb\u52a8"\u7684\u76f4\u89c9\u51fa\u53d1，\u9010\u6b65\u5f15\u5bfc\u5230"\u53cd\u5411\u601d\u8003\u56fa\u5b9a\u5143\u7d20"\u7684\u5de7\u5999\u8f6c\u5316，\u5e26\u4f60\u638c\u63e1\u4e8c\u5206\u7b54\u6848 + \u8d2a\u5fc3\u5224\u5b9a\u8fd9\u4e00\u7ecf\u5178\u7ec4\u5408\u3002<\/p>\n

    2. \u6838\u5fc3\u601d\u60f3\u7ae0\u8282<\/h3>\n

    2.1 \u76f4\u89c9\u5148\u884c：\u9650\u5236\u79fb\u52a8 vs \u56fa\u5b9a\u4e0d\u53ef\u52a8<\/h4>\n

    \u60f3\u8c61\u4f60\u6709\u4e00\u6392\u5361\u7247，\u6bcf\u5f20\u5361\u7247\u4e0a\u5199\u7740\u4e00\u4e2a\u6570\u5b57，\u6bcf\u4e2a\u6570\u5b57\u6070\u597d\u51fa\u73b0\u4e24\u6b21\u3002\u4f60\u7684\u76ee\u6807\u662f\u628a\u76f8\u540c\u7684\u4e24\u5f20\u5361\u7247\u6328\u5728\u4e00\u8d77\u3002\u6bcf\u6b21\u64cd\u4f5c\u53ef\u4ee5\u62ff\u8d77\u4e00\u5f20\u5361\u7247\u63d2\u5230\u4efb\u610f\u4f4d\u7f6e，\u4f46\u4ee3\u4ef7\u662f\u5361\u7247\u4e0a\u7684\u6570\u5b57\u2014\u2014\u6570\u5b57\u8d8a\u5927，\u642c\u52a8\u5b83\u8d8a\u8d35\u3002<\/p>\n

    \u73b0\u5728\u8001\u677f\u7ed9\u4f60\u4e00\u4e2a\u9884\u7b97 <\/p>\n

    x<\/p>\n

    x<\/p>\n

    <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>，\u53ea\u5141\u8bb8\u4f60\u642c\u52a8\u6570\u5b57 <\/p>\n

    \u2264<\/p>\n

    x<\/p>\n

    \\\\le x<\/p>\n

    <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5361\u7247\u3002\u4f60\u60f3\u77e5\u9053：\u7ed9\u5b9a\u8fd9\u4e2a\u9884\u7b97，\u80fd\u4e0d\u80fd\u5b8c\u6210\u4efb\u52a1？<\/p>\n

    \u6362\u4e2a\u89d2\u5ea6\u60f3：\u6570\u5b57 <\/p>\n

    ><\/p>\n

    x<\/p>\n

    > x<\/p>\n

    <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5361\u7247\u4e0d\u80fd\u642c\u52a8，\u6240\u4ee5\u5b83\u4eec\u7684\u4f4d\u7f6e\u662f"\u710a\u6b7b"\u7684\u3002\u5982\u679c\u4e24\u5f20\u76f8\u540c\u7684\u5361\u7247\u90fd\u662f <\/p>\n

    ><\/p>\n

    x<\/p>\n

    > x<\/p>\n

    <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>，\u90a3\u5b83\u4eec\u5728\u6700\u7ec8\u5e8f\u5217\u4e2d\u5fc5\u987b\u5df2\u7ecf\u5728\u76f8\u90bb\u4f4d\u7f6e\u2014\u2014\u56e0\u4e3a\u5b83\u4eec\u7684\u76f8\u5bf9\u4f4d\u7f6e\u6c38\u8fdc\u65e0\u6cd5\u6539\u53d8\u3002\u5373\u4f7f\u4e2d\u95f4\u9694\u7740\u51e0\u5f20 <\/p>\n

    \u2264<\/p>\n

    x<\/p>\n

    \\\\le x<\/p>\n

    <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5c0f\u5361\u7247，\u90a3\u4e9b\u5c0f\u5361\u7247\u53ef\u4ee5\u88ab\u642c\u8d70，\u6240\u4ee5"\u76f8\u90bb"\u7684\u610f\u601d\u662f：\u628a\u53ef\u642c\u8d70\u7684\u5c0f\u5361\u7247\u5168\u90e8\u5ffd\u7565\u540e，\u8fd9\u4e24\u5f20\u5927\u5361\u7247\u662f\u6328\u7740\u7684\u3002<\/p>\n

    \u4e8e\u662f\u95ee\u9898\u53d8\u6210\u4e86：\u628a\u6240\u6709 <\/p>\n

    \u2264<\/p>\n

    x<\/p>\n

    \\\\le x<\/p>\n

    <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20\u4ece\u5e8f\u5217\u4e2d"\u5220\u9664"（\u56e0\u4e3a\u5b83\u4eec\u53ef\u4ee5\u88ab\u642c\u8d70），\u5269\u4e0b\u7684 <\/p>\n

    ><\/p>\n

    x<\/p>\n

    > x<\/p>\n

    <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20\u7ec4\u6210\u7684\u5b50\u5e8f\u5217，\u662f\u5426\u7531\u82e5\u5e72\u5bf9\u76f8\u90bb\u7684\u76f8\u540c\u6570\u5b57\u6784\u6210？<\/p>\n

    2.2 \u914d\u5bf9\u68c0\u67e5\u7684\u8d2a\u5fc3\u672c\u8d28<\/h4>\n

    \u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u628a\u539f\u59cb\u5e8f\u5217\u4e2d\u6240\u6709 <\/p>\n

    \u2264<\/p>\n

    x<\/p>\n

    \\\\le x<\/p>\n

    <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20"\u64e6\u6389"\u4e86，\u5269\u4e0b\u4e00\u4e2a\u7531 <\/p>\n

    ><\/p>\n

    x<\/p>\n

    > x<\/p>\n

    <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u5143\u7d20\u7ec4\u6210\u7684\u5e8f\u5217\u3002\u600e\u4e48\u68c0\u67e5\u8fd9\u4e2a\u5e8f\u5217\u662f\u5426"\u6210\u5bf9\u76f8\u90bb"\u5462？<\/p>\n

    \u4ece\u5de6\u5230\u53f3\u626b\u63cf，\u7528\u4e00\u4e2a\u53d8\u91cf last \u8bb0\u5f55\u5f53\u524d"\u6b63\u5728\u7b49\u5f85\u914d\u5bf9"\u7684\u6570\u5b57：<\/p>\n

      \n
    • \u5982\u679c last == 0，\u8bf4\u660e\u8fd8\u6ca1\u6709\u7b49\u5f85\u914d\u5bf9\u7684\u6570\u5b57，\u5f53\u524d\u6570\u5b57\u5c31\u662f\u65b0\u7684\u914d\u5bf9\u8d77\u70b9，\u8bb0\u4e0b\u6765；<\/li>\n
    • \u5982\u679c last \u4e0d\u4e3a 0 \u4e14\u5f53\u524d\u6570\u5b57\u7b49\u4e8e last，\u914d\u5bf9\u6210\u529f，\u6e05\u7a7a last；<\/li>\n
    • \u5982\u679c last \u4e0d\u4e3a 0 \u4e14\u5f53\u524d\u6570\u5b57\u4e0d\u7b49\u4e8e last，\u8bf4\u660e\u51fa\u73b0\u4e86"\u4ea4\u9519"\u7684\u60c5\u51b5（\u6bd4\u5982 \n

      [<\/p>\n

      2<\/p>\n

      ,<\/p>\n

      3<\/p>\n

      ,<\/p>\n

      2<\/p>\n

      ,<\/p>\n

      3<\/p>\n

      ]<\/p>\n

      [2, 3, 2, 3]<\/p>\n

      <\/span><\/span>[<\/span>2<\/span>,<\/span><\/span>3<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>3<\/span>]<\/span><\/span><\/span><\/span><\/span>），\u5927\u6570\u5b57\u65e0\u6cd5\u901a\u8fc7\u79fb\u52a8\u6765\u8c03\u6574，\u76f4\u63a5\u5224\u5b9a\u5931\u8d25\u3002<\/li>\n<\/ul>\n

      \u4e3a\u4ec0\u4e48\u8fd9\u6837\u662f\u6b63\u786e\u4e14\u5145\u5206\u7684？\u56e0\u4e3a\u6700\u7ec8\u5e8f\u5217\u8981\u6ee1\u8db3"\u76f8\u540c\u6570\u5b57\u76f8\u90bb"，\u7b49\u4ef7\u4e8e\u628a\u6bcf\u5bf9\u76f8\u540c\u6570\u5b57\u770b\u6210\u4e00\u4e2a"\u5757"，\u5757\u4e0e\u5757\u4e4b\u95f4\u4e0d\u80fd\u4ea4\u53c9\u3002\u4ece\u5de6\u5230\u53f3\u626b\u63cf\u65f6，\u4e00\u65e6\u9047\u5230\u4e00\u4e2a\u672a\u914d\u5bf9\u7684\u6570\u5b57，\u4e0b\u4e00\u4e2a\u51fa\u73b0\u7684\u76f8\u540c\u6570\u5b57\u5fc5\u987b\u662f\u7d27\u6328\u7740\u7684，\u5426\u5219\u4e2d\u95f4\u5939\u7740\u5176\u4ed6\u6570\u5b57，\u5c31\u4e0d\u53ef\u80fd\u901a\u8fc7\u53ea\u79fb\u52a8\u5c0f\u6570\u5b57\u6765\u4fee\u590d（\u56e0\u4e3a\u5927\u6570\u5b57\u4e0d\u80fd\u52a8）\u3002<\/p>\n

      2.3 \u5355\u8c03\u6027：\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u4e8c\u5206？<\/h4>\n

      \u968f\u7740 <\/p>\n

      x<\/p>\n

      x<\/p>\n

      <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u589e\u5927，\u5141\u8bb8\u79fb\u52a8\u7684\u6570\u5b57\u8303\u56f4\u53d8\u5927\u4e86，\u610f\u5473\u7740：<\/p>\n

        \n
      • \u66f4\u591a\u7684\u5c0f\u6570\u5b57\u53ef\u4ee5\u88ab\u642c\u8d70，\u5e72\u6270\u9879\u51cf\u5c11；<\/li>\n
      • \u66f4\u591a\u7684\u5927\u6570\u5b57"\u964d\u7ea7"\u4e3a\u53ef\u79fb\u52a8，\u539f\u672c\u53ef\u80fd\u9020\u6210\u9519\u4f4d\u7684\u969c\u788d\u88ab\u79fb\u9664\u3002<\/li>\n<\/ul>\n

        \u6362\u53e5\u8bdd\u8bf4，<\/p>\n

        x<\/p>\n

        x<\/p>\n

        <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u8d8a\u5927，\u53ef\u884c\u6027\u8d8a\u5bb9\u6613\u6ee1\u8db3\u3002\u8fd9\u79cd\u5355\u8c03\u6027\u6b63\u662f\u4e8c\u5206\u7b54\u6848\u7684\u57fa\u77f3：<\/p>\n

          \n
        • \u5982\u679c \n

          x<\/p>\n

          x<\/p>\n

          <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u53ef\u884c，\u90a3\u4e48\u4efb\u610f <\/p>\n

          x<\/p>\n

          \u2032<\/p>\n

          ><\/p>\n

          x<\/p>\n

          x' > x<\/p>\n

          <\/span><\/span>x<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u4e5f\u53ef\u884c（\u56e0\u4e3a\u9650\u5236\u66f4\u5bbd\u677e\u4e86）；<\/li>\n

        • \u5982\u679c \n

          x<\/p>\n

          x<\/p>\n

          <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u4e0d\u53ef\u884c，\u90a3\u4e48\u4efb\u610f <\/p>\n

          x<\/p>\n

          \u2032<\/p>\n

          <<\/p>\n

          x<\/p>\n

          x' < x<\/p>\n

          <\/span><\/span>x<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u4e5f\u4e0d\u53ef\u884c（\u56e0\u4e3a\u9650\u5236\u66f4\u4e25\u683c\u4e86）\u3002<\/li>\n<\/ul>\n

          \u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u4e8c\u5206\u6700\u5c0f\u7684\u53ef\u884c <\/p>\n

          x<\/p>\n

          x<\/p>\n

          <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>，\u4ece <\/p>\n

          1<\/p>\n

          1<\/p>\n

          <\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5230 <\/p>\n

          100000<\/p>\n

          100000<\/p>\n

          <\/span><\/span>100000<\/span><\/span><\/span><\/span><\/span>（\u6216\u6570\u7ec4\u6700\u5927\u503c），\u6bcf\u6b21 <\/p>\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> \u5224\u5b9a，\u603b\u590d\u6742\u5ea6 <\/p>\n

          O<\/p>\n

          (<\/p>\n

          N<\/p>\n

          log<\/p>\n

          \u2061<\/p>\n

          M<\/p>\n

          )<\/p>\n

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

          <\/span><\/span>O<\/span>(<\/span>N<\/span><\/span>log<\/span><\/span><\/span>M<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

          2.4 \u4e3a\u4ec0\u4e48\u4e0d\u80fd\u628a <\/p>\n

          ><\/p>\n

          x<\/p>\n

          >x<\/p>\n

          <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20"\u6392\u597d\u5e8f"？<\/h4>\n

          \u6709\u4eba\u53ef\u80fd\u4f1a\u60f3：\u65e2\u7136 <\/p>\n

          ><\/p>\n

          x<\/p>\n

          >x<\/p>\n

          <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20\u4e0d\u80fd\u79fb\u52a8，\u90a3\u6211\u80fd\u4e0d\u80fd\u628a\u5b83\u4eec\u7684\u4f4d\u7f6e\u8bb0\u5f55\u4e00\u4e0b，\u7136\u540e\u770b\u770b\u6bcf\u79cd\u6570\u5b57\u7684\u4e24\u4e2a\u51fa\u73b0\u4f4d\u7f6e\u4e4b\u95f4，\u662f\u5426\u6240\u6709\u5176\u4ed6\u5143\u7d20\u90fd <\/p>\n

          \u2264<\/p>\n

          x<\/p>\n

          \\\\le x<\/p>\n

          <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>（\u5373\u53ef\u4ee5\u88ab\u79fb\u8d70）？<\/p>\n

          \u8fd9\u4e2a\u601d\u8def\u4e5f\u662f\u5bf9\u7684！\u5b9e\u9645\u4e0a\u5b83\u548c\u6211\u4eec"\u5220\u9664 <\/p>\n

          \u2264<\/p>\n

          x<\/p>\n

          \\\\le x<\/p>\n

          <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u5143\u7d20\u518d\u914d\u5bf9"\u7684\u65b9\u6cd5\u7b49\u4ef7\u3002\u4f46\u540e\u8005\u66f4\u7b80\u6d01：\u4e0d\u9700\u8981\u8bb0\u5f55\u4f4d\u7f6e，\u4e0d\u9700\u8981\u8ba1\u7b97\u533a\u95f4，\u53ea\u9700\u8981\u4e00\u6b21\u626b\u63cf\u5373\u53ef\u5b8c\u6210\u5224\u5b9a\u3002\u8fd9\u79cd"\u64e6\u9664\u5c0f\u5143\u7d20"\u7684\u89c6\u89d2，\u8ba9\u95ee\u9898\u4ece"\u4f4d\u7f6e\u5173\u7cfb"\u53d8\u6210\u4e86"\u5e8f\u5217\u7ed3\u6784"，\u5927\u5927\u7b80\u5316\u4e86\u4ee3\u7801\u3002<\/p>\n

          \u5c0f\u7ed3：\u672c\u9898\u7684\u6838\u5fc3\u8f6c\u5316\u662f"\u79fb\u52a8\u9650\u5236 <\/p>\n

          \u2192<\/p>\n

          \\\\to<\/p>\n

          <\/span><\/span>\u2192<\/span><\/span><\/span><\/span><\/span> \u56fa\u5b9a\u5143\u7d20 <\/p>\n

          \u2192<\/p>\n

          \\\\to<\/p>\n

          <\/span><\/span>\u2192<\/span><\/span><\/span><\/span><\/span> \u914d\u5bf9\u68c0\u67e5"\u3002\u4e8c\u5206\u7b54\u6848\u5904\u7406\u6700\u5c0f\u9608\u503c，\u8d2a\u5fc3\u5224\u5b9a\u5904\u7406\u53ef\u884c\u6027\u3002\u8fd9\u79cd"\u4e8c\u5206 + \u8d2a\u5fc3"\u7684\u7ec4\u5408\u5728\u7ade\u8d5b\u4e2d\u6781\u5176\u5e38\u89c1，\u662f\u4e00\u4e2a\u5fc5\u987b\u719f\u7ec3\u638c\u63e1\u7684\u5957\u8def\u3002<\/p>\n

          3. \u7b97\u6cd5\u6a21\u677f\u7ae0\u8282<\/h3>\n

          3.1 \u7b97\u6cd5\u5230\u5e95\u5728\u5e72\u4ec0\u4e48？\u2014\u2014 \u76f4\u89c9\u89e3\u91ca<\/h4>\n

          \u4f60\u6709\u4e00\u5806\u5f85\u6574\u7406\u7684\u5361\u7247\u3002\u8001\u677f\u8bf4："\u4f60\u53ea\u80fd\u642c\u52a8\u6570\u5b57\u4e0d\u8d85\u8fc7 <\/p>\n

          x<\/p>\n

          x<\/p>\n

          <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5361\u7247，\u5927\u5361\u7247\u4e0d\u8bb8\u52a8\u3002"\u4f60\u60f3\u77e5\u9053\u80fd\u4e0d\u80fd\u5b8c\u6210\u4efb\u52a1\u3002<\/p>\n

          \u5224\u65ad\u65b9\u6cd5\u5f88\u7b80\u5355：\u628a\u6240\u6709\u5c0f\u5361\u7247（<\/p>\n

          \u2264<\/p>\n

          x<\/p>\n

          \\\\le x<\/p>\n

          <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>）\u4ece\u961f\u5217\u91cc"\u62bd\u8d70"（\u56e0\u4e3a\u5b83\u4eec\u53ef\u4ee5\u968f\u4fbf\u642c，\u4e0d\u5f71\u54cd\u5927\u5361\u7247\u7684\u76f8\u5bf9\u987a\u5e8f），\u7136\u540e\u770b\u5269\u4e0b\u7684\u5927\u5361\u7247\u7ec4\u6210\u7684\u961f\u5217，\u662f\u4e0d\u662f"\u6210\u53cc\u6210\u5bf9\u7d27\u6328\u7740"\u3002<\/p>\n

          \u6bd4\u5982\u539f\u59cb\u961f\u5217\u662f 1 2 1 3 2 3，\u5047\u8bbe <\/p>\n

          x<\/p>\n

          =<\/p>\n

          1<\/p>\n

          x=1<\/p>\n

          <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>：<\/p>\n

            \n
          • \u5c0f\u5361\u7247（\n

            \u2264<\/p>\n

            1<\/p>\n

            \\\\le 1<\/p>\n

            <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>）\u6709：\u7b2c1\u4e2a 1\u3001\u7b2c3\u4e2a 1\u3002\u62bd\u8d70\u540e\u5269\u4e0b 2 3 2 3\u3002<\/li>\n

          • \u68c0\u67e5 2 3 2 3：\u4ece\u5de6\u5230\u53f3，2 \u7b49\u5f85\u914d\u5bf9，\u4e0b\u4e00\u4e2a\u662f 3 \u4e0d\u5339\u914d \u2192 \u5931\u8d25\u3002 \u6240\u4ee5 \n

            x<\/p>\n

            =<\/p>\n

            1<\/p>\n

            x=1<\/p>\n

            <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u4e0d\u884c\u3002<\/li>\n<\/ul>\n

            \u5047\u8bbe <\/p>\n

            x<\/p>\n

            =<\/p>\n

            2<\/p>\n

            x=2<\/p>\n

            <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>：<\/p>\n

              \n
            • \u5c0f\u5361\u7247（\n

              \u2264<\/p>\n

              2<\/p>\n

              \\\\le 2<\/p>\n

              <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>）\u6709：1,2,1,2\u3002\u62bd\u8d70\u540e\u5269\u4e0b 3 3\u3002<\/li>\n

            • \u68c0\u67e5 3 3：\u914d\u5bf9\u6210\u529f \u2192 \u53ef\u884c\u3002 \u6240\u4ee5\u6700\u5c0f \n

              x<\/p>\n

              =<\/p>\n

              2<\/p>\n

              x=2<\/p>\n

              <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n

              3.2 \u4e07\u80fd\u6a21\u677f \u2014\u2014 \u4f2a\u4ee3\u7801 + \u5b9e\u6218\u4ee3\u7801<\/h4>\n

              \u4f2a\u4ee3\u7801：<\/p>\n

              check(x):
              \n last = 0
              \n for each val in A:
              \n if val <= x:
              \n continue \/\/ \u53ef\u79fb\u52a8，\u5ffd\u7565
              \n if last == 0:
              \n last = val \/\/ \u5f00\u59cb\u7b49\u5f85\u914d\u5bf9
              \n else if val == last:
              \n last = 0 \/\/ \u914d\u5bf9\u6210\u529f
              \n else:
              \n return false \/\/ \u914d\u5bf9\u5931\u8d25
              \n return last == 0<\/p>\n

              \u4e8c\u5206\u67e5\u627e\u6700\u5c0f\u7684 x:
              \n l = 1, r = max(A) \u6216 100000
              \n while l < r:
              \n mid = (l + r) \/ 2
              \n if check(mid):
              \n r = mid
              \n else:
              \n l = mid + 1
              \n print(l)<\/p>\n

              \u5b8c\u6574 AC \u4ee3\u7801（C++，\u5e26\u6ce8\u91ca）：<\/p>\n

              #<\/span>include<\/span> <bits\/stdc++.h><\/span><\/span>
              \nusing<\/span> namespace<\/span> std;<\/span><\/p>\n

              const<\/span> int<\/span> N =<\/span> 100005<\/span>;<\/span>
              \nint<\/span> n;<\/span>
              \nint<\/span> a[<\/span>N]<\/span>;<\/span><\/p>\n

              \/\/ \u5224\u5b9a\u51fd\u6570：\u7ed9\u5b9a\u9650\u5236 x，\u5224\u65ad\u662f\u5426\u53ef\u884c<\/span>
              \n\/\/ \u6838\u5fc3\u601d\u60f3：\u6240\u6709 > x \u7684\u5143\u7d20\u4e0d\u80fd\u79fb\u52a8，\u5b83\u4eec\u5fc5\u987b\u5728\u5ffd\u7565\u5c0f\u5143\u7d20\u540e\u5df2\u7ecf\u6210\u5bf9\u76f8\u90bb<\/span>
              \nbool<\/span> check<\/span>(<\/span>int<\/span> x)<\/span> {<\/span>
              \n int<\/span> waiting =<\/span> 0<\/span>;<\/span> \/\/ 0 \u8868\u793a\u6ca1\u6709\u7b49\u5f85\u914d\u5bf9\u7684\u6570\u5b57，\u5426\u5219\u5b58\u50a8\u5f53\u524d\u7b49\u5f85\u914d\u5bf9\u7684\u6570\u5b57<\/span><\/p>\n

              for<\/span> (<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <=<\/span> n;<\/span> i++<\/span>)<\/span> {<\/span>
              \n \/\/ \u53ef\u79fb\u52a8\u7684\u5c0f\u5143\u7d20\u76f4\u63a5\u8df3\u8fc7（\u56e0\u4e3a\u5b83\u4eec\u53ef\u4ee5\u88ab\u79fb\u8d70，\u4e0d\u5f71\u54cd\u5927\u5143\u7d20\u7684\u76f8\u5bf9\u987a\u5e8f）<\/span>
              \n if<\/span> (<\/span>a[<\/span>i]<\/span> <=<\/span> x)<\/span> {<\/span>
              \n continue<\/span>;<\/span>
              \n }<\/span><\/p>\n

              \/\/ \u5904\u7406\u4e0d\u53ef\u79fb\u52a8\u7684\u5927\u5143\u7d20（> x）<\/span>
              \n if<\/span> (<\/span>waiting ==<\/span> 0<\/span>)<\/span> {<\/span>
              \n \/\/ \u6ca1\u6709\u7b49\u5f85\u914d\u5bf9\u7684\u6570\u5b57，\u5f53\u524d\u6570\u5b57\u6210\u4e3a\u65b0\u7684\u914d\u5bf9\u8d77\u70b9<\/span>
              \n waiting =<\/span> a[<\/span>i]<\/span>;<\/span>
              \n }<\/span> else<\/span> if<\/span> (<\/span>a[<\/span>i]<\/span> ==<\/span> waiting)<\/span> {<\/span>
              \n \/\/ \u627e\u5230\u4e86\u914d\u5bf9\u7684\u6570\u5b57，\u914d\u5bf9\u6210\u529f，\u91cd\u7f6e\u7b49\u5f85\u72b6\u6001<\/span>
              \n waiting =<\/span> 0<\/span>;<\/span>
              \n }<\/span> else<\/span> {<\/span>
              \n \/\/ \u5f53\u524d\u6570\u5b57\u4e0e\u7b49\u5f85\u914d\u5bf9\u7684\u6570\u5b57\u4e0d\u540c，\u8bf4\u660e\u5927\u5143\u7d20\u5e8f\u5217\u51fa\u73b0\u4e86\u4ea4\u9519<\/span>
              \n \/\/ \u4f8b\u5982 [2, 3, 2, 3] \u6216 [2, 3, 3, 2] \u90fd\u4e0d\u884c<\/span>
              \n return<\/span> false<\/span>;<\/span>
              \n }<\/span>
              \n }<\/span><\/p>\n

              \/\/ \u904d\u5386\u7ed3\u675f\u540e，waiting \u5fc5\u987b\u4e3a 0（\u6240\u6709\u5927\u5143\u7d20\u90fd\u914d\u5bf9\u4e86）<\/span>
              \n return<\/span> waiting ==<\/span> 0<\/span>;<\/span>
              \n}<\/span><\/p>\n

              int<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
              \n ios::<\/span>sync_with_stdio<\/span>(<\/span>false<\/span>)<\/span>;<\/span>
              \n cin.<\/span>tie<\/span>(<\/span>nullptr<\/span>)<\/span>;<\/span><\/p>\n

              cin >><\/span> n;<\/span>
              \n for<\/span> (<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <=<\/span> n;<\/span> i++<\/span>)<\/span> {<\/span>
              \n cin >><\/span> a[<\/span>i]<\/span>;<\/span>
              \n }<\/span><\/p>\n

              \/\/ \u4e8c\u5206\u7b54\u6848：\u5bfb\u627e\u6700\u5c0f\u7684\u53ef\u884c x<\/span>
              \n \/\/ \u5de6\u8fb9\u754c\u4e3a 1（\u9898\u76ee\u4fdd\u8bc1\u81f3\u5c11\u9700\u8981\u4e00\u6b21\u64cd\u4f5c，\u6240\u4ee5\u7b54\u6848\u81f3\u5c11\u4e3a 1）<\/span>
              \n \/\/ \u53f3\u8fb9\u754c\u8bbe\u4e3a 100000（\u6839\u636e\u9898\u76ee\u6570\u636e\u8303\u56f4，\u6216\u53d6\u6570\u7ec4\u6700\u5927\u503c）<\/span>
              \n int<\/span> l =<\/span> 1<\/span>,<\/span> r =<\/span> 100000<\/span>;<\/span><\/p>\n

              while<\/span> (<\/span>l <<\/span> r)<\/span> {<\/span>
              \n int<\/span> mid =<\/span> (<\/span>l +<\/span> r)<\/span> \/<\/span> 2<\/span>;<\/span>
              \n if<\/span> (<\/span>check<\/span>(<\/span>mid)<\/span>)<\/span> {<\/span>
              \n r =<\/span> mid;<\/span> \/\/ mid \u53ef\u884c，\u5c1d\u8bd5\u66f4\u5c0f\u7684\u503c<\/span>
              \n }<\/span> else<\/span> {<\/span>
              \n l =<\/span> mid +<\/span> 1<\/span>;<\/span> \/\/ mid \u4e0d\u53ef\u884c，\u9700\u8981\u66f4\u5927\u7684\u503c<\/span>
              \n }<\/span>
              \n }<\/span><\/p>\n

              cout <<<\/span> l <<<\/span> endl;<\/span>
              \n return<\/span> 0<\/span>;<\/span>
              \n}<\/span><\/p>\n

              3.3 \u4f8b\u9898\u5b9e\u73b0 \u2014\u2014 \u672c\u9898\u5b8c\u6574\u8fd0\u884c\u6d41\u7a0b<\/h4>\n

              \u4ee5\u6837\u4f8b\u4e3a\u4f8b：<\/p>\n

              N = 6, A = [1, 2, 1, 3, 2, 3]<\/p>\n

              \u4e8c\u5206\u8fc7\u7a0b（<\/p>\n

              l<\/p>\n

              =<\/p>\n

              1<\/p>\n

              ,<\/p>\n

              r<\/p>\n

              =<\/p>\n

              100000<\/p>\n

              l=1, r=100000<\/p>\n

              <\/span><\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>,<\/span><\/span>r<\/span><\/span>=<\/span><\/span><\/span><\/span>100000<\/span><\/span><\/span><\/span><\/span>）：<\/p>\n

                \n
              • mid = 50000：check \u663e\u7136\u53ef\u884c（\u6240\u6709\u5143\u7d20\u90fd <= 50000，\u53ef\u5168\u90e8\u79fb\u8d70），r = 50000<\/li>\n
              • mid = 25000：\u540c\u6837\u53ef\u884c，r = 25000<\/li>\n
              • \u2026 \u4e8c\u5206\u4e0d\u65ad\u7f29\u5c0f，\u76f4\u5230 mid \u6765\u5230 \n

                2<\/p>\n

                2<\/p>\n

                <\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u9644\u8fd1<\/li>\n<\/ul>\n

                \u68c0\u67e5 <\/p>\n

                x<\/p>\n

                =<\/p>\n

                1<\/p>\n

                x=1<\/p>\n

                <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>：<\/p>\n

                  \n
                • \u904d\u5386：1(\u8df3\u8fc7), 2(\u7b49\u5f85=2), 1(\u8df3\u8fc7), 3(\u7b49\u5f85=2 \u4f46\u5f53\u524d=3 \u2192 \u8fd4\u56de false)<\/li>\n
                • \u4e0d\u53ef\u884c，\u6240\u4ee5\u7b54\u6848 > 1<\/li>\n<\/ul>\n

                  \u68c0\u67e5 <\/p>\n

                  x<\/p>\n

                  =<\/p>\n

                  2<\/p>\n

                  x=2<\/p>\n

                  <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>：<\/p>\n

                    \n
                  • \u904d\u5386：1(\u8df3\u8fc7), 2(\u8df3\u8fc7), 1(\u8df3\u8fc7), 3(\u7b49\u5f85=3), 2(\u8df3\u8fc7), 3(\u7b49\u5f85=3 \u4e14\u5f53\u524d=3 \u2192 \u914d\u5bf9\u6210\u529f)<\/li>\n
                  • \u904d\u5386\u7ed3\u675f，waiting == 0，\u8fd4\u56de true<\/li>\n
                  • \u53ef\u884c，\u6240\u4ee5\u7b54\u6848 <= 2<\/li>\n<\/ul>\n

                    \u6700\u7ec8 l = 2，\u8f93\u51fa 2，\u4e0e\u6837\u4f8b\u4e00\u81f4\u3002\u2705<\/p>\n

                    3.4 \u5bf9\u6bd4\u5b9e\u73b0 \u2014\u2014 \u5982\u679c\u4e0d\u7528\u4e8c\u5206，\u76f4\u63a5\u8d2a\u5fc3\u6c42\u7b54\u6848？<\/h4>\n

                    \u6709\u4eba\u53ef\u80fd\u4f1a\u60f3：\u80fd\u4e0d\u80fd\u4e0d\u7528\u4e8c\u5206，\u76f4\u63a5\u8d2a\u5fc3\u6c42\u51fa\u6700\u5c0f <\/p>\n

                    x<\/p>\n

                    x<\/p>\n

                    <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>？<\/p>\n

                    \u6bd4\u5982，\u627e\u5230\u6240\u6709"\u5bfc\u81f4\u914d\u5bf9\u5931\u8d25\u7684\u5927\u5143\u7d20\u5bf9"，\u53d6\u5176\u4e2d\u7684\u6700\u5927\u503c\u4f5c\u4e3a\u7b54\u6848？\u8fd9\u79cd\u601d\u8def\u5728\u672c\u9898\u4e2d\u5e76\u4e0d\u7b80\u5355，\u56e0\u4e3a <\/p>\n

                    x<\/p>\n

                    x<\/p>\n

                    <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u53d8\u5316\u65f6，\u54ea\u4e9b\u5143\u7d20\u88ab"\u964d\u7ea7"\u4e3a\u53ef\u79fb\u52a8\u662f\u52a8\u6001\u53d8\u5316\u7684，\u5931\u8d25\u6761\u4ef6\u4e5f\u5728\u53d8\u5316\u3002\u76f4\u63a5\u6c42\u89e3\u9700\u8981\u590d\u6742\u7684\u626b\u63cf\u548c\u66f4\u65b0\u903b\u8f91\u3002<\/p>\n

                    \u800c\u4e8c\u5206\u7b54\u6848 + \u5224\u5b9a\u51fd\u6570\u7684\u65b9\u5f0f，\u628a"\u6c42\u6700\u4f18\u89e3"\u8f6c\u5316\u4e3a"\u5224\u5b9a\u53ef\u884c\u6027"，\u6bcf\u6b21\u5224\u5b9a\u7684\u903b\u8f91\u6781\u5176\u7b80\u5355（<\/p>\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> \u626b\u63cf），\u603b\u5171\u53ea\u9700\u8981 <\/p>\n

                    log<\/p>\n

                    \u2061<\/p>\n

                    M<\/p>\n

                    \\\\log M<\/p>\n

                    <\/span><\/span>log<\/span><\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u6b21\u5224\u5b9a，\u6e05\u6670\u4e14\u9ad8\u6548\u3002\u8fd9\u6b63\u662f\u4e8c\u5206\u7b54\u6848\u7c7b\u95ee\u9898\u7684\u9b45\u529b\u6240\u5728\u3002<\/p>\n

                    3.5 \u53d8\u4f53\u6e05\u5355<\/h4>\n\n\u53d8\u4f53\u573a\u666f\u5904\u7406\u65b9\u6cd5\u4e0e\u672c\u9898\u7684\u5dee\u5f02<\/tr>\n\n\n\n\n\n\n\n
                    \u6bcf\u6b21\u79fb\u52a8\u82b1\u8d39\u7b49\u4e8e\u6570\u5b57\u7684\u5e73\u65b9\u6216\u4f4d\u6570<\/td>\n\u5224\u5b9a\u6761\u4ef6\u6539\u4e3a a[i]^2 <= x \u6216 digit_count(a[i]) <= x<\/td>\n\u5224\u5b9a\u9608\u503c\u4e0d\u540c<\/td>\n<\/tr>\n
                    \u6bcf\u4e2a\u6570\u5b57\u51fa\u73b0 <\/p>\n

                    k<\/p>\n

                    k<\/p>\n

                    <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u6b21（<\/p>\n

                    k<\/p>\n

                    ><\/p>\n

                    2<\/p>\n

                    k>2<\/p>\n

                    <\/span><\/span>k<\/span><\/span>><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>）<\/td>\n

                    		\u914d\u5bf9\u903b\u8f91\u6539\u4e3a：\u7528\u8ba1\u6570\u5668\u8bb0\u5f55\u5f53\u524d\u7b49\u5f85\u914d\u5bf9\u7684\u6570\u5b57\u51fa\u73b0\u6b21\u6570，\u6ee1 <\/p>\n

                    k<\/p>\n

                    k<\/p>\n

                    <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u6b21\u624d\u6e05\u7a7a<\/td>\n

                    		\u51fa\u73b0\u6b21\u6570\u53d8\u5316<\/td>\n<\/tr>\n
                    \u9700\u8981\u8f93\u51fa\u5177\u4f53\u79fb\u52a8\u65b9\u6848<\/td>\n\u5728 check \u4e4b\u5916\u989d\u5916\u6784\u9020\u65b9\u6848<\/td>\n\u672c\u9898\u53ea\u6c42\u9608\u503c<\/td>\n<\/tr>\n
                    \u76ee\u6807\u4e0d\u662f"\u76f8\u90bb"\u800c\u662f"\u6709\u5e8f\u6392\u5217"<\/td>\n\u5224\u5b9a\u903b\u8f91\u6539\u4e3a\u68c0\u67e5\u5269\u4f59\u5e8f\u5217\u662f\u5426\u4e25\u683c\u5347\u5e8f\u7b49<\/td>\n\u76ee\u6807\u6761\u4ef6\u53d8\u5316<\/td>\n<\/tr>\n
                    \u5141\u8bb8\u79fb\u52a8 <\/p>\n

                    ><\/p>\n

                    x<\/p>\n

                    >x<\/p>\n

                    <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20\u4f46\u989d\u5916\u82b1\u8d39<\/td>\n

                    		\u53ef\u5f15\u5165\u4e8c\u7ef4\u72b6\u6001\u6216\u66f4\u590d\u6742\u7684 DP<\/td>\n\u7ea6\u675f\u66f4\u590d\u6742<\/td>\n<\/tr>\n
                    \u5e8f\u5217\u4e2d\u6570\u5b57\u51fa\u73b0\u6b21\u6570\u4e0d\u4e00\u5b9a\u4e3a 2<\/td>\n\u9700\u8981\u5148\u7edf\u8ba1\u6bcf\u4e2a\u6570\u5b57\u7684\u51fa\u73b0\u6b21\u6570，\u7136\u540e\u914d\u5bf9\u903b\u8f91\u6309\u51fa\u73b0\u6b21\u6570\u8c03\u6574<\/td>\n\u51fa\u73b0\u6b21\u6570\u4e0d\u56fa\u5b9a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                    3.6 \u4ec0\u4e48\u65f6\u5019\u4e0d\u80fd\u7528？<\/h4>\n
                      \n
                    • \u5224\u5b9a\u51fd\u6570\u4e0d\u5177\u6709\u5355\u8c03\u6027：\u5982\u679c \n

                      x<\/p>\n

                      x<\/p>\n

                      <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u589e\u5927\u65f6\u53ef\u884c\u6027\u53ef\u80fd\u4ece"\u53ef\u884c"\u53d8"\u4e0d\u53ef\u884c"，\u5219\u4e0d\u80fd\u4e8c\u5206\u3002\u672c\u9898\u7684\u5355\u8c03\u6027\u662f\u663e\u7136\u6210\u7acb\u7684（\u9650\u5236\u653e\u5bbd\u4e0d\u4f1a\u8ba9\u53ef\u884c\u53d8\u4e0d\u53ef\u884c）\u3002<\/li>\n

                    • \n

                      x<\/p>\n

                      x<\/p>\n

                      <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u53d6\u503c\u8303\u56f4\u8fc7\u5927：\u5982\u679c <\/p>\n

                      x<\/p>\n

                      x<\/p>\n

                      <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u53ef\u4ee5\u53d6\u5230 <\/p>\n

                      10<\/p>\n

                      9<\/p>\n

                      10^9<\/p>\n

                      <\/span><\/span>1<\/span>0<\/span><\/span>9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u751a\u81f3\u66f4\u5927，\u4e8c\u5206\u4ecd\u7136\u53ef\u884c（<\/p>\n

                      log<\/p>\n

                      \u2061<\/p>\n

                      10<\/p>\n

                      9<\/p>\n

                      \u2248<\/p>\n

                      30<\/p>\n

                      \\\\log 10^9 \\\\approx 30<\/p>\n

                      <\/span><\/span>log<\/span><\/span><\/span>1<\/span>0<\/span><\/span>9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>30<\/span><\/span><\/span><\/span><\/span> \u6b21），\u4f46\u5982\u679c\u5224\u5b9a\u51fd\u6570\u672c\u8eab\u5f88\u6162（\u5982 <\/p>\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>），\u5219\u603b\u590d\u6742\u5ea6\u53ef\u80fd\u8fc7\u9ad8\u3002\u672c\u9898\u5224\u5b9a\u4e3a <\/p>\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>，\u975e\u5e38\u9ad8\u6548\u3002<\/li>\n

                    • \u76ee\u6807\u4e0d\u662f"\u6700\u5c0f\u503c"\u800c\u662f"\u67d0\u79cd\u5177\u4f53\u6784\u9020"：\u4e8c\u5206\u7b54\u6848\u53ea\u6c42\u9608\u503c，\u5982\u679c\u9700\u8981\u8f93\u51fa\u5177\u4f53\u65b9\u6848，\u8fd8\u9700\u8981\u989d\u5916\u6784\u9020\u3002<\/li>\n
                    • \u64cd\u4f5c\u6b21\u6570\u4e5f\u6709\u9650\u5236：\u5982\u679c\u9664\u4e86\u82b1\u8d39\u9650\u5236\u5916\u8fd8\u6709\u64cd\u4f5c\u6b21\u6570\u9650\u5236，\u5224\u5b9a\u51fd\u6570\u9700\u8981\u989d\u5916\u8bb0\u5f55\u64cd\u4f5c\u6570，\u53ef\u80fd\u53d8\u5f97\u590d\u6742\u3002<\/li>\n<\/ul>\n

                      4. \u5e95\u5c42\u903b\u8f91\u7ae0\u8282<\/h3>\n

                      4.1 \u4e3a\u4ec0\u4e48"\u8df3\u8fc7 <\/p>\n

                      \u2264<\/p>\n

                      x<\/p>\n

                      \\\\le x<\/p>\n

                      <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20"\u662f\u5b89\u5168\u7684？<\/h4>\n

                      \u5173\u952e\u5728\u4e8e：\u53ef\u79fb\u52a8\u5143\u7d20\u53ef\u4ee5\u88ab\u79fb\u8d70，\u4e5f\u53ef\u4ee5\u88ab\u79fb\u6765，\u4f46\u5b83\u4eec\u4e0d\u80fd\u6539\u53d8\u4e0d\u53ef\u79fb\u52a8\u5143\u7d20\u7684\u76f8\u5bf9\u987a\u5e8f\u3002<\/p>\n

                      \u5f53\u6211\u4eec\u4ece\u539f\u59cb\u5e8f\u5217\u4e2d"\u5220\u9664"\u6240\u6709 <\/p>\n

                      \u2264<\/p>\n

                      x<\/p>\n

                      \\\\le x<\/p>\n

                      <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20\u65f6，\u6211\u4eec\u5176\u5b9e\u662f\u5728\u95ee：\u5728\u6700\u7ec8\u76ee\u6807\u5e8f\u5217\u4e2d，\u6240\u6709 <\/p>\n

                      ><\/p>\n

                      x<\/p>\n

                      >x<\/p>\n

                      <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20\u4f1a\u4ee5\u4ec0\u4e48\u987a\u5e8f\u51fa\u73b0？<\/p>\n

                      \u7531\u4e8e <\/p>\n

                      \u2264<\/p>\n

                      x<\/p>\n

                      \\\\le x<\/p>\n

                      <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20\u53ef\u4ee5\u88ab\u4efb\u610f\u79fb\u52a8，\u5b83\u4eec\u53ef\u4ee5\u5728\u6700\u7ec8\u5e8f\u5217\u4e2d\u586b\u5145\u4efb\u610f\u4f4d\u7f6e，\u4e0d\u4f1a\u5bf9 <\/p>\n

                      ><\/p>\n

                      x<\/p>\n

                      >x<\/p>\n

                      <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u5143\u7d20\u4e4b\u95f4\u7684\u76f8\u5bf9\u987a\u5e8f\u9020\u6210\u4efb\u4f55\u9650\u5236\u3002\u56e0\u6b64，<\/p>\n

                      ><\/p>\n

                      x<\/p>\n

                      >x<\/p>\n

                      <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u5143\u7d20\u5728\u6700\u7ec8\u5e8f\u5217\u4e2d\u7684\u76f8\u5bf9\u987a\u5e8f，\u5fc5\u987b\u4e0e\u5b83\u4eec\u5728\u539f\u59cb\u5e8f\u5217\u4e2d\u7684\u76f8\u5bf9\u987a\u5e8f\u5b8c\u5168\u76f8\u540c（\u56e0\u4e3a\u5b83\u4eec\u4e0d\u80fd\u79fb\u52a8）\u3002<\/p>\n

                      \u800c\u6700\u7ec8\u76ee\u6807\u8981\u6c42"\u76f8\u540c\u6570\u5b57\u76f8\u90bb"，\u8fd9\u610f\u5473\u7740\u5728\u6700\u7ec8\u5e8f\u5217\u4e2d，<\/p>\n

                      ><\/p>\n

                      x<\/p>\n

                      >x<\/p>\n

                      <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u5143\u7d20\u7684\u5b50\u5e8f\u5217\u5fc5\u987b\u7531\u82e5\u5e72\u5bf9\u76f8\u90bb\u7684\u76f8\u540c\u6570\u5b57\u7ec4\u6210\u3002\u8fd9\u4e0e"\u5728\u5220\u9664 <\/p>\n

                      \u2264<\/p>\n

                      x<\/p>\n

                      \\\\le x<\/p>\n

                      <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u5143\u7d20\u540e\u7684\u5b50\u5e8f\u5217\u4e2d，\u76f8\u540c\u6570\u5b57\u6210\u5bf9\u76f8\u90bb"\u5b8c\u5168\u7b49\u4ef7\u3002<\/p>\n

                      \u6240\u4ee5，\u8df3\u8fc7 <\/p>\n

                      \u2264<\/p>\n

                      x<\/p>\n

                      \\\\le x<\/p>\n

                      <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u5143\u7d20\u518d\u68c0\u67e5\u914d\u5bf9，\u4e0d\u4ec5\u5b89\u5168，\u800c\u4e14\u662f\u5fc5\u8981\u6761\u4ef6，\u4e5f\u662f\u5145\u5206\u6761\u4ef6\u3002<\/p>\n

                      4.2 \u4e3a\u4ec0\u4e48\u914d\u5bf9\u68c0\u67e5\u7528"\u7b49\u5f85\u914d\u5bf9"\u5c31\u80fd\u8986\u76d6\u6240\u6709\u60c5\u51b5？<\/h4>\n

                      \u8003\u8651\u4e00\u4e2a\u7531 <\/p>\n

                      ><\/p>\n

                      x<\/p>\n

                      >x<\/p>\n

                      <\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u5143\u7d20\u7ec4\u6210\u7684\u5e8f\u5217，\u6bcf\u4e2a\u6570\u5b57\u51fa\u73b0\u4e24\u6b21\u3002\u6211\u4eec\u8981\u68c0\u67e5\u5b83\u662f\u5426"\u6210\u5bf9\u76f8\u90bb"（\u5373\u5f62\u5982 <\/p>\n

                      [<\/p>\n

                      a<\/p>\n

                      ,<\/p>\n

                      a<\/p>\n

                      ,<\/p>\n

                      b<\/p>\n

                      ,<\/p>\n

                      b<\/p>\n

                      ,<\/p>\n

                      c<\/p>\n

                      ,<\/p>\n

                      c<\/p>\n

                      ,<\/p>\n

                      \u2026
                      \n \u2009<\/p>\n

                      ]<\/p>\n

                      [a,a,b,b,c,c,\\\\dots]<\/p>\n

                      <\/span><\/span>[<\/span>a<\/span>,<\/span><\/span>a<\/span>,<\/span><\/span>b<\/span>,<\/span><\/span>b<\/span>,<\/span><\/span>c<\/span>,<\/span><\/span>c<\/span>,<\/span><\/span>\u2026<\/span><\/span>]<\/span><\/span><\/span><\/span><\/span> \u7684\u5f62\u5f0f）\u3002<\/p>\n

                      \u4ece\u5de6\u5230\u53f3\u626b\u63cf，\u7528 waiting \u8bb0\u5f55\u5f53\u524d"\u6b63\u5728\u7b49\u5f85\u5176\u914d\u5bf9"\u7684\u6570\u5b57：<\/p>\n

                        \n
                      • \u5982\u679c waiting == 0，\u8bf4\u660e\u524d\u9762\u7684\u90e8\u5206\u5df2\u7ecf\u5168\u90e8\u914d\u5bf9\u5b8c\u6210，\u5f53\u524d\u6570\u5b57\u4e00\u5b9a\u662f\u4e00\u4e2a\u65b0\u5bf9\u7684\u7b2c\u4e00\u4e2a\u5143\u7d20\u3002<\/li>\n
                      • \u5982\u679c waiting != 0，\u8bf4\u660e\u6211\u4eec\u6b63\u5728\u7b49\u5f85\u67d0\u4e2a\u6570\u5b57\u7684\u914d\u5bf9\u51fa\u73b0，\u5f53\u524d\u6570\u5b57\u5fc5\u987b\u6070\u597d\u7b49\u4e8e waiting，\u5426\u5219\u5c31\u51fa\u73b0\u4e86\u4ea4\u9519\u3002<\/li>\n<\/ul>\n

                        \u8fd9\u79cd"\u4ece\u5de6\u5230\u53f3\u5339\u914d\u62ec\u53f7"\u5f0f\u7684\u68c0\u67e5，\u672c\u8d28\u4e0a\u662f\u5224\u65ad\u5e8f\u5217\u662f\u5426\u5c5e\u4e8e\u6b63\u5219\u8bed\u8a00 <\/p>\n

                        (<\/p>\n

                        a<\/p>\n

                        a<\/p>\n

                        \u2223<\/p>\n

                        b<\/p>\n

                        b<\/p>\n

                        \u2223<\/p>\n

                        c<\/p>\n

                        c<\/p>\n

                        \u2223<\/p>\n

                        .<\/p>\n

                        .<\/p>\n

                        .<\/p>\n

                        )<\/p>\n

                        \u2217<\/p>\n

                        (aa|bb|cc|…)^*<\/p>\n

                        <\/span><\/span>(<\/span>aa<\/span>\u2223<\/span>bb<\/span>\u2223<\/span>cc<\/span>\u2223…<\/span>)<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u6570\u5b57\u6070\u597d\u51fa\u73b0\u4e24\u6b21\u7684\u60c5\u51b5，\u8fd9\u4e2a\u68c0\u67e5\u662f\u5145\u5206\u5fc5\u8981\u7684\u3002<\/p>\n

                        4.3 \u4e0e"\u62ec\u53f7\u5339\u914d"\u7684\u7c7b\u6bd4<\/h4>\n

                        \u5982\u679c\u628a\u6bcf\u4e2a\u6570\u5b57\u7684\u51fa\u73b0\u770b\u4f5c\u4e00\u5bf9\u62ec\u53f7\u2014\u2014\u7b2c\u4e00\u6b21\u51fa\u73b0\u662f\u5de6\u62ec\u53f7，\u7b2c\u4e8c\u6b21\u51fa\u73b0\u662f\u53f3\u62ec\u53f7\u2014\u2014\u90a3\u4e48"\u76f8\u540c\u6570\u5b57\u76f8\u90bb"\u5c31\u610f\u5473\u7740\u62ec\u53f7\u5bf9\u4e4b\u95f4\u4e0d\u80fd\u4ea4\u53c9（\u5373\u4e0d\u80fd\u51fa\u73b0 <\/p>\n

                        [<\/p>\n

                        a<\/p>\n

                        ,<\/p>\n

                        b<\/p>\n

                        ,<\/p>\n

                        a<\/p>\n

                        ,<\/p>\n

                        b<\/p>\n

                        ]<\/p>\n

                        [a,b,a,b]<\/p>\n

                        <\/span><\/span>[<\/span>a<\/span>,<\/span><\/span>b<\/span>,<\/span><\/span>a<\/span>,<\/span><\/span>b<\/span>]<\/span><\/span><\/span><\/span><\/span> \u8fd9\u6837\u7684\u5d4c\u5957）\u3002<\/p>\n

                        \u800c"\u5220\u9664 <\/p>\n

                        \u2264<\/p>\n

                        x<\/p>\n

                        \\\\le x<\/p>\n

                        <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20"\u76f8\u5f53\u4e8e\u79fb\u9664\u4e00\u4e9b\u62ec\u53f7\u5bf9（\u6216\u90e8\u5206\u62ec\u53f7），\u5269\u4e0b\u7684\u5927\u62ec\u53f7\u5bf9\u5fc5\u987b\u5df2\u7ecf\u662f\u4e0d\u4ea4\u53c9\u7684\u3002\u6211\u4eec\u7684 waiting \u68c0\u67e5，\u672c\u8d28\u4e0a\u5c31\u662f\u5728\u68c0\u67e5\u5269\u4f59\u62ec\u53f7\u5e8f\u5217\u662f\u5426"\u5408\u6cd5\u5d4c\u5957"（\u4f46\u8fd9\u91cc\u7684"\u5408\u6cd5"\u662f\u76f8\u90bb\u5339\u914d，\u4e0d\u662f\u62ec\u53f7\u5339\u914d\u7684\u6808\u5f0f\u5339\u914d，\u56e0\u4e3a\u76f8\u90bb\u5339\u914d\u662f\u66f4\u4e25\u683c\u7684\u6761\u4ef6）\u3002<\/p>\n

                        5. \u51b3\u7b56\u8868：\u4e0d\u540c\u601d\u8def\u7684\u9002\u7528\u573a\u666f<\/h3>\n\n\u573a\u666f\u65b9\u6848\u65f6\u95f4\u590d\u6742\u5ea6\u7a7a\u95f4\u590d\u6742\u5ea6\u4f18\u70b9\u7f3a\u70b9<\/tr>\n\n\n\n\n\n\n
                        \u6c42\u6700\u5c0f\u53ef\u884c\u9608\u503c<\/td>\n\u4e8c\u5206\u7b54\u6848 + \u8d2a\u5fc3\u5224\u5b9a（\u672c\u9898\u89e3\u6cd5）<\/td>\n<\/p>\n

                        O<\/p>\n

                        (<\/p>\n

                        N<\/p>\n

                        log<\/p>\n

                        \u2061<\/p>\n

                        M<\/p>\n

                        )<\/p>\n

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

                        <\/span><\/span>O<\/span>(<\/span>N<\/span><\/span>log<\/span><\/span><\/span>M<\/span>)<\/span><\/span><\/span><\/span><\/span><\/td>\n

                        		<\/p>\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><\/td>\n

                        		\u7b80\u6d01\u9ad8\u6548，\u901a\u7528\u6027\u5f3a<\/td>\n\u9700\u8981\u5224\u5b9a\u51fd\u6570\u6709\u5355\u8c03\u6027<\/td>\n<\/tr>\n
                        \u76f4\u63a5\u8d2a\u5fc3\u6c42\u9608\u503c<\/td>\n\u626b\u63cf\u6240\u6709\u6570\u5b57，\u53d6"\u5173\u952e\u51b2\u7a81"\u7684\u6700\u5927\u503c<\/td>\n\u53ef\u80fd <\/p>\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> \u4f46\u6b63\u786e\u6027\u5b58\u7591<\/td>\n

                        		<\/p>\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><\/td>\n

                        		\u770b\u4f3c\u66f4\u5feb<\/td>\n\u903b\u8f91\u590d\u6742，\u5bb9\u6613\u51fa\u9519<\/td>\n<\/tr>\n
                        \u66b4\u529b\u679a\u4e3e\u6240\u6709 <\/p>\n

                        x<\/p>\n

                        x<\/p>\n

                        <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/td>\n

                        		\u4ece 1 \u5230 <\/p>\n

                        M<\/p>\n

                        M<\/p>\n

                        <\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u9010\u4e2a\u5c1d\u8bd5<\/td>\n

                        		<\/p>\n

                        O<\/p>\n

                        (<\/p>\n

                        N<\/p>\n

                        \u22c5<\/p>\n

                        M<\/p>\n

                        )<\/p>\n

                        O(N \\\\cdot M)<\/p>\n

                        <\/span><\/span>O<\/span>(<\/span>N<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>M<\/span>)<\/span><\/span><\/span><\/span><\/span><\/td>\n

                        		<\/p>\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><\/td>\n

                        		\u7b80\u5355\u76f4\u89c2<\/td>\n\u5f53 <\/p>\n

                        M<\/p>\n

                        M<\/p>\n

                        <\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u5f88\u5927\u65f6\u8d85\u65f6<\/td>\n<\/tr>\n

                        \u6bcf\u4e2a\u6570\u5b57\u51fa\u73b0 <\/p>\n

                        k<\/p>\n

                        k<\/p>\n

                        <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u6b21<\/td>\n

                        		\u4e8c\u5206\u5224\u5b9a\u4e2d\u914d\u5bf9\u903b\u8f91\u6539\u4e3a\u8ba1\u6570\u5668<\/td>\n<\/p>\n

                        O<\/p>\n

                        (<\/p>\n

                        N<\/p>\n

                        log<\/p>\n

                        \u2061<\/p>\n

                        M<\/p>\n

                        )<\/p>\n

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

                        <\/span><\/span>O<\/span>(<\/span>N<\/span><\/span>log<\/span><\/span><\/span>M<\/span>)<\/span><\/span><\/span><\/span><\/span><\/td>\n

                        		<\/p>\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><\/td>\n

                        		\u6269\u5c55\u6027\u597d<\/td>\n\u5224\u5b9a\u903b\u8f91\u7565\u590d\u6742<\/td>\n<\/tr>\n
                        \u79fb\u52a8\u4ee3\u4ef7\u4e0e\u4f4d\u7f6e\u6709\u5173<\/td>\n\u4e0d\u80fd\u7b80\u5355\u7528\u9608\u503c\u4e8c\u5206，\u9700\u7528 DP \u6216\u8d39\u7528\u6d41<\/td>\n\u66f4\u9ad8<\/td>\n\u66f4\u9ad8<\/td>\n\u53ef\u5904\u7406\u590d\u6742\u4ee3\u4ef7<\/td>\n\u5b9e\u73b0\u96be\u5ea6\u5927<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                        6. \u5de5\u7a0b\u89c6\u89d2<\/h3>\n

                        "\u4e8c\u5206\u7b54\u6848 + \u8d2a\u5fc3\u5224\u5b9a"\u8fd9\u4e00\u8303\u5f0f\u5728\u5b9e\u9645\u5de5\u7a0b\u4e2d\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528：<\/p>\n

                      • \u4efb\u52a1\u8c03\u5ea6\u4e2d\u7684\u8d44\u6e90\u5206\u914d：\u7ed9\u5b9a\u4e00\u7cfb\u5217\u4efb\u52a1，\u6bcf\u4e2a\u4efb\u52a1\u9700\u8981\u4e00\u5b9a\u8d44\u6e90，\u6c42\u6700\u5c0f\u7684\u8d44\u6e90\u4e0a\u9650\u4f7f\u5f97\u6240\u6709\u4efb\u52a1\u53ef\u5b8c\u6210\u3002\u5178\u578b\u5e94\u7528\u5305\u62ec\u4e91\u8ba1\u7b97\u4e2d\u7684\u8d1f\u8f7d\u5747\u8861\u3001\u5de5\u5382\u751f\u4ea7\u7ebf\u7684\u4ea7\u80fd\u5206\u914d\u7b49\u3002<\/li>\n
                      • \u7f51\u7edc\u4f20\u8f93\u4e2d\u7684\u5e26\u5bbd\u9650\u5236：\u6c42\u6700\u5c0f\u5e26\u5bbd\u9608\u503c，\u4f7f\u5f97\u6240\u6709\u6570\u636e\u6d41\u80fd\u5728\u4e0d\u8d85\u8fc7\u8be5\u5e26\u5bbd\u7684\u60c5\u51b5\u4e0b\u6309\u65f6\u4f20\u8f93\u3002\u5224\u5b9a\u51fd\u6570\u901a\u5e38\u7528\u8d2a\u5fc3\u6216\u7f51\u7edc\u6d41\u5b9e\u73b0\u3002<\/li>\n
                      • \u7269\u6d41\u914d\u9001\u4e2d\u7684\u8f66\u8f86\u8f7d\u91cd：\u6c42\u6700\u5c0f\u8f7d\u91cd \n

                        x<\/p>\n

                        x<\/p>\n

                        <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>，\u4f7f\u5f97\u6240\u6709\u8d27\u7269\u80fd\u7528\u82e5\u5e72\u8f86\u8f66\u8fd0\u5b8c\u3002\u5224\u5b9a\u51fd\u6570\u7528\u8d2a\u5fc3\u88c5\u7bb1（First Fit \u7b49）\u5b9e\u73b0\u3002<\/li>\n

                      • \u4ee3\u7801\u5ba1\u67e5\u4e2d\u7684"\u6700\u5927\u53ef\u5bb9\u5fcd\u590d\u6742\u5ea6"：\u7ed9\u5b9a\u4e00\u7cfb\u5217\u4ee3\u7801\u6a21\u5757\u7684\u590d\u6742\u5ea6\u8bc4\u5206，\u6c42\u6700\u5c0f\u7684\u590d\u6742\u5ea6\u9608\u503c，\u4f7f\u5f97\u8d85\u8fc7\u8be5\u9608\u503c\u7684\u6a21\u5757\u4e4b\u95f4\u4e0d\u5f62\u6210\u4f9d\u8d56\u73af（\u4e0d\u53ef\u79fb\u52a8\u7684\u9ad8\u590d\u6742\u5ea6\u6a21\u5757\u5fc5\u987b\u5df2\u7ecf\u89e3\u8026）\u3002<\/li>\n
                      • \u6e38\u620f\u5e73\u8861\u6027\u4e2d\u7684\u6570\u503c\u8c03\u6574：\u5728\u5361\u724c\u6e38\u620f\u4e2d，\u6c42\u6700\u5c0f\u7684\u5355\u5361\u5f3a\u5ea6\u4e0a\u9650，\u4f7f\u5f97\u6240\u6709\u8d85\u8fc7\u8be5\u4e0a\u9650\u7684\u5361\u724c\u5728\u539f\u59cb\u5361\u7ec4\u4e2d\u5df2\u7ecf"\u6210\u5bf9\u5e73\u8861"\u3002<\/li>\n

                        7. \u5c0f\u7ed3<\/h3>\n

                        \u6838\u5fc3\u516c\u5f0f：<\/p>\n

                        \u7ed9\u5b9a\u9608\u503c <\/p>\n

                        x<\/p>\n

                        x<\/p>\n

                        <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>，\u4ee4\u5e8f\u5217 <\/p>\n

                        B<\/p>\n

                        (<\/p>\n

                        x<\/p>\n

                        )<\/p>\n

                        =<\/p>\n

                        [<\/p>\n

                        A<\/p>\n

                        i<\/p>\n

                        \u2223<\/p>\n

                        A<\/p>\n

                        i<\/p>\n

                        ><\/p>\n

                        x<\/p>\n

                        ]<\/p>\n

                        B(x) = [A_i \\\\mid A_i > x]<\/p>\n

                        <\/span><\/span>B<\/span>(<\/span>x<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>A<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span>A<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span>]<\/span><\/span><\/span><\/span><\/span>（\u5373\u5220\u9664\u6240\u6709 <\/p>\n

                        \u2264<\/p>\n

                        x<\/p>\n

                        \\\\le x<\/p>\n

                        <\/span><\/span>\u2264<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u5143\u7d20）\u3002<\/p>\n

                        x<\/p>\n

                        x<\/p>\n

                        <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u53ef\u884c\u5f53\u4e14\u4ec5\u5f53 <\/p>\n

                        B<\/p>\n

                        (<\/p>\n

                        x<\/p>\n

                        )<\/p>\n

                        B(x)<\/p>\n

                        <\/span><\/span>B<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u5143\u7d20\u53ef\u4ee5\u5212\u5206\u4e3a\u82e5\u5e72\u5bf9\u76f8\u90bb\u7684\u76f8\u540c\u6570\u5b57，\u5373： <\/p>\n

                        B<\/p>\n

                        (<\/p>\n

                        x<\/p>\n

                        )<\/p>\n

                        \u2208<\/p>\n

                        (<\/p>\n

                        a<\/p>\n

                        1<\/p>\n

                        a<\/p>\n

                        1<\/p>\n

                        a<\/p>\n

                        2<\/p>\n

                        a<\/p>\n

                        2<\/p>\n

                        \u22ef<\/p>\n

                        a<\/p>\n

                        k<\/p>\n

                        a<\/p>\n

                        k<\/p>\n

                        )<\/p>\n

                        \u5176\u4e2d\u00a0<\/p>\n

                        a<\/p>\n

                        i<\/p>\n

                        \u00a0\u4e24\u4e24\u4e0d\u540c<\/p>\n

                        B(x) \\\\in (a_1a_1a_2a_2\\\\cdots a_ka_k) \\\\quad \\\\text{\u5176\u4e2d } a_i \\\\text{ \u4e24\u4e24\u4e0d\u540c} <\/p>\n

                        <\/span><\/span>B<\/span>(<\/span>x<\/span>)<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22ef<\/span><\/span>a<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u5176\u4e2d<\/span>\u00a0<\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0<\/span>\u4e24\u4e24\u4e0d\u540c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                        \u4e8c\u5206\u641c\u7d22\u6700\u5c0f\u7684 <\/p>\n

                        x<\/p>\n

                        x<\/p>\n

                        <\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u6ee1\u8db3\u4e0a\u8ff0\u6761\u4ef6\u3002<\/p>\n

                        \u6838\u5fc3\u8ba4\u77e5：<\/p>\n

                          \n
                        • \u201c\u6700\u5c0f\u5316\u6700\u5927\u503c"\u7c7b\u95ee\u9898，\u4f18\u5148\u8003\u8651\u4e8c\u5206\u7b54\u6848\u3002\u5173\u952e\u662f\u628a"\u6c42\u6700\u4f18\u89e3"\u8f6c\u5316\u4e3a"\u5224\u5b9a\u7ed9\u5b9a\u9608\u503c\u662f\u5426\u53ef\u884c\u201d\u3002<\/li>\n
                        • \u79fb\u52a8\u9650\u5236\u95ee\u9898\u4e2d，\u4e0d\u53ef\u79fb\u52a8\u7684\u5143\u7d20\u662f"\u951a\u70b9"，\u5b83\u4eec\u7684\u76f8\u5bf9\u987a\u5e8f\u5fc5\u987b\u5df2\u7ecf\u6ee1\u8db3\u76ee\u6807\u6761\u4ef6\u3002\u53ef\u79fb\u52a8\u5143\u7d20\u53ef\u4ee5\u88ab\u5ffd\u7565\u3002<\/li>\n
                        • \u8d2a\u5fc3\u5224\u5b9a\u51fd\u6570\u8981\u5145\u5206\u5229\u7528\u95ee\u9898\u7684\u7ed3\u6784\u2014\u2014\u672c\u9898\u4e2d"\u6bcf\u4e2a\u6570\u5b57\u6070\u597d\u51fa\u73b0\u4e24\u6b21"\u8ba9\u914d\u5bf9\u68c0\u67e5\u53d8\u5f97\u6781\u5176\u7b80\u5355\u3002\u5982\u679c\u51fa\u73b0\u6b21\u6570\u4e0d\u540c，\u5224\u5b9a\u903b\u8f91\u9700\u8981\u76f8\u5e94\u8c03\u6574\u3002<\/li>\n
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