{"id":118971,"date":"2026-10-28T15:40:40","date_gmt":"2026-10-28T07:40:40","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/118971.html"},"modified":"2026-10-28T15:40:40","modified_gmt":"2026-10-28T07:40:40","slug":"java%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84-%e6%8e%92%e5%ba%8f","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/118971.html","title":{"rendered":"JAVA\u6570\u636e\u7ed3\u6784--\u6392\u5e8f"},"content":{"rendered":"

\u6392\u5e8f\u7b97\u6cd5\u8be6\u89e3：\u4e03\u5927\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u4e0e\u975e\u6bd4\u8f83\u6392\u5e8f<\/h2>\n

\u5b66\u4e60\u76ee\u6807<\/p>\n

  • \u638c\u63e1\u4e03\u5927\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u7b97\u6cd5\u7684\u57fa\u672c\u539f\u7406\u53ca\u5b9e\u73b0；<\/li>\n
  • \u638c\u63e1\u6392\u5e8f\u7b97\u6cd5\u7684\u6027\u80fd\u5206\u6790（\u65f6\u95f4\u590d\u6742\u5ea6\u3001\u7a7a\u95f4\u590d\u6742\u5ea6\u3001\u7a33\u5b9a\u6027）；<\/li>\n
  • \u638c\u63e1 Java \u4e2d\u7684\u5e38\u7528\u6392\u5e8f\u65b9\u6cd5\u3002<\/li>\n

    \u76ee\u5f55<\/h3>\n
      \n
    • 1. \u6392\u5e8f\u7684\u6982\u5ff5\u53ca\u8fd0\u7528\n
        \n
      • 1.1 \u6392\u5e8f\u7684\u6982\u5ff5<\/li>\n
      • 1.2 \u6392\u5e8f\u7684\u8fd0\u7528<\/li>\n<\/ul>\n<\/li>\n
      • 2. \u5e38\u89c1\u6392\u5e8f\u7b97\u6cd5\n
          \n
        • 2.1 \u63d2\u5165\u6392\u5e8f\n
            \n
          • 2.1.1 \u76f4\u63a5\u63d2\u5165\u6392\u5e8f<\/li>\n
          • 2.1.2 \u5e0c\u5c14\u6392\u5e8f（\u7f29\u5c0f\u589e\u91cf\u6392\u5e8f）<\/li>\n<\/ul>\n<\/li>\n
          • 2.2 \u9009\u62e9\u6392\u5e8f\n
              \n
            • 2.2.1 \u76f4\u63a5\u9009\u62e9\u6392\u5e8f<\/li>\n
            • 2.2.2 \u5806\u6392\u5e8f<\/li>\n<\/ul>\n<\/li>\n
            • 2.3 \u4ea4\u6362\u6392\u5e8f\n
                \n
              • 2.3.1 \u5192\u6ce1\u6392\u5e8f<\/li>\n
              • 2.3.2 \u5feb\u901f\u6392\u5e8f<\/li>\n
              • 2.3.3 \u5feb\u901f\u6392\u5e8f\u7684\u4f18\u5316<\/li>\n
              • 2.3.4 \u5feb\u901f\u6392\u5e8f\u7684\u975e\u9012\u5f52\u5b9e\u73b0<\/li>\n
              • 2.3.5 \u5feb\u901f\u6392\u5e8f\u603b\u7ed3<\/li>\n<\/ul>\n<\/li>\n
              • 2.4 \u5f52\u5e76\u6392\u5e8f\n
                  \n
                • 2.4.1 \u57fa\u672c\u601d\u60f3\u4e0e\u5b9e\u73b0<\/li>\n
                • 2.4.2 \u5f52\u5e76\u6392\u5e8f\u603b\u7ed3<\/li>\n
                • 2.4.3 \u6d77\u91cf\u6570\u636e\u7684\u6392\u5e8f\u95ee\u9898<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n
                • 3. \u6392\u5e8f\u7b97\u6cd5\u590d\u6742\u5ea6\u53ca\u7a33\u5b9a\u6027\u5206\u6790<\/li>\n
                • 4. \u5176\u4ed6\u975e\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\n
                    \n
                  • 4.1 \u8ba1\u6570\u6392\u5e8f<\/li>\n
                  • 4.2 \u57fa\u6570\u6392\u5e8f<\/li>\n
                  • 4.3 \u6876\u6392\u5e8f<\/li>\n<\/ul>\n<\/li>\n
                  • 5. \u5168\u6587\u603b\u7ed3<\/li>\n<\/ul>\n
                    \n

                    1. \u6392\u5e8f\u7684\u6982\u5ff5\u53ca\u8fd0\u7528<\/h3>\n

                    1.1 \u6392\u5e8f\u7684\u6982\u5ff5<\/h4>\n

                    \u6392\u5e8f：\u6240\u8c13\u6392\u5e8f，\u5c31\u662f\u4f7f\u4e00\u4e32\u8bb0\u5f55，\u6309\u7167\u5176\u4e2d\u7684\u67d0\u4e2a\u6216\u67d0\u4e9b\u5173\u952e\u5b57\u7684\u5927\u5c0f，\u9012\u589e\u6216\u9012\u51cf\u5730\u6392\u5217\u8d77\u6765\u7684\u64cd\u4f5c\u3002\u901a\u5e38\u8ba8\u8bba\u7684\u662f**\u975e\u9012\u51cf（\u5347\u5e8f）**\u6392\u5217；\u82e5\u5f85\u6392\u5e8f\u5217\u4e2d\u6240\u6709\u5173\u952e\u5b57\u4e92\u4e0d\u76f8\u540c，\u5219\u6392\u5e8f\u7ed3\u679c\u662f\u552f\u4e00\u7684\u3002<\/p>\n

                    \u7a33\u5b9a\u6027：\u5047\u5b9a\u5728\u5f85\u6392\u5e8f\u7684\u8bb0\u5f55\u5e8f\u5217\u4e2d，\u5b58\u5728\u591a\u4e2a\u5177\u6709\u76f8\u540c\u5173\u952e\u5b57\u7684\u8bb0\u5f55\u3002\u82e5\u7ecf\u8fc7\u6392\u5e8f，\u8fd9\u4e9b\u8bb0\u5f55\u7684\u76f8\u5bf9\u6b21\u5e8f\u4fdd\u6301\u4e0d\u53d8\u2014\u2014\u5373\u5728\u539f\u5e8f\u5217\u4e2d r[i] = r[j]，\u4e14 r[i] \u5728 r[j] \u4e4b\u524d，\u800c\u5728\u6392\u5e8f\u540e\u7684\u5e8f\u5217\u4e2d r[i] \u4ecd\u7136\u5728 r[j] \u4e4b\u524d\u2014\u2014\u5219\u79f0\u8fd9\u79cd\u6392\u5e8f\u7b97\u6cd5\u662f\u7a33\u5b9a\u7684；\u5426\u5219\u79f0\u4e3a\u4e0d\u7a33\u5b9a\u7684\u3002<\/p>\n

                    \u7a33\u5b9a\u6027\u4e3a\u4ec0\u4e48\u91cd\u8981？\u8003\u8651\u591a\u5173\u952e\u5b57\u6392\u5e8f：\u5148\u6309"\u6570\u5b66\u6210\u7ee9"\u6392\u597d，\u518d\u6309"\u8bed\u6587\u6210\u7ee9"\u505a\u4e00\u6b21\u7a33\u5b9a\u6392\u5e8f，\u5219\u8bed\u6587\u6210\u7ee9\u76f8\u540c\u7684\u540c\u5b66\u4ecd\u7136\u4fdd\u6301\u6570\u5b66\u6210\u7ee9\u7684\u76f8\u5bf9\u987a\u5e8f\u3002\u5982\u679c\u7b2c\u4e8c\u6b21\u6392\u5e8f\u4e0d\u7a33\u5b9a，\u7b2c\u4e00\u6b21\u7684\u7ed3\u679c\u5c31\u88ab\u7834\u574f\u4e86\u3002\u56e0\u6b64\u7a33\u5b9a\u6027\u76f4\u63a5\u51b3\u5b9a\u4e86\u6392\u5e8f\u7b97\u6cd5\u80fd\u5426\u7528\u4e8e\u591a\u5173\u952e\u5b57\u573a\u666f\u3002<\/p>\n

                    \u5185\u90e8\u6392\u5e8f：\u6574\u4e2a\u6392\u5e8f\u8fc7\u7a0b\u5b8c\u5168\u5728\u5185\u5b58\u4e2d\u8fdb\u884c\u7684\u6392\u5e8f（\u6570\u636e\u5143\u7d20\u5168\u90e8\u653e\u5728\u5185\u5b58\u4e2d）\u3002\u672c\u6587\u8ba8\u8bba\u7684\u4e03\u5927\u6392\u5e8f\u90fd\u5c5e\u4e8e\u5185\u90e8\u6392\u5e8f\u3002<\/p>\n

                    \u5916\u90e8\u6392\u5e8f：\u6570\u636e\u5143\u7d20\u592a\u591a\u3001\u4e0d\u80fd\u540c\u65f6\u653e\u5728\u5185\u5b58\u4e2d，\u9700\u8981\u6839\u636e\u6392\u5e8f\u8fc7\u7a0b\u7684\u8981\u6c42\u4e0d\u65ad\u5728\u5185\u5916\u5b58\u4e4b\u95f4\u79fb\u52a8\u6570\u636e\u7684\u6392\u5e8f\u3002\u4f8b\u5982\u5bf9\u78c1\u76d8\u4e0a\u7684\u5927\u6587\u4ef6\u6392\u5e8f（\u8be6\u89c1 2.4.3 \u8282）\u3002<\/p>\n

                    1.2 \u6392\u5e8f\u7684\u8fd0\u7528<\/h4>\n

                    \u6392\u5e8f\u5728\u5b9e\u9645\u751f\u6d3b\u4e2d\u65e0\u5904\u4e0d\u5728，\u6700\u5178\u578b\u7684\u5c31\u662f\u7535\u5546\u5546\u54c1\u5217\u8868\u7684\u591a\u7ef4\u5ea6\u6392\u5e8f\u3002\u4ee5\u4eac\u4e1c\u4e3a\u4f8b，\u5546\u54c1\u5217\u8868\u9875\u9876\u90e8\u63d0\u4f9b\u4e86\u300c\u7efc\u5408\u3001\u9500\u91cf\u3001\u8bc4\u8bba\u6570\u3001\u65b0\u54c1\u3001\u4ef7\u683c\u300d\u7b49\u6392\u5e8f\u65b9\u5f0f：<\/p>\n

                      \n
                    • \u70b9\u51fb\u300c\u4ef7\u683c\u300d，\u540e\u53f0\u5c31\u628a\u8be5\u7c7b\u76ee\u4e0b\u7684\u5546\u54c1\u6309\u7167\u4ef7\u683c\u5b57\u6bb5\u505a\u5347\u5e8f\u6216\u964d\u5e8f\u6392\u5217；<\/li>\n
                    • \u70b9\u51fb\u300c\u9500\u91cf\u300d，\u5219\u6309\u7167\u9500\u91cf\u5b57\u6bb5\u964d\u5e8f\u6392\u5217；<\/li>\n
                    • \u300c\u7efc\u5408\u300d\u5219\u662f\u4e00\u4e2a\u52a0\u6743\u540e\u7684\u590d\u5408\u5173\u952e\u5b57\u6392\u5e8f\u3002<\/li>\n<\/ul>\n

                      \u9664\u6b64\u4e4b\u5916，\u6392\u5e8f\u8fd8\u5e7f\u6cdb\u5e94\u7528\u4e8e：\u6570\u636e\u5e93\u7684 ORDER BY \u67e5\u8be2\u3001\u64cd\u4f5c\u7cfb\u7edf\u7684\u8fdb\u7a0b\u8c03\u5ea6\u3001\u641c\u7d22\u5f15\u64ce\u7684\u7ed3\u679c\u6392\u540d\u3001\u6587\u4ef6\u7cfb\u7edf\u7684\u76ee\u5f55\u7ec4\u7ec7\u3001\u4ee5\u53ca\u4f5c\u4e3a\u4e8c\u5206\u67e5\u627e\u7b49\u7b97\u6cd5\u7684\u524d\u7f6e\u6761\u4ef6（\u4e8c\u5206\u67e5\u627e\u8981\u6c42\u5e8f\u5217\u6709\u5e8f）\u3002\u53ef\u4ee5\u8bf4，\u6392\u5e8f\u662f\u7a0b\u5e8f\u8bbe\u8ba1\u4e2d\u4f7f\u7528\u9891\u7387\u6700\u9ad8\u3001\u4e5f\u662f\u6700\u91cd\u8981\u7684\u57fa\u7840\u64cd\u4f5c\u4e4b\u4e00\u3002<\/p>\n

                      \n

                      2. \u5e38\u89c1\u6392\u5e8f\u7b97\u6cd5<\/h3>\n

                      \u6392\u5e8f\u7b97\u6cd5\u4e3b\u8981\u5206\u4e3a\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u548c\u975e\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u4e24\u5927\u7c7b\u3002\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u6709\u4e03\u5927\u7c7b：\u63d2\u5165\u6392\u5e8f（\u76f4\u63a5\u63d2\u5165\u3001\u5e0c\u5c14\u6392\u5e8f）\u3001\u9009\u62e9\u6392\u5e8f（\u76f4\u63a5\u9009\u62e9\u3001\u5806\u6392\u5e8f）\u3001\u4ea4\u6362\u6392\u5e8f（\u5192\u6ce1\u3001\u5feb\u901f\u6392\u5e8f）\u3001\u5f52\u5e76\u6392\u5e8f\u3002\u672c\u7ae0\u9010\u4e00\u8bb2\u89e3\u3002<\/p>\n

                      2.1 \u63d2\u5165\u6392\u5e8f<\/h4>\n

                      2.1.1 \u76f4\u63a5\u63d2\u5165\u6392\u5e8f<\/h5>\n

                      \u57fa\u672c\u601d\u60f3：\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u662f\u4e00\u79cd\u6700\u7b80\u5355\u7684\u63d2\u5165\u6392\u5e8f\u6cd5，\u5176\u57fa\u672c\u601d\u60f3\u662f：\u628a\u5f85\u6392\u5e8f\u7684\u8bb0\u5f55\u6309\u5176\u5173\u952e\u7801\u503c\u7684\u5927\u5c0f\u9010\u4e2a\u63d2\u5165\u5230\u4e00\u4e2a\u5df2\u7ecf\u6392\u597d\u5e8f\u7684\u6709\u5e8f\u5e8f\u5217\u4e2d，\u76f4\u5230\u6240\u6709\u7684\u8bb0\u5f55\u63d2\u5165\u5b8c\u4e3a\u6b62，\u5f97\u5230\u4e00\u4e2a\u65b0\u7684\u6709\u5e8f\u5e8f\u5217\u3002<\/p>\n

                      \u751f\u6d3b\u4e2d\u6211\u4eec\u6253\u6251\u514b\u724c\u65f6\u6293\u724c\u3001\u7406\u724c\u7684\u8fc7\u7a0b\u7528\u7684\u5c31\u662f\u63d2\u5165\u6392\u5e8f\u601d\u60f3：\u624b\u4e2d\u724c\u59cb\u7ec8\u662f\u6709\u5e8f\u7684，\u6bcf\u6b21\u6478\u4e00\u5f20\u65b0\u724c，\u5c31\u628a\u5b83\u63d2\u5165\u5230\u624b\u4e2d\u5df2\u6392\u5e8f\u5e8f\u5217\u7684\u5408\u9002\u4f4d\u7f6e\u3002<\/p>\n

                      \u5f53\u63d2\u5165\u7b2c i (i >= 1) \u4e2a\u5143\u7d20\u65f6，\u524d\u9762\u7684 array[0], array[1], \u2026, array[i-1] \u5df2\u7ecf\u6392\u597d\u5e8f，\u6b64\u65f6\u7528 array[i] \u7684\u6392\u5e8f\u7801\u4e0e array[i-1], array[i-2], \u2026 \u7684\u6392\u5e8f\u7801\u987a\u5e8f（\u4ece\u540e\u5f80\u524d）\u8fdb\u884c\u6bd4\u8f83，\u627e\u5230\u63d2\u5165\u4f4d\u7f6e\u540e\u5c06 array[i] \u63d2\u5165，\u539f\u6765\u4f4d\u7f6e\u4e0a\u7684\u5143\u7d20\u987a\u5e8f\u540e\u79fb\u3002<\/p>\n

                      \/\/ \u76f4\u63a5\u63d2\u5165\u6392\u5e8f：\u5347\u5e8f<\/span>
                      \npublic<\/span> static<\/span> void<\/span> insertionSort<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array)<\/span> {<\/span>
                      \n \/\/ \u628a array[i] \u63d2\u5165\u5230 [0, i-1] \u7684\u6709\u5e8f\u533a\u95f4\u4e2d<\/span>
                      \n for<\/span> (<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <<\/span> array.<\/span>length;<\/span> i++<\/span>)<\/span> {<\/span>
                      \n int<\/span> tmp =<\/span> array[<\/span>i]<\/span>;<\/span> \/\/ \u5f85\u63d2\u5165\u5143\u7d20，\u5148\u53d6\u51fa"\u54e8\u5175"\u9632\u6b62\u88ab\u8986\u76d6<\/span>
                      \n int<\/span> j =<\/span> i –<\/span> 1<\/span>;<\/span>
                      \n \/\/ \u6bd4 tmp \u5927\u7684\u5143\u7d20\u7edf\u4e00\u540e\u79fb\u4e00\u4f4d，\u4e3a tmp \u817e\u4f4d\u7f6e<\/span>
                      \n while<\/span> (<\/span>j >=<\/span> 0<\/span> &&<\/span> array[<\/span>j]<\/span> ><\/span> tmp)<\/span> {<\/span>
                      \n array[<\/span>j +<\/span> 1<\/span>]<\/span> =<\/span> array[<\/span>j]<\/span>;<\/span>
                      \n j—<\/span>;<\/span>
                      \n }<\/span>
                      \n \/\/ \u5faa\u73af\u7ed3\u675f，j+1 \u5373\u4e3a\u63d2\u5165\u4f4d\u7f6e<\/span>
                      \n array[<\/span>j +<\/span> 1<\/span>]<\/span> =<\/span> tmp;<\/span>
                      \n }<\/span>
                      \n}<\/span><\/p>\n

                      \u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u7684\u7279\u6027\u603b\u7ed3：<\/p>\n

                    • \u5143\u7d20\u96c6\u5408\u8d8a\u63a5\u8fd1\u6709\u5e8f，\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u6548\u7387\u8d8a\u9ad8（\u6700\u4f18\u60c5\u51b5\u4e0b\u6bcf\u6b21\u6bd4\u8f83\u4e00\u6b21\u5373\u63d2\u5165，\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u964d\u4e3a O(N)）；<\/li>\n
                    • \u65f6\u95f4\u590d\u6742\u5ea6：O(N\u00b2)\u3002\u6700\u574f\u60c5\u51b5（\u9006\u5e8f）\u65f6，\u7b2c i \u4e2a\u5143\u7d20\u9700\u8981\u79fb\u52a8 i \u6b21，\u603b\u79fb\u52a8\u6b21\u6570\u4e3a 1 + 2 + \u2026 + (N-1) = N(N-1)\/2；<\/li>\n
                    • \u7a7a\u95f4\u590d\u6742\u5ea6：O(1)，\u53ea\u7528\u5230\u5e38\u6570\u4e2a\u4e34\u65f6\u53d8\u91cf；<\/li>\n
                    • \u7a33\u5b9a\u6027：\u7a33\u5b9a\u3002\u56e0\u4e3a\u53ea\u628a\u300c\u4e25\u683c\u5927\u4e8e\u300d\u5f85\u63d2\u5143\u7d20\u7684\u503c\u540e\u79fb，\u76f8\u7b49\u5143\u7d20\u4e0d\u4f1a\u88ab\u8d8a\u8fc7\u3002<\/li>\n
                      2.1.2 \u5e0c\u5c14\u6392\u5e8f（\u7f29\u5c0f\u589e\u91cf\u6392\u5e8f）<\/h5>\n

                      \u5e0c\u5c14\u6392\u5e8f\u6cd5\u53c8\u79f0\u7f29\u5c0f\u589e\u91cf\u6cd5，\u662f\u5bf9\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u7684\u4f18\u5316\u3002<\/p>\n

                      \u57fa\u672c\u601d\u60f3：\u5148\u9009\u5b9a\u4e00\u4e2a\u6574\u6570 gap，\u628a\u5f85\u6392\u5e8f\u6587\u4ef6\u4e2d\u6240\u6709\u8bb0\u5f55\u5206\u6210 gap \u4e2a\u7ec4，\u6240\u6709\u8ddd\u79bb\u4e3a gap \u7684\u8bb0\u5f55\u5206\u5728\u540c\u4e00\u7ec4\u5185，\u5e76\u5bf9\u6bcf\u4e00\u7ec4\u5185\u7684\u8bb0\u5f55\u8fdb\u884c\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u3002\u7136\u540e\u53d6 gap = gap \/ 2（\u6216 \/ 3），\u91cd\u590d\u4e0a\u8ff0\u5206\u7ec4\u548c\u6392\u5e8f\u7684\u5de5\u4f5c\u3002\u5f53 gap = 1 \u65f6，\u6240\u6709\u8bb0\u5f55\u88ab\u5206\u5728\u7edf\u4e00\u7ec4\u5185，\u6b64\u65f6\u6570\u7ec4\u5df2\u7ecf\u63a5\u8fd1\u6709\u5e8f，\u518d\u8d70\u4e00\u904d\u63d2\u5165\u6392\u5e8f\u5373\u53ef\u5feb\u901f\u5b8c\u6210\u3002<\/p>\n

                      \/\/ \u5e0c\u5c14\u6392\u5e8f：\u5347\u5e8f<\/span>
                      \npublic<\/span> static<\/span> void<\/span> shellSort<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array)<\/span> {<\/span>
                      \n int<\/span> gap =<\/span> array.<\/span>length;<\/span>
                      \n while<\/span> (<\/span>gap ><\/span> 1<\/span>)<\/span> {<\/span>
                      \n gap =<\/span> gap \/<\/span> 3<\/span> +<\/span> 1<\/span>;<\/span> \/\/ +1 \u4fdd\u8bc1\u6700\u540e\u4e00\u8f6e gap \u4e00\u5b9a\u7b49\u4e8e 1<\/span>
                      \n \/\/ \u5206\u522b\u5bf9 gap \u4e2a\u5206\u7ec4\u505a\u76f4\u63a5\u63d2\u5165\u6392\u5e8f<\/span>
                      \n for<\/span> (<\/span>int<\/span> i =<\/span> gap;<\/span> i <<\/span> array.<\/span>length;<\/span> i++<\/span>)<\/span> {<\/span>
                      \n int<\/span> tmp =<\/span> array[<\/span>i]<\/span>;<\/span>
                      \n int<\/span> j =<\/span> i –<\/span> gap;<\/span>
                      \n while<\/span> (<\/span>j >=<\/span> 0<\/span> &&<\/span> array[<\/span>j]<\/span> ><\/span> tmp)<\/span> {<\/span>
                      \n array[<\/span>j +<\/span> gap]<\/span> =<\/span> array[<\/span>j]<\/span>;<\/span>
                      \n j -=<\/span> gap;<\/span>
                      \n }<\/span>
                      \n array[<\/span>j +<\/span> gap]<\/span> =<\/span> tmp;<\/span>
                      \n }<\/span>
                      \n }<\/span>
                      \n}<\/span><\/p>\n

                      \u5e0c\u5c14\u6392\u5e8f\u7684\u7279\u6027\u603b\u7ed3：<\/p>\n

                    • \u5e0c\u5c14\u6392\u5e8f\u662f\u5bf9\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u7684\u4f18\u5316\u3002gap \u8d8a\u5927，\u5206\u7ec4\u8d8a\u5c11\u3001\u6bcf\u7ec4\u5143\u7d20\u8d8a\u5c11，\u9884\u6392\u5e8f\u8d8a\u4e0d\u7a33\u5b9a；gap \u8d8a\u5c0f，\u5206\u7ec4\u8d8a\u591a\u3001\u6bcf\u7ec4\u5143\u7d20\u8d8a\u591a，\u6570\u7ec4\u8d8a\u63a5\u8fd1\u6709\u5e8f；<\/li>\n
                    • \u5f53 gap > 1 \u65f6\u90fd\u662f\u9884\u6392\u5e8f，\u76ee\u7684\u662f\u8ba9\u6570\u7ec4\u66f4\u63a5\u8fd1\u6709\u5e8f；\u5f53 gap == 1 \u65f6，\u6570\u7ec4\u5df2\u7ecf\u63a5\u8fd1\u6709\u5e8f，\u8fd9\u4e00\u8d9f\u5f88\u5feb\u5c31\u80fd\u5b8c\u6210\u3002\u6574\u4f53\u800c\u8a00\u53ef\u4ee5\u8fbe\u5230\u4f18\u5316\u6548\u679c（\u5b9e\u73b0\u540e\u53ef\u901a\u8fc7\u6027\u80fd\u6d4b\u8bd5\u4e0e\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u5bf9\u6bd4\u9a8c\u8bc1）；<\/li>\n
                    • \u7a7a\u95f4\u590d\u6742\u5ea6：O(1)；<\/li>\n
                    • \u7a33\u5b9a\u6027：\u4e0d\u7a33\u5b9a\u3002\u76f8\u540c\u7684\u4e24\u4e2a\u5143\u7d20\u53ef\u80fd\u88ab\u5206\u5230\u4e0d\u540c\u7684\u7ec4\u4e2d，\u4ece\u800c\u6539\u53d8\u76f8\u5bf9\u6b21\u5e8f\u3002<\/li>\n

                      \u5e0c\u5c14\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4f30\u7b97：<\/p>\n

                        \n
                      • \n

                        \u5916\u5c42\u5faa\u73af：gap \u6bcf\u6b21\u7f29\u5c0f\u4e00\u534a（\u6216\u4e09\u5206\u4e4b\u4e00），\u4ece N \u7f29\u5230 1，\u56e0\u6b64\u5916\u5c42\u5faa\u73af\u6b21\u6570\u4e3a O(log\u2082n) \u6216 O(log\u2083n)，\u5373 O(log n)\u3002<\/p>\n<\/li>\n

                      • \n

                        \u5185\u5c42\u5faa\u73af：\u5047\u8bbe\u4e00\u5171\u6709 n \u4e2a\u6570\u636e，\u5206\u6210 gap \u7ec4，\u5219\u6bcf\u7ec4\u4e3a n\/gap \u4e2a\u3002\u5728\u6bcf\u7ec4\u4e2d\u63d2\u5165\u79fb\u52a8\u7684\u6b21\u6570\u6700\u574f\u60c5\u51b5\u4e0b\u4e3a 1 + 2 + 3 + \u2026 + (n\/gap – 1)，\u4e00\u5171 gap \u7ec4，\u56e0\u6b64\u603b\u8ba1\u6700\u574f\u60c5\u51b5\u4e0b\u7684\u79fb\u52a8\u603b\u6570\u4e3a：<\/p>\n

                        gap \u00d7 [1 + 2 + 3 + \u2026 + (n\/gap – 1)]<\/p>\n

                        \u4ee5\u300c\u9664 3\u300d\u4e3a\u4f8b，gap \u7684\u53d6\u503c\u6709：n\/3, n\/9, n\/27, \u2026, 2, 1：<\/p>\n

                          \n
                        • \u5f53 gap = n\/3 \u65f6，\u79fb\u52a8\u603b\u6570\u4e3a (n\/3) \u00d7 (1 + 2) = n；<\/li>\n
                        • \u5f53 gap = n\/9 \u65f6，\u79fb\u52a8\u603b\u6570\u4e3a (n\/9) \u00d7 (1 + 2 + \u2026 + 8) = (n\/9) \u00d7 [8 \u00d7 (1 + 8) \/ 2] = 4n；<\/li>\n
                        • \u6700\u540e\u4e00\u8d9f gap = 1，\u5373\u76f4\u63a5\u63d2\u5165\u6392\u5e8f，\u5185\u5c42\u5faa\u73af\u6392\u5e8f\u6d88\u8017\u4e3a n\u3002<\/li>\n<\/ul>\n

                          \u7531\u6b64\u53ef\u4ee5\u753b\u51fa\u4e00\u6761\u66f2\u7ebf：\u5e0c\u5c14\u6392\u5e8f\u5728\u6700\u521d\u548c\u6700\u540e\u9636\u6bb5\u7684\u6392\u5e8f\u6b21\u6570\u90fd\u4e3a n，\u4e2d\u95f4\u9636\u6bb5\u5148\u9010\u6e10\u4e0a\u5347\u5230\u67d0\u4e2a\u9876\u70b9\u540e\u518d\u9010\u6e10\u4e0b\u964d\u56de n，\u800c\u8be5\u9876\u70b9\u7684\u503c\u76ee\u524d\u65e0\u6cd5\u7ed9\u51fa\u7cbe\u786e\u7684\u95ed\u5f0f\u8ba1\u7b97\u8fc7\u7a0b\u3002<\/p>\n<\/li>\n<\/ul>\n

                          \u5173\u4e8e\u5e0c\u5c14\u6392\u5e8f\u590d\u6742\u5ea6\u7684\u7ed3\u8bba：\u5e0c\u5c14\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u597d\u7cbe\u786e\u8ba1\u7b97，\u56e0\u4e3a gap \u7684\u53d6\u503c\u65b9\u6848\u6709\u5f88\u591a\u79cd，\u4e0d\u540c\u7684\u589e\u91cf\u5e8f\u5217\u4f1a\u5f97\u5230\u4e0d\u540c\u7684\u590d\u6742\u5ea6，\u56e0\u6b64\u5f88\u591a\u6559\u6750\u7ed9\u51fa\u7684\u590d\u6742\u5ea6\u90fd\u4e0d\u7edf\u4e00：<\/p>\n

                            \n
                          • \u300a\u6570\u636e\u7ed3\u6784（C \u8bed\u8a00\u7248）\u300b\u2014\u2014\u4e25\u851a\u654f：\u7ed9\u51fa\u4e86\u4e0e\u589e\u91cf\u5e8f\u5217\u76f8\u5173\u7684\u754c；<\/li>\n
                          • \u300a\u6570\u636e\u7ed3\u6784\u2014\u2014\u7528\u9762\u5411\u5bf9\u8c61\u65b9\u6cd5\u4e0e C++ \u63cf\u8ff0\u300b\u2014\u2014\u6bb7\u4eba\u6606：O(n^1.25)（\u53d6\u7279\u5b9a\u589e\u91cf\u5e8f\u5217\u65f6）\u3002<\/li>\n<\/ul>\n

                            \u5de5\u7a0b\u4e0a\u4e00\u822c\u628a\u5e0c\u5c14\u6392\u5e8f\u7684\u5e73\u5747\u590d\u6742\u5ea6\u8bb0\u4f5c O(N^1.3) \u91cf\u7ea7（\u4ecb\u4e8e O(N) \u4e0e O(N\u00b2) \u4e4b\u95f4，\u4f18\u4e8e\u76f4\u63a5\u63d2\u5165\u6392\u5e8f）\u3002<\/p>\n

                            2.2 \u9009\u62e9\u6392\u5e8f<\/h4>\n

                            2.2.1 \u76f4\u63a5\u9009\u62e9\u6392\u5e8f<\/h5>\n

                            \u57fa\u672c\u601d\u60f3：\u6bcf\u4e00\u6b21\u4ece\u5f85\u6392\u5e8f\u7684\u6570\u636e\u5143\u7d20\u4e2d\u9009\u51fa\u6700\u5c0f（\u6216\u6700\u5927）\u7684\u4e00\u4e2a\u5143\u7d20，\u5b58\u653e\u5728\u5e8f\u5217\u7684\u8d77\u59cb\u4f4d\u7f6e，\u76f4\u5230\u5168\u90e8\u5f85\u6392\u5e8f\u7684\u6570\u636e\u5143\u7d20\u6392\u5b8c\u3002<\/p>\n

                            \u6392\u5e8f\u8fc7\u7a0b：<\/p>\n

                              \n
                            • \u5728\u5143\u7d20\u96c6\u5408 array[i] \u2026 array[n-1] \u4e2d\u9009\u62e9\u5173\u952e\u7801\u6700\u5927（\u5c0f）\u7684\u6570\u636e\u5143\u7d20；<\/li>\n
                            • \u82e5\u5b83\u4e0d\u662f\u8fd9\u7ec4\u5143\u7d20\u4e2d\u7684\u6700\u540e\u4e00\u4e2a（\u7b2c\u4e00\u4e2a）\u5143\u7d20，\u5219\u5c06\u5b83\u4e0e\u8fd9\u7ec4\u5143\u7d20\u4e2d\u7684\u6700\u540e\u4e00\u4e2a（\u7b2c\u4e00\u4e2a）\u5143\u7d20\u4ea4\u6362；<\/li>\n
                            • \u5728\u5269\u4f59\u7684 array[i] \u2026 array[n-2]（\u6216 array[i+1] \u2026 array[n-1]）\u96c6\u5408\u4e2d，\u91cd\u590d\u4e0a\u8ff0\u6b65\u9aa4，\u76f4\u5230\u96c6\u5408\u5269\u4f59 1 \u4e2a\u5143\u7d20\u3002<\/li>\n<\/ul>\n

                              \/\/ \u76f4\u63a5\u9009\u62e9\u6392\u5e8f：\u5347\u5e8f<\/span>
                              \npublic<\/span> static<\/span> void<\/span> selectSort<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array)<\/span> {<\/span>
                              \n \/\/ \u6bcf\u4e00\u8f6e\u4ece [i, length) \u4e2d\u9009\u51fa\u6700\u5c0f\u503c\u7684\u4e0b\u6807，\u4e0e array[i] \u4ea4\u6362<\/span>
                              \n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> array.<\/span>length –<\/span> 1<\/span>;<\/span> i++<\/span>)<\/span> {<\/span>
                              \n int<\/span> minIndex =<\/span> i;<\/span>
                              \n for<\/span> (<\/span>int<\/span> j =<\/span> i +<\/span> 1<\/span>;<\/span> j <<\/span> array.<\/span>length;<\/span> j++<\/span>)<\/span> {<\/span>
                              \n if<\/span> (<\/span>array[<\/span>j]<\/span> <<\/span> array[<\/span>minIndex]<\/span>)<\/span> {<\/span>
                              \n minIndex =<\/span> j;<\/span>
                              \n }<\/span>
                              \n }<\/span>
                              \n swap<\/span>(<\/span>array,<\/span> i,<\/span> minIndex)<\/span>;<\/span>
                              \n }<\/span>
                              \n}<\/span><\/p>\n

                              \u76f4\u63a5\u9009\u62e9\u6392\u5e8f\u7684\u7279\u6027\u603b\u7ed3：<\/p>\n

                            • \u76f4\u63a5\u9009\u62e9\u6392\u5e8f\u601d\u8def\u975e\u5e38\u597d\u7406\u89e3，\u4f46\u6548\u7387\u4e0d\u597d，\u5b9e\u9645\u4e2d\u5f88\u5c11\u4f7f\u7528；<\/li>\n
                            • \u65f6\u95f4\u590d\u6742\u5ea6：O(N\u00b2)\u3002\u65e0\u8bba\u6570\u636e\u662f\u5426\u6709\u5e8f，\u6bcf\u8f6e\u90fd\u8981\u904d\u5386\u5b8c\u5269\u4f59\u5143\u7d20；<\/li>\n
                            • \u7a7a\u95f4\u590d\u6742\u5ea6：O(1)；<\/li>\n
                            • \u7a33\u5b9a\u6027：\u4e0d\u7a33\u5b9a\u3002\u4f8b\u5982\u5e8f\u5217 [5a, 5b, 2]，\u7b2c\u4e00\u8d9f\u628a 2 \u4e0e 5a \u4ea4\u6362\u540e\u53d8\u6210 [2, 5b, 5a]，\u4e24\u4e2a 5 \u7684\u76f8\u5bf9\u987a\u5e8f\u88ab\u7834\u574f\u3002<\/li>\n
                              2.2.2 \u5806\u6392\u5e8f<\/h5>\n

                              \u5806\u6392\u5e8f（Heapsort）\u662f\u6307\u5229\u7528\u5806\u79ef\u6811（\u5806）\u8fd9\u79cd\u6570\u636e\u7ed3\u6784\u6240\u8bbe\u8ba1\u7684\u4e00\u79cd\u6392\u5e8f\u7b97\u6cd5，\u5b83\u662f\u9009\u62e9\u6392\u5e8f\u7684\u4e00\u79cd\u2014\u2014\u672c\u8d28\u4e0a\u662f\u300c\u901a\u8fc7\u5806\u6765\u8fdb\u884c\u9009\u62e9\u6570\u636e\u300d，\u4ece\u800c\u628a\u300c\u9009\u6700\u503c\u300d\u7684\u4ee3\u4ef7\u4ece O(N) \u964d\u5230\u4e86 O(log N)\u3002<\/p>\n

                              \u5173\u952e\u6613\u9519\u70b9：\u6392\u5347\u5e8f\u8981\u5efa\u5927\u5806，\u6392\u964d\u5e8f\u8981\u5efa\u5c0f\u5806\u3002 \u539f\u56e0\u662f\u5806\u6392\u5e8f\u7684\u601d\u8def\u662f\u300c\u53cd\u590d\u628a\u5806\u9876（\u6700\u503c）\u4e0e\u672b\u5c3e\u5143\u7d20\u4ea4\u6362\u3001\u7136\u540e\u5806\u7684\u89c4\u6a21\u7f29\u5c0f\u300d\u3002\u6392\u5347\u5e8f\u65f6\u5e0c\u671b\u6700\u5927\u7684\u5143\u7d20\u6700\u7ec8\u843d\u5230\u672b\u5c3e，\u6240\u4ee5\u5806\u9876\u5fc5\u987b\u662f\u5f53\u524d\u533a\u95f4\u7684\u6700\u5927\u503c，\u56e0\u6b64\u5efa\u5927\u5806\u3002\u82e5\u6392\u5347\u5e8f\u5efa\u5c0f\u5806，\u4ea4\u6362\u540e\u5806\u9876（\u6700\u5c0f\u503c）\u88ab\u6362\u5230\u4e86\u672b\u5c3e，\u53cd\u800c\u7834\u574f\u4e86\u6709\u5e8f\u6027\u3002<\/p>\n

                              \/\/ \u5411\u4e0b\u8c03\u6574：\u4ee5 root \u4e3a\u6839\u7684 [root, end] \u533a\u95f4\u7ef4\u62a4\u4e3a\u5927\u9876\u5806<\/span>
                              \nprivate<\/span> static<\/span> void<\/span> adjustDown<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array,<\/span> int<\/span> root,<\/span> int<\/span> end)<\/span> {<\/span>
                              \n int<\/span> parent =<\/span> root;<\/span>
                              \n int<\/span> child =<\/span> parent *<\/span> 2<\/span> +<\/span> 1<\/span>;<\/span> \/\/ \u5de6\u5b69\u5b50<\/span>
                              \n while<\/span> (<\/span>child <=<\/span> end)<\/span> {<\/span>
                              \n \/\/ \u9009\u51fa\u5de6\u53f3\u5b69\u5b50\u4e2d\u8f83\u5927\u7684\u90a3\u4e2a<\/span>
                              \n if<\/span> (<\/span>child +<\/span> 1<\/span> <=<\/span> end &&<\/span> array[<\/span>child +<\/span> 1<\/span>]<\/span> ><\/span> array[<\/span>child]<\/span>)<\/span> {<\/span>
                              \n child++<\/span>;<\/span>
                              \n }<\/span>
                              \n if<\/span> (<\/span>array[<\/span>child]<\/span> ><\/span> array[<\/span>parent]<\/span>)<\/span> {<\/span>
                              \n swap<\/span>(<\/span>array,<\/span> child,<\/span> parent)<\/span>;<\/span>
                              \n parent =<\/span> child;<\/span>
                              \n child =<\/span> parent *<\/span> 2<\/span> +<\/span> 1<\/span>;<\/span>
                              \n }<\/span> else<\/span> {<\/span>
                              \n break<\/span>;<\/span> \/\/ \u5df2\u7ecf\u6ee1\u8db3\u5806\u7684\u6027\u8d28，\u65e0\u9700\u7ee7\u7eed\u5411\u4e0b\u8c03\u6574<\/span>
                              \n }<\/span>
                              \n }<\/span>
                              \n}<\/span><\/p>\n

                              \/\/ \u5806\u6392\u5e8f：\u5347\u5e8f<\/span>
                              \npublic<\/span> static<\/span> void<\/span> heapSort<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array)<\/span> {<\/span>
                              \n \/\/ 1. \u5efa\u5927\u5806：\u4ece\u6700\u540e\u4e00\u4e2a\u975e\u53f6\u5b50\u7ed3\u70b9\u5f00\u59cb\u5411\u4e0b\u8c03\u6574<\/span>
                              \n for<\/span> (<\/span>int<\/span> i =<\/span> (<\/span>array.<\/span>length –<\/span> 1<\/span> –<\/span> 1<\/span>)<\/span> \/<\/span> 2<\/span>;<\/span> i >=<\/span> 0<\/span>;<\/span> i—<\/span>)<\/span> {<\/span>
                              \n adjustDown<\/span>(<\/span>array,<\/span> i,<\/span> array.<\/span>length –<\/span> 1<\/span>)<\/span>;<\/span>
                              \n }<\/span>
                              \n \/\/ 2. \u53cd\u590d\u628a\u5806\u9876（\u6700\u5927\u503c）\u4e0e\u65e0\u5e8f\u533a\u672b\u5c3e\u4ea4\u6362，\u65e0\u5e8f\u533a\u7f29\u5c0f 1<\/span>
                              \n int<\/span> end =<\/span> array.<\/span>length –<\/span> 1<\/span>;<\/span>
                              \n while<\/span> (<\/span>end ><\/span> 0<\/span>)<\/span> {<\/span>
                              \n swap<\/span>(<\/span>array,<\/span> 0<\/span>,<\/span> end)<\/span>;<\/span>
                              \n adjustDown<\/span>(<\/span>array,<\/span> 0<\/span>,<\/span> end –<\/span> 1<\/span>)<\/span>;<\/span>
                              \n end—<\/span>;<\/span>
                              \n }<\/span>
                              \n}<\/span><\/p>\n

                              \u5806\u6392\u5e8f\u7684\u7279\u6027\u603b\u7ed3：<\/p>\n

                            • \u5806\u6392\u5e8f\u4f7f\u7528\u5806\u6765\u9009\u6570，\u6548\u7387\u6bd4\u76f4\u63a5\u9009\u62e9\u6392\u5e8f\u9ad8\u4e86\u5f88\u591a；<\/li>\n
                            • \u65f6\u95f4\u590d\u6742\u5ea6：O(N * logN)\u3002\u5efa\u5806\u4e3a O(N)，N-1 \u6b21\u300c\u5220\u9664\u5806\u9876 + \u8c03\u6574\u300d\u6bcf\u6b21 O(logN)；\u65e0\u8bba\u6700\u597d\u3001\u6700\u574f\u3001\u5e73\u5747\u90fd\u7a33\u5b9a\u5728 O(NlogN)；<\/li>\n
                            • \u7a7a\u95f4\u590d\u6742\u5ea6：O(1)，\u539f\u5730\u6392\u5e8f，\u4e0d\u9700\u8981\u989d\u5916\u6570\u7ec4；<\/li>\n
                            • \u7a33\u5b9a\u6027：\u4e0d\u7a33\u5b9a\u3002\u4ea4\u6362\u5806\u9876\u4e0e\u672b\u5c3e\u5143\u7d20\u4f1a\u6253\u4e71\u76f8\u540c\u5173\u952e\u5b57\u7684\u76f8\u5bf9\u987a\u5e8f\u3002<\/li>\n

                              \u5806\u6392\u5e8f\u7684\u9690\u85cf\u4f18\u52bf：\u5b83\u4e0d\u4f9d\u8d56\u6570\u636e\u7684\u521d\u59cb\u5206\u5e03，\u4e0d\u5b58\u5728\u300c\u6709\u5e8f\u6570\u636e\u53cd\u800c\u9000\u5316\u6210 O(N\u00b2)\u300d\u7684\u60c5\u51b5，\u56e0\u6b64\u5728**\u9700\u8981\u6c42 Top-K（\u524d K \u5927 \/ \u524d K \u5c0f）**\u4ee5\u53ca\u5185\u5b58\u53d7\u9650\u7684\u573a\u666f\u4e2d\u975e\u5e38\u5e38\u7528\u3002<\/p>\n

                              2.3 \u4ea4\u6362\u6392\u5e8f<\/h4>\n

                              \u57fa\u672c\u601d\u60f3：\u6240\u8c13\u4ea4\u6362，\u5c31\u662f\u6839\u636e\u5e8f\u5217\u4e2d\u4e24\u4e2a\u8bb0\u5f55\u952e\u503c\u7684\u6bd4\u8f83\u7ed3\u679c\u6765\u5bf9\u6362\u8fd9\u4e24\u4e2a\u8bb0\u5f55\u5728\u5e8f\u5217\u4e2d\u7684\u4f4d\u7f6e\u3002\u4ea4\u6362\u6392\u5e8f\u7684\u7279\u70b9\u662f：\u5c06\u952e\u503c\u8f83\u5927\u7684\u8bb0\u5f55\u5411\u5e8f\u5217\u7684\u5c3e\u90e8\u79fb\u52a8，\u952e\u503c\u8f83\u5c0f\u7684\u8bb0\u5f55\u5411\u5e8f\u5217\u7684\u524d\u90e8\u79fb\u52a8\u3002<\/p>\n

                              2.3.1 \u5192\u6ce1\u6392\u5e8f<\/h5>\n

                              \/\/ \u5192\u6ce1\u6392\u5e8f：\u5347\u5e8f<\/span>
                              \npublic<\/span> static<\/span> void<\/span> bubbleSort<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array)<\/span> {<\/span>
                              \n \/\/ \u6bcf\u8d9f\u628a [0, length-i-1] \u4e2d\u7684\u6700\u5927\u503c"\u5192\u6ce1"\u5230\u53f3\u7aef<\/span>
                              \n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> array.<\/span>length –<\/span> 1<\/span>;<\/span> i++<\/span>)<\/span> {<\/span>
                              \n boolean<\/span> swapped =<\/span> false<\/span>;<\/span> \/\/ \u4f18\u5316：\u4e00\u8d9f\u6ca1\u6709\u53d1\u751f\u4ea4\u6362\u8bf4\u660e\u5df2\u6709\u5e8f<\/span>
                              \n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> array.<\/span>length –<\/span> 1<\/span> –<\/span> i;<\/span> j++<\/span>)<\/span> {<\/span>
                              \n if<\/span> (<\/span>array[<\/span>j]<\/span> ><\/span> array[<\/span>j +<\/span> 1<\/span>]<\/span>)<\/span> {<\/span>
                              \n swap<\/span>(<\/span>array,<\/span> j,<\/span> j +<\/span> 1<\/span>)<\/span>;<\/span>
                              \n swapped =<\/span> true<\/span>;<\/span>
                              \n }<\/span>
                              \n }<\/span>
                              \n if<\/span> (<\/span>!<\/span>swapped)<\/span> {<\/span>
                              \n break<\/span>;<\/span>
                              \n }<\/span>
                              \n }<\/span>
                              \n}<\/span><\/p>\n

                              \u5192\u6ce1\u6392\u5e8f\u7684\u7279\u6027\u603b\u7ed3：<\/p>\n

                            • \u5192\u6ce1\u6392\u5e8f\u662f\u4e00\u79cd\u975e\u5e38\u5bb9\u6613\u7406\u89e3\u7684\u6392\u5e8f；<\/li>\n
                            • \u65f6\u95f4\u590d\u6742\u5ea6：O(N\u00b2)（\u52a0\u4e0a swapped \u4f18\u5316\u540e，\u6700\u597d\u60c5\u51b5\u4e3a O(N)）；<\/li>\n
                            • \u7a7a\u95f4\u590d\u6742\u5ea6：O(1)；<\/li>\n
                            • \u7a33\u5b9a\u6027：\u7a33\u5b9a\u3002\u76f8\u7b49\u5143\u7d20\u4e0d\u4f1a\u88ab\u4ea4\u6362，\u76f8\u5bf9\u987a\u5e8f\u4fdd\u6301\u4e0d\u53d8\u3002<\/li>\n
                              2.3.2 \u5feb\u901f\u6392\u5e8f<\/h5>\n

                              \u5feb\u901f\u6392\u5e8f\u662f Hoare \u4e8e 1962 \u5e74\u63d0\u51fa\u7684\u4e00\u79cd\u4e8c\u53c9\u6811\u7ed3\u6784\u7684\u4ea4\u6362\u6392\u5e8f\u65b9\u6cd5\u3002<\/p>\n

                              \u57fa\u672c\u601d\u60f3：\u4efb\u53d6\u5f85\u6392\u5e8f\u5143\u7d20\u5e8f\u5217\u4e2d\u7684\u67d0\u5143\u7d20\u4f5c\u4e3a\u57fa\u51c6\u503c（pivot），\u6309\u7167\u8be5\u6392\u5e8f\u7801\u5c06\u5f85\u6392\u5e8f\u96c6\u5408\u5206\u5272\u6210\u4e24\u5b50\u5e8f\u5217，\u5de6\u5b50\u5e8f\u5217\u4e2d\u6240\u6709\u5143\u7d20\u5747\u5c0f\u4e8e\u57fa\u51c6\u503c，\u53f3\u5b50\u5e8f\u5217\u4e2d\u6240\u6709\u5143\u7d20\u5747\u5927\u4e8e\u57fa\u51c6\u503c，\u7136\u540e\u5bf9\u5de6\u53f3\u5b50\u5e8f\u5217\u91cd\u590d\u8be5\u8fc7\u7a0b，\u76f4\u5230\u6240\u6709\u5143\u7d20\u90fd\u6392\u5217\u5728\u76f8\u5e94\u4f4d\u7f6e\u4e0a\u4e3a\u6b62\u3002<\/p>\n

                              \u9012\u5f52\u4e3b\u6846\u67b6：<\/p>\n

                              \/\/ \u5047\u8bbe\u6309\u7167\u5347\u5e8f\u5bf9 array \u6570\u7ec4\u4e2d [left, right] \u533a\u95f4\u4e2d\u7684\u5143\u7d20\u8fdb\u884c\u6392\u5e8f<\/span>
                              \npublic<\/span> static<\/span> void<\/span> quickSort<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array,<\/span> int<\/span> left,<\/span> int<\/span> right)<\/span> {<\/span>
                              \n if<\/span> (<\/span>right –<\/span> left <<\/span> 1<\/span>)<\/span> {<\/span>
                              \n return<\/span>;<\/span> \/\/ \u533a\u95f4\u53ea\u5269 0 \u6216 1 \u4e2a\u5143\u7d20，\u5929\u7136\u6709\u5e8f<\/span>
                              \n }<\/span><\/p>\n

                              \/\/ \u6309\u7167\u57fa\u51c6\u503c\u5bf9 [left, right] \u533a\u95f4\u4e2d\u7684\u5143\u7d20\u8fdb\u884c\u5212\u5206<\/span>
                              \n int<\/span> div =<\/span> partition<\/span>(<\/span>array,<\/span> left,<\/span> right)<\/span>;<\/span><\/p>\n

                              \/\/ \u5212\u5206\u6210\u529f\u540e\u4ee5 div \u4e3a\u8fb9\u754c\u5f62\u6210\u4e86\u5de6\u53f3\u4e24\u90e8\u5206 [left, div-1] \u548c [div+1, right]<\/span>
                              \n quickSort<\/span>(<\/span>array,<\/span> left,<\/span> div –<\/span> 1<\/span>)<\/span>;<\/span> \/\/ \u9012\u5f52\u6392\u5de6\u534a\u90e8\u5206<\/span>
                              \n quickSort<\/span>(<\/span>array,<\/span> div +<\/span> 1<\/span>,<\/span> right)<\/span>;<\/span> \/\/ \u9012\u5f52\u6392\u53f3\u534a\u90e8\u5206<\/span>
                              \n}<\/span><\/p>\n

                              \u4e0a\u8ff0\u9012\u5f52\u4e3b\u6846\u67b6\u4e0e\u4e8c\u53c9\u6811\u7684\u524d\u5e8f\u904d\u5386\u89c4\u5219\u975e\u5e38\u50cf：\u5199\u9012\u5f52\u6846\u67b6\u65f6\u8054\u60f3\u4e8c\u53c9\u6811\u524d\u5e8f\u904d\u5386\u5373\u53ef\u5feb\u901f\u5199\u51fa，\u5269\u4e0b\u7684\u5173\u952e\u5728\u4e8e\u5206\u6790\u5982\u4f55\u6309\u7167\u57fa\u51c6\u503c\u5bf9\u533a\u95f4\u6570\u636e\u8fdb\u884c\u5212\u5206\u3002<\/p>\n

                              \u5c06\u533a\u95f4\u6309\u7167\u57fa\u51c6\u503c\u5212\u5206\u4e3a\u5de6\u53f3\u4e24\u534a\u90e8\u5206\u7684\u5e38\u89c1\u65b9\u5f0f\u6709\u4e09\u79cd：<\/p>\n

                              \u65b9\u5f0f\u4e00：Hoare \u7248（\u53cc\u6307\u9488\u4ece\u4e24\u7aef\u5411\u4e2d\u95f4\u626b\u63cf）<\/p>\n

                              private<\/span> static<\/span> int<\/span> partitionHoare<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array,<\/span> int<\/span> left,<\/span> int<\/span> right)<\/span> {<\/span>
                              \n int<\/span> i =<\/span> left;<\/span>
                              \n int<\/span> j =<\/span> right;<\/span>
                              \n int<\/span> pivot =<\/span> array[<\/span>left]<\/span>;<\/span> \/\/ \u53d6\u6700\u5de6\u5143\u7d20\u4e3a\u57fa\u51c6<\/span>
                              \n while<\/span> (<\/span>i <<\/span> j)<\/span> {<\/span>
                              \n \/\/ \u53f3：\u627e\u6bd4\u57fa\u51c6\u5c0f\u7684（\u5347\u5e8f\u65f6\u4ece\u53f3\u5f80\u5de6\u627e\u7b2c\u4e00\u4e2a < pivot）<\/span>
                              \n while<\/span> (<\/span>i <<\/span> j &&<\/span> array[<\/span>j]<\/span> >=<\/span> pivot)<\/span> {<\/span>
                              \n j—<\/span>;<\/span>
                              \n }<\/span>
                              \n \/\/ \u5de6：\u627e\u6bd4\u57fa\u51c6\u5927\u7684（\u4ece\u5de6\u5f80\u53f3\u627e\u7b2c\u4e00\u4e2a > pivot）<\/span>
                              \n while<\/span> (<\/span>i <<\/span> j &&<\/span> array[<\/span>i]<\/span> <=<\/span> pivot)<\/span> {<\/span>
                              \n i++<\/span>;<\/span>
                              \n }<\/span>
                              \n swap<\/span>(<\/span>array,<\/span> i,<\/span> j)<\/span>;<\/span>
                              \n }<\/span>
                              \n \/\/ \u76f8\u9047\u70b9\u653e\u56de\u57fa\u51c6\u503c<\/span>
                              \n swap<\/span>(<\/span>array,<\/span> i,<\/span> left)<\/span>;<\/span>
                              \n return<\/span> i;<\/span>
                              \n}<\/span><\/p>\n

                              \u6ce8\u610f：Hoare \u7248\u5fc5\u987b\u4ece right \u7aef\u5148\u5f00\u59cb\u626b\u63cf，\u8fd9\u6837\u4e24\u4e2a\u6307\u9488\u76f8\u9047\u4f4d\u7f6e\u7684\u503c\u4e00\u5b9a \u2264 \u57fa\u51c6\u503c，\u6700\u540e\u628a\u57fa\u51c6\u503c\u653e\u5230\u76f8\u9047\u70b9\u624d\u6ee1\u8db3\u300c\u5de6\u8fb9\u90fd\u6bd4\u5b83\u5c0f\u3001\u53f3\u8fb9\u90fd\u6bd4\u5b83\u5927\u300d\u3002<\/p>\n

                              \u65b9\u5f0f\u4e8c：\u6316\u5751\u6cd5<\/p>\n

                              private<\/span> static<\/span> int<\/span> partitionHoare2<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array,<\/span> int<\/span> left,<\/span> int<\/span> right)<\/span> {<\/span>
                              \n int<\/span> i =<\/span> left;<\/span>
                              \n int<\/span> j =<\/span> right;<\/span>
                              \n int<\/span> pivot =<\/span> array[<\/span>left]<\/span>;<\/span> \/\/ \u5148\u628a\u57fa\u51c6\u503c"\u6316"\u51fa\u6765，left \u5904\u6210\u4e3a\u7b2c\u4e00\u4e2a\u5751<\/span>
                              \n while<\/span> (<\/span>i <<\/span> j)<\/span> {<\/span>
                              \n while<\/span> (<\/span>i <<\/span> j &&<\/span> array[<\/span>j]<\/span> >=<\/span> pivot)<\/span> {<\/span>
                              \n j—<\/span>;<\/span>
                              \n }<\/span>
                              \n array[<\/span>i]<\/span> =<\/span> array[<\/span>j]<\/span>;<\/span> \/\/ \u53f3\u5751\u5143\u7d20\u586b\u5de6\u5751，\u53f3\u8fb9\u5f62\u6210\u65b0\u5751<\/span>
                              \n while<\/span> (<\/span>i <<\/span> j &&<\/span> array[<\/span>i]<\/span> <=<\/span> pivot)<\/span> {<\/span>
                              \n i++<\/span>;<\/span>
                              \n }<\/span>
                              \n array[<\/span>j]<\/span> =<\/span> array[<\/span>i]<\/span>;<\/span> \/\/ \u5de6\u5751\u5143\u7d20\u586b\u53f3\u5751，\u5de6\u8fb9\u5f62\u6210\u65b0\u5751<\/span>
                              \n }<\/span>
                              \n array[<\/span>i]<\/span> =<\/span> pivot;<\/span> \/\/ \u57fa\u51c6\u503c\u843d\u5751<\/span>
                              \n return<\/span> i;<\/span>
                              \n}<\/span><\/p>\n

                              \u65b9\u5f0f\u4e09：\u524d\u540e\u6307\u9488\u6cd5<\/p>\n

                              private<\/span> static<\/span> int<\/span> partitionHoare3<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array,<\/span> int<\/span> left,<\/span> int<\/span> right)<\/span> {<\/span>
                              \n int<\/span> prev =<\/span> left;<\/span> \/\/ prev \u6307\u5411"\u5c0f\u4e8e\u57fa\u51c6\u533a\u95f4"\u7684\u6700\u540e\u4e00\u4e2a\u5143\u7d20<\/span>
                              \n int<\/span> cur =<\/span> left +<\/span> 1<\/span>;<\/span>
                              \n while<\/span> (<\/span>cur <=<\/span> right)<\/span> {<\/span>
                              \n \/\/ cur \u627e\u5230\u6bd4\u57fa\u51c6\u5c0f\u7684\u5143\u7d20，prev \u524d\u79fb\u540e\u4e0e cur \u4ea4\u6362<\/span>
                              \n if<\/span> (<\/span>array[<\/span>cur]<\/span> <<\/span> array[<\/span>left]<\/span> &&<\/span> array[<\/span>++<\/span>prev]<\/span> !=<\/span> array[<\/span>cur]<\/span>)<\/span> {<\/span>
                              \n swap<\/span>(<\/span>array,<\/span> cur,<\/span> prev)<\/span>;<\/span>
                              \n }<\/span>
                              \n cur++<\/span>;<\/span>
                              \n }<\/span>
                              \n \/\/ \u6700\u540e\u628a\u57fa\u51c6\u503c\u653e\u5230 prev \u4f4d\u7f6e，\u5de6\u8fb9\u90fd \u2264 \u57fa\u51c6，\u53f3\u8fb9\u90fd \u2265 \u57fa\u51c6<\/span>
                              \n swap<\/span>(<\/span>array,<\/span> prev,<\/span> left)<\/span>;<\/span>
                              \n return<\/span> prev;<\/span>
                              \n}<\/span><\/p>\n

                              \u5feb\u901f\u6392\u5e8f\u6700\u574f\u60c5\u51b5：\u5f53\u5e8f\u5217\u5df2\u7ecf\u6709\u5e8f\u6216\u9006\u5e8f\u65f6，\u6bcf\u6b21\u5212\u5206\u6781\u4e0d\u5747\u8861（\u4e00\u4e2a\u5b50\u533a\u95f4 N-1 \u4e2a\u3001\u53e6\u4e00\u4e2a 0 \u4e2a），\u9012\u5f52\u6811\u9000\u5316\u6210\u4e00\u6761\u94fe，\u65f6\u95f4\u590d\u6742\u5ea6\u9000\u5316\u5230 O(N\u00b2)，\u5e76\u4e14\u9012\u5f52\u6df1\u5ea6\u8fbe\u5230 O(N)，\u53ef\u80fd\u9020\u6210\u6808\u6ea2\u51fa\u3002<\/p>\n

                              2.3.3 \u5feb\u901f\u6392\u5e8f\u7684\u4f18\u5316<\/h5>\n

                              \u9488\u5bf9\u4e0a\u8ff0\u6700\u574f\u60c5\u51b5，\u5de5\u7a0b\u4e0a\u6709\u4e24\u4e2a\u7ecf\u5178\u4f18\u5316：<\/p>\n

                            • \u4e09\u6570\u53d6\u4e2d\u6cd5\u9009 key：\u53d6 left\u3001mid\u3001right \u4e09\u4e2a\u4f4d\u7f6e\u4e2d\u6570\u503c\u5904\u4e8e\u4e2d\u95f4\u7684\u90a3\u4e2a\u5143\u7d20\u4f5c\u4e3a\u57fa\u51c6（\u5e76\u4e0e left \u4ea4\u6362\u540e\u518d\u5212\u5206），\u907f\u514d\u5728\u300c\u6709\u5e8f \/ \u8fd1\u4e4e\u6709\u5e8f\u300d\u6570\u636e\u4e0a\u6bcf\u6b21\u9009\u5230\u6700\u503c\u5bfc\u81f4\u5212\u5206\u4e0d\u5747\u3002<\/li>\n
                            • \u9012\u5f52\u5230\u5c0f\u7684\u5b50\u533a\u95f4\u65f6\u6539\u7528\u63d2\u5165\u6392\u5e8f：\u5f53\u533a\u95f4\u5143\u7d20\u4e2a\u6570\u5c0f\u4e8e\u67d0\u4e2a\u9608\u503c（\u4e00\u822c 5～20）\u65f6，\u9012\u5f52\u7684\u51fd\u6570\u8c03\u7528\u5f00\u9500\u53cd\u800c\u5927\u4e8e\u6392\u5e8f\u6536\u76ca，\u4e14\u6b64\u65f6\u6570\u7ec4\u5df2\u63a5\u8fd1\u6709\u5e8f，\u800c\u63d2\u5165\u6392\u5e8f\u6070\u6070\u5bf9\u8fd1\u4e4e\u6709\u5e8f\u7684\u6570\u636e\u6548\u7387\u6700\u9ad8，\u56e0\u6b64\u6539\u8d70\u76f4\u63a5\u63d2\u5165\u6392\u5e8f，\u53ef\u663e\u8457\u964d\u4f4e\u5e38\u6570\u56e0\u5b50\u3002<\/li>\n
                              2.3.4 \u5feb\u901f\u6392\u5e8f\u7684\u975e\u9012\u5f52\u5b9e\u73b0<\/h5>\n

                              \u9012\u5f52\u672c\u8d28\u4e0a\u662f\u5229\u7528\u7cfb\u7edf\u6808\u4fdd\u5b58\u300c\u5f85\u5904\u7406\u533a\u95f4\u300d\u3002\u5f53\u6570\u636e\u91cf\u5f88\u5927\u3001\u53c8\u62c5\u5fc3\u9012\u5f52\u9000\u5316\u4e3a\u6df1\u94fe\u5bfc\u81f4\u6808\u6ea2\u51fa（StackOverflow）\u65f6，\u53ef\u4ee5\u7528\u4e00\u4e2a\u663e\u5f0f\u7684\u6808\u6765\u6a21\u62df\u9012\u5f52：\u6bcf\u6b21\u628a\u5b50\u533a\u95f4\u7684\u5de6\u53f3\u8fb9\u754c\u538b\u6808，\u518d\u5f39\u6808\u5904\u7406\u3002<\/p>\n

                              public<\/span> static<\/span> void<\/span> quickSortNonR<\/span>(<\/span>int<\/span>[<\/span>]<\/span> a,<\/span> int<\/span> left,<\/span> int<\/span> right)<\/span> {<\/span>
                              \n Stack<\/span><<\/span>Integer<\/span>><\/span><\/span> st =<\/span> new<\/span> Stack<\/span><<\/span>><\/span><\/span>(<\/span>)<\/span>;<\/span>
                              \n st.<\/span>push<\/span>(<\/span>right)<\/span>;<\/span>
                              \n st.<\/span>push<\/span>(<\/span>left)<\/span>;<\/span> \/\/ \u5148\u628a\u6574\u4e2a\u533a\u95f4\u7684\u5de6\u53f3\u8fb9\u754c\u5165\u6808<\/span>
                              \n while<\/span> (<\/span>!<\/span>st.<\/span>empty<\/span>(<\/span>)<\/span>)<\/span> {<\/span>
                              \n int<\/span> l =<\/span> st.<\/span>pop<\/span>(<\/span>)<\/span>;<\/span> \/\/ \u6ce8\u610f\u51fa\u6808\u987a\u5e8f\u4e0e\u5165\u6808\u987a\u5e8f\u76f8\u53cd<\/span>
                              \n int<\/span> r =<\/span> st.<\/span>pop<\/span>(<\/span>)<\/span>;<\/span>
                              \n if<\/span> (<\/span>r –<\/span> l <<\/span> 1<\/span>)<\/span> {<\/span>
                              \n continue<\/span>;<\/span> \/\/ \u533a\u95f4\u53ea\u6709 0\/1 \u4e2a\u5143\u7d20，\u8df3\u8fc7<\/span>
                              \n }<\/span>
                              \n int<\/span> div =<\/span> partitionHoare<\/span>(<\/span>a,<\/span> l,<\/span> r)<\/span>;<\/span> \/\/ \u4e00\u6b21\u5212\u5206，\u5f97\u5230\u57fa\u51c6\u6700\u7ec8\u4f4d\u7f6e<\/span>
                              \n \/\/ \u628a\u5de6\u53f3\u4e24\u90e8\u5206 [l, div-1] \u548c [div+1, r] \u7684\u8fb9\u754c\u538b\u6808<\/span>
                              \n st.<\/span>push<\/span>(<\/span>div –<\/span> 1<\/span>)<\/span>;<\/span>
                              \n st.<\/span>push<\/span>(<\/span>l)<\/span>;<\/span>
                              \n st.<\/span>push<\/span>(<\/span>r)<\/span>;<\/span>
                              \n st.<\/span>push<\/span>(<\/span>div +<\/span> 1<\/span>)<\/span>;<\/span>
                              \n }<\/span>
                              \n}<\/span><\/p>\n

                              2.3.5 \u5feb\u901f\u6392\u5e8f\u603b\u7ed3<\/h5>\n
                            • \u5feb\u901f\u6392\u5e8f\u6574\u4f53\u7684\u7efc\u5408\u6027\u80fd\u548c\u4f7f\u7528\u573a\u666f\u90fd\u662f\u6bd4\u8f83\u597d\u7684，\u6240\u4ee5\u624d\u6562\u53eb"\u5feb\u901f\u6392\u5e8f"\u3002\u5728\u5e73\u5747\u60c5\u51b5\u4e0b\u5b83\u7684\u5e38\u6570\u56e0\u5b50\u5f88\u5c0f\u3001\u7f13\u5b58\u53cb\u597d，\u662f\u5b9e\u9645\u5e94\u7528\u4e2d\u6700\u5e38\u7528\u7684\u6392\u5e8f\u4e4b\u4e00（qsort\u3001Arrays.sort \u7684\u539f\u59cb\u7248\u672c\u5e95\u5c42\u90fd\u57fa\u4e8e\u5feb\u6392）；<\/li>\n
                            • \u65f6\u95f4\u590d\u6742\u5ea6：O(N * logN)（\u5e73\u5747），\u6700\u574f O(N\u00b2)；<\/li>\n
                            • \u7a7a\u95f4\u590d\u6742\u5ea6：O(logN)，\u6765\u81ea\u9012\u5f52\u8c03\u7528\u6808\u7684\u6df1\u5ea6（\u4f18\u5316\u540e\u8fd1\u4f3c log\u2082N）；<\/li>\n
                            • \u7a33\u5b9a\u6027：\u4e0d\u7a33\u5b9a\u3002<\/li>\n

                              2.4 \u5f52\u5e76\u6392\u5e8f<\/h4>\n

                              2.4.1 \u57fa\u672c\u601d\u60f3\u4e0e\u5b9e\u73b0<\/h5>\n

                              \u5f52\u5e76\u6392\u5e8f（MERGE-SORT）\u662f\u5efa\u7acb\u5728\u5f52\u5e76\u64cd\u4f5c\u4e0a\u7684\u4e00\u79cd\u6709\u6548\u6392\u5e8f\u7b97\u6cd5，\u8be5\u7b97\u6cd5\u662f\u91c7\u7528\u5206\u6cbb\u6cd5（Divide and Conquer）\u7684\u4e00\u4e2a\u975e\u5e38\u5178\u578b\u7684\u5e94\u7528\u3002\u5c06\u5df2\u6709\u5e8f\u7684\u5b50\u5e8f\u5217\u5408\u5e76，\u5f97\u5230\u5b8c\u5168\u6709\u5e8f\u7684\u5e8f\u5217；\u5373\u5148\u4f7f\u6bcf\u4e2a\u5b50\u5e8f\u5217\u6709\u5e8f，\u518d\u4f7f\u5b50\u5e8f\u5217\u6bb5\u95f4\u6709\u5e8f\u3002\u82e5\u5c06\u4e24\u4e2a\u6709\u5e8f\u8868\u5408\u5e76\u6210\u4e00\u4e2a\u6709\u5e8f\u8868，\u79f0\u4e3a\u4e8c\u8def\u5f52\u5e76\u3002<\/p>\n

                              \u6838\u5fc3\u6b65\u9aa4（\u628a\u533a\u95f4\u4e0d\u65ad\u4e8c\u5206\u5230\u53ea\u5269 1 \u4e2a\u5143\u7d20 \u2192 \u5929\u7136\u6709\u5e8f \u2192 \u81ea\u5e95\u5411\u4e0a\u4e24\u4e24\u5f52\u5e76）：<\/p>\n

                              \/\/ \u5f52\u5e76\u6392\u5e8f：\u5347\u5e8f（\u9012\u5f52\u7248）<\/span>
                              \npublic<\/span> static<\/span> void<\/span> mergeSort<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array,<\/span> int<\/span> left,<\/span> int<\/span> right,<\/span> int<\/span>[<\/span>]<\/span> tmp)<\/span> {<\/span>
                              \n \/\/ [left, right] \u95ed\u533a\u95f4，\u53ea\u5269\u4e00\u4e2a\u5143\u7d20\u65f6\u4e0d\u7528\u518d\u5f52\u5e76<\/span>
                              \n if<\/span> (<\/span>right –<\/span> left <<\/span> 1<\/span>)<\/span> {<\/span>
                              \n return<\/span>;<\/span>
                              \n }<\/span>
                              \n int<\/span> mid =<\/span> (<\/span>left +<\/span> right)<\/span> \/<\/span> 2<\/span>;<\/span>
                              \n \/\/ 1. \u62c6：\u5148\u8ba9\u5de6\u53f3\u4e24\u4e2a\u5b50\u533a\u95f4\u5206\u522b\u6709\u5e8f<\/span>
                              \n mergeSort<\/span>(<\/span>array,<\/span> left,<\/span> mid,<\/span> tmp)<\/span>;<\/span>
                              \n mergeSort<\/span>(<\/span>array,<\/span> mid +<\/span> 1<\/span>,<\/span> right,<\/span> tmp)<\/span>;<\/span>
                              \n \/\/ 2. \u5408：\u628a\u4e24\u4e2a\u6709\u5e8f\u533a\u95f4\u5f52\u5e76\u6210\u4e00\u4e2a\u6709\u5e8f\u533a\u95f4<\/span>
                              \n merge<\/span>(<\/span>array,<\/span> left,<\/span> mid,<\/span> right,<\/span> tmp)<\/span>;<\/span>
                              \n}<\/span><\/p>\n

                              \/\/ \u5f52\u5e76\u4e24\u4e2a\u6709\u5e8f\u533a\u95f4 [left, mid] \u4e0e [mid+1, right]<\/span>
                              \nprivate<\/span> static<\/span> void<\/span> merge<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array,<\/span> int<\/span> left,<\/span> int<\/span> mid,<\/span> int<\/span> right,<\/span> int<\/span>[<\/span>]<\/span> tmp)<\/span> {<\/span>
                              \n int<\/span> leftStart =<\/span> left;<\/span>
                              \n int<\/span> rightStart =<\/span> mid +<\/span> 1<\/span>;<\/span>
                              \n int<\/span> i =<\/span> left;<\/span>
                              \n while<\/span> (<\/span>left <=<\/span> mid &&<\/span> rightStart <=<\/span> right)<\/span> {<\/span>
                              \n \/\/ \u53d6\u7b49\u65f6\u4f18\u5148\u53d6\u5de6\u8fb9，\u4fdd\u8bc1\u7a33\u5b9a\u6027<\/span>
                              \n tmp[<\/span>i++<\/span>]<\/span> =<\/span> (<\/span>array[<\/span>left]<\/span> <=<\/span> array[<\/span>rightStart]<\/span>)<\/span> ?<\/span> array[<\/span>left++<\/span>]<\/span> :<\/span> array[<\/span>rightStart++<\/span>]<\/span>;<\/span>
                              \n }<\/span>
                              \n \/\/ \u628a\u5269\u4f59\u672a\u62f7\u8d1d\u7684\u90e8\u5206\u8865\u8fdb\u4e34\u65f6\u6570\u7ec4<\/span>
                              \n while<\/span> (<\/span>left <=<\/span> mid)<\/span> {<\/span>
                              \n tmp[<\/span>i++<\/span>]<\/span> =<\/span> array[<\/span>left++<\/span>]<\/span>;<\/span>
                              \n }<\/span>
                              \n while<\/span> (<\/span>rightStart <=<\/span> right)<\/span> {<\/span>
                              \n tmp[<\/span>i++<\/span>]<\/span> =<\/span> array[<\/span>rightStart++<\/span>]<\/span>;<\/span>
                              \n }<\/span>
                              \n \/\/ \u628a\u6392\u597d\u5e8f\u7684\u533a\u95f4\u62f7\u56de\u539f\u6570\u7ec4<\/span>
                              \n System<\/span>.<\/span>arraycopy<\/span>(<\/span>tmp,<\/span> leftStart,<\/span> array,<\/span> leftStart,<\/span> right –<\/span> leftStart +<\/span> 1<\/span>)<\/span>;<\/span>
                              \n}<\/span><\/p>\n

                              \u5f52\u5e76\u6392\u5e8f\u5fc5\u987b\u989d\u5916\u7533\u8bf7\u4e00\u4e2a tmp \u8f85\u52a9\u6570\u7ec4，\u5e76\u4e14\u9012\u5f52\u7684\u7ec8\u6b62\u6761\u4ef6\u662f\u300c\u53ea\u5269\u4e00\u4e2a\u5143\u7d20\u300d，\u8fd9\u4e0e\u5feb\u901f\u6392\u5e8f\u300c\u5212\u5206\u5b8c\u5373\u7ed3\u675f\u300d\u4e0d\u540c：\u5feb\u6392\u662f"\u8fb9\u9012\u5f52\u8fb9\u5e72\u6d3b"，\u5f52\u5e76\u662f"\u9012\u5f52\u56de\u6765\u4e4b\u540e\u624d\u5e72\u6d3b"\u3002<\/p>\n

                              2.4.2 \u5f52\u5e76\u6392\u5e8f\u603b\u7ed3<\/h5>\n
                            • \u5f52\u5e76\u7684\u7f3a\u70b9\u5728\u4e8e\u9700\u8981 O(N) \u7684\u7a7a\u95f4\u590d\u6742\u5ea6；\u6b63\u56e0\u4e3a\u5982\u6b64，\u5f52\u5e76\u6392\u5e8f\u7684\u601d\u8003\u66f4\u591a\u7684\u662f\u7528\u4e8e\u89e3\u51b3\u78c1\u76d8\u4e2d\u7684\u5916\u90e8\u6392\u5e8f\u95ee\u9898（\u5916\u90e8\u6392\u5e8f\u8be6\u89c1\u4e0b\u8282）；<\/li>\n
                            • \u65f6\u95f4\u590d\u6742\u5ea6：O(N * logN)\u3002\u9012\u5f52\u6811\u6df1\u5ea6 logN，\u6bcf\u5c42\u5f52\u5e76\u603b\u4ee3\u4ef7 O(N)；\u65e0\u8bba\u6700\u597d\u6700\u574f\u90fd\u662f O(NlogN)，\u6027\u80fd\u7a33\u5b9a；<\/li>\n
                            • \u7a7a\u95f4\u590d\u6742\u5ea6：O(N)（\u8f85\u52a9\u6570\u7ec4），\u82e5\u518d\u52a0\u4e0a\u9012\u5f52\u6808\u5219\u4e3a O(N + logN)，\u91cf\u7ea7\u4ecd\u8bb0 O(N)；<\/li>\n
                            • \u7a33\u5b9a\u6027：\u7a33\u5b9a（\u5f52\u5e76\u53d6\u7b49\u65f6\u4f18\u5148\u53d6\u5de6\u4fa7\u5143\u7d20\u5373\u53ef\u4fdd\u8bc1）\u3002<\/li>\n
                              2.4.3 \u6d77\u91cf\u6570\u636e\u7684\u6392\u5e8f\u95ee\u9898<\/h5>\n

                              \u5916\u90e8\u6392\u5e8f：\u6392\u5e8f\u8fc7\u7a0b\u9700\u8981\u5728\u78c1\u76d8\u7b49\u5916\u90e8\u5b58\u50a8\u8fdb\u884c\u7684\u6392\u5e8f\u3002<\/p>\n

                              \u524d\u63d0：\u5185\u5b58\u53ea\u6709 1G，\u800c\u9700\u8981\u6392\u5e8f\u7684\u6570\u636e\u6709 100G\u3002\u7531\u4e8e\u5185\u5b58\u4e2d\u65e0\u6cd5\u628a\u6240\u6709\u6570\u636e\u5168\u90e8\u653e\u4e0b，\u6240\u4ee5\u5fc5\u987b\u4f7f\u7528\u5916\u90e8\u6392\u5e8f，\u800c\u5f52\u5e76\u6392\u5e8f\u662f\u6700\u5e38\u7528\u7684\u5916\u90e8\u6392\u5e8f\u3002<\/p>\n

                              \u5178\u578b\u505a\u6cd5：<\/p>\n

                            • \u5148\u628a\u6587\u4ef6\u5207\u5206\u6210 200 \u4efd，\u6bcf\u4e2a 512M（\u4fdd\u8bc1\u6bcf\u4e00\u4efd\u90fd\u80fd\u88c5\u8fdb\u5185\u5b58）；<\/li>\n
                            • \u5206\u522b\u5bf9\u8fd9 200 \u4efd 512M \u7684\u6570\u636e\u5728\u5185\u5b58\u5185\u6392\u5e8f，\u56e0\u4e3a\u5185\u5b58\u5df2\u7ecf\u653e\u5f97\u4e0b，\u6240\u4ee5\u4efb\u610f\u6392\u5e8f\u65b9\u5f0f（\u5feb\u6392\u3001\u5806\u6392\u2026\u2026）\u90fd\u53ef\u4ee5，\u6392\u5b8c\u5199\u56de\u78c1\u76d8，\u5f97\u5230 200 \u4e2a\u5c40\u90e8\u6709\u5e8f\u7684\u6587\u4ef6；<\/li>\n
                            • \u5bf9\u8fd9 200 \u4efd\u6709\u5e8f\u6587\u4ef6\u8fdb\u884c \u591a\u8def（2 \u8def）\u5f52\u5e76，\u540c\u65f6\u5f52\u5e76，\u6700\u7ec8\u7ed3\u679c\u5c31\u6574\u4f53\u6709\u5e8f\u4e86\u3002<\/li>\n

                              \u8fd9\u6b63\u662f\u5f52\u5e76\u6392\u5e8f\u300c\u7a7a\u95f4\u6362\u7a33\u5b9a\u300d\u7279\u6027\u7684\u7528\u6b66\u4e4b\u5730：\u5f52\u5e76\u64cd\u4f5c\u53ea\u9700\u8981\u7ebf\u6027\u7a7a\u95f4 + \u987a\u5e8f\u8bfb\u5199\u7684\u78c1\u76d8\u8bbf\u95ee\u6a21\u5f0f，\u5929\u751f\u5951\u5408\u5916\u5b58\u3002<\/p>\n

                              \n

                              3. \u6392\u5e8f\u7b97\u6cd5\u590d\u6742\u5ea6\u53ca\u7a33\u5b9a\u6027\u5206\u6790<\/h3>\n\n\u6392\u5e8f\u65b9\u6cd5\u6700\u597d\u5e73\u5747\u6700\u574f\u7a7a\u95f4\u590d\u6742\u5ea6\u7a33\u5b9a\u6027<\/tr>\n\n\n\n\n\n\n\n\n
                              \u63d2\u5165\u6392\u5e8f<\/td>\nO(N)<\/td>\nO(N\u00b2)<\/td>\nO(N\u00b2)<\/td>\nO(1)<\/td>\n\u7a33\u5b9a<\/td>\n<\/tr>\n
                              \u5e0c\u5c14\u6392\u5e8f<\/td>\n\u53d6\u51b3\u4e8e\u589e\u91cf<\/td>\nO(N^1.3)<\/td>\nO(N\u00b2)<\/td>\nO(1)<\/td>\n\u4e0d\u7a33\u5b9a<\/td>\n<\/tr>\n
                              \u9009\u62e9\u6392\u5e8f<\/td>\nO(N\u00b2)<\/td>\nO(N\u00b2)<\/td>\nO(N\u00b2)<\/td>\nO(1)<\/td>\n\u4e0d\u7a33\u5b9a<\/td>\n<\/tr>\n
                              \u5806\u6392\u5e8f<\/td>\nO(NlogN)<\/td>\nO(NlogN)<\/td>\nO(NlogN)<\/td>\nO(1)<\/td>\n\u4e0d\u7a33\u5b9a<\/td>\n<\/tr>\n
                              \u5192\u6ce1\u6392\u5e8f<\/td>\nO(N)<\/td>\nO(N\u00b2)<\/td>\nO(N\u00b2)<\/td>\nO(1)<\/td>\n\u7a33\u5b9a<\/td>\n<\/tr>\n
                              \u5feb\u901f\u6392\u5e8f<\/td>\nO(NlogN)<\/td>\nO(NlogN)<\/td>\nO(N\u00b2)<\/td>\nO(logN)<\/td>\n\u4e0d\u7a33\u5b9a<\/td>\n<\/tr>\n
                              \u5f52\u5e76\u6392\u5e8f<\/td>\nO(NlogN)<\/td>\nO(NlogN)<\/td>\nO(NlogN)<\/td>\nO(N)<\/td>\n\u7a33\u5b9a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                              \u51e0\u6761\u5fc5\u987b\u8bb0\u4f4f\u7684\u7ed3\u8bba（\u4e5f\u5e38\u4f5c\u4e3a\u8003\u70b9）：<\/p>\n

                                \n
                              • \u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(N\u00b2) \u7684：\u63d2\u5165\u3001\u5e0c\u5c14\u3001\u9009\u62e9\u3001\u5192\u6ce1（\u524d\u56db\u79cd\u300c\u6162\u300d\u6392\u5e8f）；<\/li>\n
                              • \u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(NlogN) \u7684：\u5806\u6392\u5e8f\u3001\u5feb\u901f\u6392\u5e8f\u3001\u5f52\u5e76\u6392\u5e8f；\u5176\u4e2d\u5feb\u901f\u6392\u5e8f\u6700\u574f\u4f1a\u9000\u5316\u5230 O(N\u00b2)；<\/li>\n
                              • \u4e0d\u7a33\u5b9a\u7684\u56db\u79cd：\u5e0c\u5c14\u3001\u9009\u62e9\u3001\u5feb\u6392\u3001\u5806\u6392（\u53e3\u8bc0："\u4e9b（\u9009）\u8c22（\u5e0c\u5c14）\u5feb\u5806"\u4e0d\u7a33\u5b9a）；<\/li>\n
                              • \u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a O(N) \u7684：\u5f52\u5e76\u6392\u5e8f（\u552f\u4e00\u9700\u8981\u7ebf\u6027\u8f85\u52a9\u7a7a\u95f4\u7684\u4e3b\u6d41\u5185\u90e8\u6392\u5e8f）；<\/li>\n
                              • \u57fa\u672c\u6709\u5e8f\u65f6，\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u6700\u5feb（\u53ef\u964d\u81f3 O(N)）；\u800c\u5feb\u901f\u6392\u5e8f\u5728\u6570\u636e\u6709\u5e8f\u65f6\u5212\u5206\u6781\u4e0d\u5747，\u53cd\u800c\u9000\u5316\u6210\u63a5\u8fd1\u5192\u6ce1\u6392\u5e8f\u7684 O(N\u00b2)\u3002<\/li>\n<\/ul>\n

                                \u8bb0\u5fc6\u5c0f\u8d34\u58eb：\u60f3\u8bb0\u7a33\u5b9a\u6027，\u53ef\u4ee5\u8054\u60f3\u2014\u2014\u300c\u8c01\u8de8\u5f97\u8fdc\u8c01\u5c31\u4e0d\u7a33\u5b9a\u300d\u3002\u5e0c\u5c14\u6392\u5e8f\u8de8 gap \u8ddd\u79bb\u4ea4\u6362\u3001\u9009\u62e9\u6392\u5e8f\u8de8\u533a\u95f4\u9009\u6700\u503c\u4ea4\u6362\u3001\u5feb\u6392\u8de8\u8d8a\u57fa\u51c6\u503c\u5212\u5206\u3001\u5806\u6392\u5e8f\u5806\u9876\u4e0e\u672b\u5c3e\u8fdc\u8ddd\u79bb\u4ea4\u6362，\u8fd9\u56db\u8005\u90fd\u4f1a\u8d8a\u8fc7\u76f8\u7b49\u5143\u7d20\u3001\u7834\u574f\u76f8\u5bf9\u6b21\u5e8f；\u800c\u63d2\u5165\u3001\u5192\u6ce1\u53ea\u5728\u76f8\u90bb\/\u5c40\u90e8\u79fb\u52a8，\u5f52\u5e76\u53d6\u7b49\u4f18\u5148\u53d6\u5de6\u4fa7，\u90fd\u4fdd\u6301\u4e86\u7a33\u5b9a\u6027\u3002<\/p>\n

                                \n

                                4. \u5176\u4ed6\u975e\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f<\/h3>\n

                                \u524d\u9762\u4e03\u5927\u6392\u5e8f\u90fd\u9760\u300c\u6bd4\u8f83 + \u79fb\u52a8\u300d，\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4e0b\u754c\u5df2\u88ab\u8bc1\u660e\u662f O(NlogN)\u3002\u800c\u975e\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u7a81\u7834\u4e86\u8fd9\u4e00\u9650\u5236，\u53ef\u4ee5\u505a\u5230\u7ebf\u6027\u65f6\u95f4 O(N)，\u4ee3\u4ef7\u662f\u7528\u7a7a\u95f4\u6362\u65f6\u95f4\u3001\u4e14\u901a\u5e38\u5bf9\u6570\u636e\u5206\u5e03\u6709\u8981\u6c42\u3002<\/p>\n

                                4.1 \u8ba1\u6570\u6392\u5e8f<\/h4>\n

                                \u601d\u60f3：\u8ba1\u6570\u6392\u5e8f\u53c8\u79f0\u4e3a\u9e3d\u5de2\u539f\u7406（\u62bd\u5c49\u539f\u7406），\u662f\u5bf9\u54c8\u5e0c\u76f4\u63a5\u5b9a\u5740\u6cd5\u7684\u53d8\u5f62\u5e94\u7528\u3002<\/p>\n

                                \u64cd\u4f5c\u6b65\u9aa4：<\/p>\n

                              • \u7edf\u8ba1：\u7edf\u8ba1\u6bcf\u4e2a\u5143\u7d20\u51fa\u73b0\u7684\u6b21\u6570\u2014\u2014\u4ee5\u300c\u5143\u7d20\u7684\u503c\u300d\u4f5c\u4e3a\u4e0b\u6807，\u5728\u4e00\u4e2a cnt \u6570\u7ec4\u5bf9\u5e94\u4f4d\u7f6e\u8ba1\u6570；<\/li>\n
                              • \u56de\u6536：\u6839\u636e\u7edf\u8ba1\u7684\u7ed3\u679c，\u6309\u4e0b\u6807\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f，\u628a\u5143\u7d20\u56de\u6536\u5230\u539f\u6765\u7684\u5e8f\u5217\u4e2d\u3002<\/li>\n

                                \/\/ \u8ba1\u6570\u6392\u5e8f：\u9002\u7528\u4e8e\u6574\u6570\u4e14\u6570\u636e\u8303\u56f4\u96c6\u4e2d<\/span>
                                \npublic<\/span> static<\/span> void<\/span> countSort<\/span>(<\/span>int<\/span>[<\/span>]<\/span> array)<\/span> {<\/span>
                                \n int<\/span> min =<\/span> array[<\/span>0<\/span>]<\/span>,<\/span> max =<\/span> array[<\/span>0<\/span>]<\/span>;<\/span>
                                \n for<\/span> (<\/span>int<\/span> num :<\/span> array)<\/span> {<\/span> \/\/ 1. \u627e\u51fa\u8303\u56f4，\u51b3\u5b9a\u8ba1\u6570\u6570\u7ec4\u5927\u5c0f<\/span>
                                \n if<\/span> (<\/span>num <<\/span> min)<\/span> min =<\/span> num;<\/span>
                                \n if<\/span> (<\/span>num ><\/span> max)<\/span> max =<\/span> num;<\/span>
                                \n }<\/span>
                                \n int<\/span>[<\/span>]<\/span> cnt =<\/span> new<\/span> int<\/span>[<\/span>max –<\/span> min +<\/span> 1<\/span>]<\/span>;<\/span>
                                \n for<\/span> (<\/span>int<\/span> num :<\/span> array)<\/span> {<\/span> \/\/ 2. \u7edf\u8ba1\u6bcf\u4e2a\u503c\u51fa\u73b0\u6b21\u6570<\/span>
                                \n cnt[<\/span>num –<\/span> min]<\/span>++<\/span>;<\/span> \/\/ \u51cf\u53bb min \u505a\u504f\u79fb，\u652f\u6301\u8d1f\u6570<\/span>
                                \n }<\/span>
                                \n int<\/span> i =<\/span> 0<\/span>;<\/span>
                                \n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> cnt.<\/span>length;<\/span> j++<\/span>)<\/span> {<\/span> \/\/ 3. \u6309\u4e0b\u6807\u987a\u5e8f\u56de\u6536<\/span>
                                \n while<\/span> (<\/span>cnt[<\/span>j]<\/span>—<\/span> ><\/span> 0<\/span>)<\/span> {<\/span>
                                \n array[<\/span>i++<\/span>]<\/span> =<\/span> j +<\/span> min;<\/span>
                                \n }<\/span>
                                \n }<\/span>
                                \n}<\/span><\/p>\n

                                \u8ba1\u6570\u6392\u5e8f\u7684\u7279\u6027\u603b\u7ed3：<\/p>\n

                              • \u8ba1\u6570\u6392\u5e8f\u5728\u6570\u636e\u8303\u56f4\u96c6\u4e2d\u65f6\u6548\u7387\u5f88\u9ad8，\u4f46\u9002\u7528\u8303\u56f4\u53ca\u573a\u666f\u6709\u9650（\u53ea\u9002\u5408\u6574\u6570\u3001\u4e14 \u8303\u56f4 \u4e0d\u80fd\u8fdc\u5927\u4e8e N，\u5426\u5219\u8ba1\u6570\u6570\u7ec4\u8fc7\u5927\u6d6a\u8d39\u7a7a\u95f4）；<\/li>\n
                              • \u65f6\u95f4\u590d\u6742\u5ea6：O(MAX(N, \u8303\u56f4))；<\/li>\n
                              • \u7a7a\u95f4\u590d\u6742\u5ea6：O(\u8303\u56f4)；<\/li>\n
                              • \u7a33\u5b9a\u6027：\u7a33\u5b9a\u3002<\/li>\n

                                \u7ecf\u5178\u5e94\u7528：\u5bf9 1 \u4ebf\u4e2a\u6574\u6570\u6392\u5e8f，\u4f46\u6bcf\u4e2a\u6570\u7684\u53d6\u503c\u8303\u56f4\u53ea\u6709 0～100（\u5982\u5e74\u9f84\u3001\u5206\u6570），\u6b64\u65f6\u8ba1\u6570\u6392\u5e8f\u8fdc\u5feb\u4e8e\u5feb\u6392\u3002<\/p>\n

                                4.2 \u57fa\u6570\u6392\u5e8f<\/h4>\n

                                \u601d\u60f3：\u57fa\u6570\u6392\u5e8f（Radix Sort）\u662f\u501f\u52a9\u591a\u5173\u952e\u5b57\u6392\u5e8f\u601d\u60f3\u5bf9\u5355\u903b\u8f91\u5173\u952e\u5b57\u8fdb\u884c\u6392\u5e8f\u7684\u65b9\u6cd5\u3002\u5b83\u4e0d\u6bd4\u8f83\u5173\u952e\u5b57\u5927\u5c0f，\u800c\u662f\u6309\u7167\u5173\u952e\u5b57\u7684\u6bcf\u4e00\u4f4d（\u4e2a\u4f4d \u2192 \u5341\u4f4d \u2192 \u767e\u4f4d\u2026\u2026）\u8fdb\u884c\u300c\u5206\u914d + \u6536\u96c6\u300d，\u91cd\u590d\u82e5\u5e72\u8f6e\u3002<\/p>\n

                                \u4ee5 LSD（\u4f4e\u4f4d\u4f18\u5148）\u4e3a\u4f8b，\u5bf9 [297, 35, 200, 9] \u6392\u5e8f：<\/p>\n

                              • \u6309\u4e2a\u4f4d\u5206\u914d\u5230 0～9 \u5341\u4e2a\u300c\u6876\u300d\u4e2d，\u518d\u6309\u6876\u7f16\u53f7\u4ece\u5c0f\u5230\u5927\u6536\u96c6；<\/li>\n
                              • \u6309\u5341\u4f4d\u518d\u6b21\u5206\u914d\u3001\u6536\u96c6；<\/li>\n
                              • \u6309\u767e\u4f4d\u518d\u6b21\u5206\u914d\u3001\u6536\u96c6，\u6536\u96c6\u5b8c\u5373\u6709\u5e8f\u3002<\/li>\n

                                \u57fa\u6570\u6392\u5e8f\u7684\u7279\u6027\u603b\u7ed3：<\/p>\n

                              • \u65f6\u95f4\u590d\u6742\u5ea6：O(d \u00d7 (N + r))，\u5176\u4e2d d \u4e3a\u6700\u5927\u4f4d\u6570\u3001r \u4e3a\u57fa\u6570（\u6876\u6570，\u5341\u8fdb\u5236\u5373 10）；<\/li>\n
                              • \u7a7a\u95f4\u590d\u6742\u5ea6：O(r)（\u6876\u7684\u6570\u91cf）；<\/li>\n
                              • \u7a33\u5b9a\u6027：\u7a33\u5b9a（\u6bcf\u4e00\u8f6e\u300c\u5206\u914d + \u6536\u96c6\u300d\u5fc5\u987b\u662f\u7a33\u5b9a\u7684，\u5426\u5219\u524d\u4e00\u4f4d\u7684\u6709\u5e8f\u6027\u4f1a\u88ab\u7834\u574f）\u3002<\/li>\n

                                4.3 \u6876\u6392\u5e8f<\/h4>\n

                                \u601d\u60f3：\u6876\u6392\u5e8f（Bucket Sort）\u662f\u8ba1\u6570\u6392\u5e8f\u7684\u5347\u7ea7\u7248\u3002\u5b83\u7684\u5de5\u4f5c\u539f\u7406\u662f\u628a\u6570\u7ec4\u5212\u5206\u6210\u6709\u9650\u4e2a\u300c\u6876\u300d，\u5c06\u5f85\u6392\u6570\u636e\u6620\u5c04\u5230\u8fd9\u4e9b\u6876\u4e2d，\u518d\u5bf9\u6bcf\u4e2a\u6876\u5355\u72ec\u6392\u5e8f（\u53ef\u7528\u63d2\u5165\u6392\u5e8f，\u4e5f\u53ef\u9012\u5f52\u4f7f\u7528\u6876\u6392\u5e8f），\u6700\u540e\u628a\u6240\u6709\u6876\u91cc\u7684\u6570\u636e\u6309\u987a\u5e8f\u62fc\u63a5\u8d77\u6765\u3002<\/p>\n

                                  \n
                                • \u9002\u7528\u524d\u63d0：\u6570\u636e\u5728\u503c\u57df\u4e0a\u8fd1\u4f3c\u5747\u5300\u5206\u5e03，\u8fd9\u6837\u6bcf\u4e2a\u6876\u91cc\u7684\u5143\u7d20\u624d\u4f1a\u8db3\u591f\u5c11，\u5355\u6876\u6392\u5e8f\u4ee3\u4ef7\u624d\u4f4e；<\/li>\n
                                • \u65f6\u95f4\u590d\u6742\u5ea6：\u6570\u636e\u5747\u5300\u5206\u5e03\u65f6\u5e73\u5747\u53ef\u8fbe O(N)，\u6700\u574f（\u5168\u90e8\u6324\u8fdb\u4e00\u4e2a\u6876）\u9000\u5316\u4e3a\u5355\u6876\u5185\u6240\u7528\u6392\u5e8f\u7684\u590d\u6742\u5ea6；<\/li>\n
                                • \u7a7a\u95f4\u590d\u6742\u5ea6：O(N + K)（K \u4e3a\u6876\u6570）；<\/li>\n
                                • \u7a33\u5b9a\u6027：\u53d6\u51b3\u4e8e\u6876\u5185\u6240\u7528\u7684\u6392\u5e8f\u7b97\u6cd5（\u7528\u7a33\u5b9a\u7684\u63d2\u5165\u6392\u5e8f，\u5219\u6574\u4f53\u7a33\u5b9a）\u3002<\/li>\n<\/ul>\n

                                  \u4e09\u8005\u5173\u7cfb\u53ef\u4ee5\u8fd9\u6837\u7406\u89e3：\u8ba1\u6570\u6392\u5e8f\u662f\u300c\u6876 = \u6bcf\u4e00\u4e2a\u53d6\u503c\u300d\u7684\u6781\u7aef\u6876\u6392\u5e8f；\u6876\u6392\u5e8f\u662f\u300c\u4e00\u4e2a\u6876\u88c5\u4e00\u6bb5\u8303\u56f4\u300d\u7684\u6cdb\u5316\u8ba1\u6570\u6392\u5e8f；\u57fa\u6570\u6392\u5e8f\u5219\u662f\u300c\u6309\u4f4d\u53cd\u590d\u505a\u7a33\u5b9a\u5206\u6876\u300d\u3002<\/p>\n

                                  \n

                                  5. \u5168\u6587\u603b\u7ed3<\/h3>\n

                                  \u56de\u5230\u6700\u521d\u7684\u5b66\u4e60\u76ee\u6807，\u672c\u7bc7\u56f4\u7ed5\u300c\u4e03\u5927\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u300d\u5b8c\u6210\u4e86\u5982\u4e0b\u68b3\u7406：<\/p>\n

                                • \n

                                  \u6982\u5ff5\u5c42\u9762：\u660e\u786e\u4e86\u6392\u5e8f\u3001\u7a33\u5b9a\u6027\u3001\u5185\u90e8 \/ \u5916\u90e8\u6392\u5e8f\u56db\u4e2a\u57fa\u672c\u6982\u5ff5，\u5e76\u4ee5\u7535\u5546\u591a\u7ef4\u6392\u5e8f\u8bf4\u660e\u6392\u5e8f\u7684\u5b9e\u9645\u5e94\u7528；<\/p>\n<\/li>\n

                                • \n

                                  \u7b97\u6cd5\u5c42\u9762：\u9010\u4e00\u638c\u63e1\u4e86\u63d2\u5165（\u76f4\u63a5\u63d2\u5165\u3001\u5e0c\u5c14）\u3001\u9009\u62e9（\u76f4\u63a5\u9009\u62e9\u3001\u5806\u6392\u5e8f）\u3001\u4ea4\u6362（\u5192\u6ce1\u3001\u5feb\u901f）\u3001\u5f52\u5e76\u56db\u5927\u5bb6\u65cf\u5171\u4e03\u79cd\u6392\u5e8f\u7684\u601d\u60f3\u3001\u4ee3\u7801\u5b9e\u73b0\u4e0e\u7279\u6027，\u5e76\u8865\u5145\u4e86\u8ba1\u6570\u3001\u57fa\u6570\u3001\u6876\u4e09\u79cd\u975e\u6bd4\u8f83\u6392\u5e8f；<\/p>\n<\/li>\n

                                • \n

                                  \u6027\u80fd\u5c42\u9762：\u5efa\u7acb\u4e86\u4e00\u5f20\u5b8c\u6574\u7684\u300c\u65f6\u95f4 \/ \u7a7a\u95f4\u590d\u6742\u5ea6 + \u7a33\u5b9a\u6027\u300d\u5bf9\u7167\u8868，\u5e76\u7ed9\u51fa\u4e86\u9009\u578b\u5efa\u8bae\u2014\u2014<\/p>\n

                                    \n
                                  • \u6570\u636e\u91cf\u5c0f \/ \u57fa\u672c\u6709\u5e8f \u2192 \u76f4\u63a5\u63d2\u5165\u6392\u5e8f；<\/li>\n
                                  • \u4e0d\u8981\u6c42\u7a33\u5b9a\u3001\u8ffd\u6c42\u7efc\u5408\u6700\u5feb \u2192 \u5feb\u901f\u6392\u5e8f（\u5b9e\u9645\u9996\u9009，\u6ce8\u610f\u6700\u574f\u9000\u5316\u4e0e\u4f18\u5316）；<\/li>\n
                                  • \u8981\u6c42\u7a33\u5b9a\u4e14\u9700\u8981 O(NlogN) \u2192 \u5f52\u5e76\u6392\u5e8f（\u4e14\u662f\u5916\u90e8\u6392\u5e8f\u7684\u4e0d\u4e8c\u4e4b\u9009）；<\/li>\n
                                  • \u5185\u5b58\u6781\u7d27\u5f20\u3001\u8981\u6c42\u6700\u574f\u4e5f\u7a33\u5b9a O(NlogN) \u2192 \u5806\u6392\u5e8f（\u4ee5\u53ca Top-K \u573a\u666f）；<\/li>\n
                                  • \u6574\u6570\u4e14\u6570\u636e\u8303\u56f4\u96c6\u4e2d \u2192 \u8ba1\u6570 \/ \u57fa\u6570 \/ \u6876\u6392\u5e8f（\u7ebf\u6027\u65f6\u95f4）\u3002<\/li>\n<\/ul>\n<\/li>\n

                                    \u6392\u5e8f\u662f\u6570\u636e\u7ed3\u6784\u7684"\u57fa\u672c\u529f"，\u770b\u4f3c\u7b80\u5355，\u5b9e\u5219\u6bcf\u4e2a\u7b97\u6cd5\u80cc\u540e\u90fd\u5bf9\u5e94\u7740\u4e00\u79cd\u91cd\u8981\u7684\u7b97\u6cd5\u601d\u60f3：\u63d2\u5165\u662f\u300c\u7ef4\u6301\u4e0d\u53d8\u5f0f\u300d\u3001\u5e0c\u5c14\u662f\u300c\u589e\u91cf\u4f18\u5316\u300d\u3001\u9009\u62e9\u662f\u300c\u8d2a\u5fc3\u9009\u6700\u503c\u300d\u3001\u5806\u662f\u300c\u7528\u7ed3\u6784\u52a0\u901f\u9009\u62e9\u300d\u3001\u5feb\u6392\u662f\u300c\u5206\u6cbb + \u5212\u5206\u300d\u3001\u5f52\u5e76\u662f\u300c\u5206\u6cbb + \u5408\u5e76\u300d\u3002\u7406\u89e3\u8fd9\u4e9b\u601d\u60f3，\u6bd4\u5355\u7eaf\u80cc\u4e0b\u590d\u6742\u5ea6\u8868\u66f4\u6709\u4ef7\u503c\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

                                    \u6392\u5e8f\u7b97\u6cd5\u8be6\u89e3：\u4e03\u5927\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u4e0e\u975e\u6bd4\u8f83\u6392\u5e8f \u5b66\u4e60\u76ee\u6807 \u638c\u63e1\u4e03\u5927\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u7b97\u6cd5\u7684\u57fa\u672c\u539f\u7406\u53ca\u5b9e\u73b0；\u638c\u63e1\u6392\u5e8f\u7b97\u6cd5\u7684\u6027\u80fd\u5206\u6790（\u65f6\u95f4\u590d\u6742\u5ea6\u3001\u7a7a\u95f4\u590d\u6742\u5ea6\u3001\u7a33\u5b9a\u6027）；\u638c\u63e1 Java \u4e2d\u7684\u5e38\u7528\u6392\u5e8f\u65b9\u6cd5\u3002 \u76ee\u5f55
                                    \n1. \u6392\u5e8f\u7684\u6982\u5ff5\u53ca\u8fd0\u7528 1.1 \u6392\u5e8f\u7684\u6982\u5ff51.2 \u6392\u5e8f\u7684\u8fd0\u7528 2. \u5e38\u89c1\u6392\u5e8f\u7b97\u6cd5 2.1 \u63d2\u5165\u6392\u5e8f 2.1.1 \u76f4\u63a5\u63d2\u5165\u6392\u5e8f2.1.2 \u5e0c\u5c14\u6392\u5e8f（\u7f29\u5c0f\u589e\u91cf\u6392\u5e8f） 2.2 \u9009\u62e9\u6392\u5e8f <\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[99,3226,1813],"topic":[],"class_list":["post-118971","post","type-post","status-publish","format-standard","hentry","category-server","tag-java","tag-3226","tag-1813"],"yoast_head":"\nJAVA\u6570\u636e\u7ed3\u6784-\u6392\u5e8f - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/118971.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"JAVA\u6570\u636e\u7ed3\u6784-\u6392\u5e8f - 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