{"id":67464,"date":"2026-01-28T20:24:45","date_gmt":"2026-01-28T12:24:45","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/67464.html"},"modified":"2026-01-28T20:24:45","modified_gmt":"2026-01-28T12:24:45","slug":"%e6%8f%92%e5%85%a5%e6%8e%92%e5%ba%8f%ef%bc%9a%e4%bb%8e%e6%89%91%e5%85%8b%e7%89%8c%e7%90%86%e7%89%8c%e8%af%b4%e8%b5%b7%ef%bc%8c%e8%bd%bb%e6%9d%be%e6%8e%8c%e6%8f%a1%e7%bb%8f%e5%85%b8%e6%8e%92%e5%ba%8f","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/67464.html","title":{"rendered":"\u63d2\u5165\u6392\u5e8f\uff1a\u4ece\u6251\u514b\u724c\u7406\u724c\u8bf4\u8d77\uff0c\u8f7b\u677e\u638c\u63e1\u7ecf\u5178\u6392\u5e8f\u7b97\u6cd5\uff08\u542b\u8fdb\u9636\u4f18\u5316\u4e0e\u7a33\u5b9a\u6027\u5206\u6790\uff09"},"content":{"rendered":"

\u63d2\u5165\u6392\u5e8f：\u4ece\u6251\u514b\u724c\u7406\u724c\u8bf4\u8d77，\u8f7b\u677e\u638c\u63e1\u7ecf\u5178\u6392\u5e8f\u7b97\u6cd5（\u542b\u8fdb\u9636\u4f18\u5316\u4e0e\u7a33\u5b9a\u6027\u5206\u6790）<\/h2>\n

\u201c\u7b80\u5355\u5374\u4f18\u96c5，\u7a33\u5b9a\u53c8\u5b9e\u7528\u201d\u2014\u2014\u63d2\u5165\u6392\u5e8f\u7684\u9b45\u529b<\/p>\n

\u5927\u5bb6\u597d！\u4eca\u5929\u6211\u4eec\u6df1\u5165\u804a\u804a\u6570\u636e\u7ed3\u6784\u4e2d\u4e00\u4e2a\u65e2\u57fa\u7840\u53c8\u5b9e\u7528\u7684\u6392\u5e8f\u7b97\u6cd5\u2014\u2014\u63d2\u5165\u6392\u5e8f（Insertion Sort）\u3002\u65e0\u8bba\u4f60\u662f\u521a\u63a5\u89e6\u7f16\u7a0b\u7684\u65b0\u624b，\u8fd8\u662f\u6b63\u5728\u51c6\u5907\u9762\u8bd5\u7684\u6c42\u804c\u8005，\u7406\u89e3\u63d2\u5165\u6392\u5e8f\u90fd\u5927\u6709\u88e8\u76ca\u3002<\/p>\n

\n

🃏 \u4ece\u7406\u6251\u514b\u724c\u8bf4\u8d77<\/h3>\n

\u60f3\u8c61\u4e00\u4e0b，\u4f60\u624b\u91cc\u62ff\u7740\u4e00\u645e\u6253\u4e71\u7684\u6251\u514b\u724c，\u8981\u6309\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f\u6574\u7406\u3002\u4f60\u4f1a\u600e\u4e48\u505a？<\/p>\n

\u901a\u5e38，\u6211\u4eec\u4f1a：<\/p>\n

  • \n

    \u62ff\u8d77\u7b2c\u4e00\u5f20\u724c（\u9ed8\u8ba4\u6709\u5e8f）；<\/p>\n<\/li>\n

  • \n

    \u62ff\u8d77\u7b2c\u4e8c\u5f20\u724c，\u548c\u7b2c\u4e00\u5f20\u6bd4\u8f83，\u51b3\u5b9a\u653e\u524d\u9762\u8fd8\u662f\u540e\u9762；<\/p>\n<\/li>\n

  • \n

    \u62ff\u8d77\u7b2c\u4e09\u5f20\u724c，\u5728\u5df2\u6392\u597d\u7684\u524d\u4e24\u5f20\u4e2d\u627e\u5230\u5408\u9002\u4f4d\u7f6e\u63d2\u5165；<\/p>\n<\/li>\n

  • \n

    \u4ee5\u6b64\u7c7b\u63a8\u2026\u2026<\/p>\n<\/li>\n

    \u8fd9，\u5c31\u662f\u63d2\u5165\u6392\u5e8f\u7684\u601d\u60f3！<\/p>\n

    \n

    🔢 \u63d2\u5165\u6392\u5e8f\u5168\u8fc7\u7a0b\u6f14\u793a（\u9644\u4f8b\u5b50）<\/h3>\n

    \u6211\u4eec\u4ee5\u6570\u7ec4\u00a0arr = [5, 2, 4, 6, 1, 3]\u00a0\u4e3a\u4f8b，\u4e00\u6b65\u6b65\u770b\u63d2\u5165\u6392\u5e8f\u5982\u4f55\u5de5\u4f5c：<\/p>\n\n\n

    \u6b65\u9aa4<\/p>\n

    \u5f53\u524d\u6570\u7ec4\u72b6\u6001<\/p>\n

    \u8bf4\u660e<\/p>\n<\/tr>\n

    \n\n\n\n\n\n\n
    \n

    \u521d\u59cb<\/p>\n<\/td>\n

    		[5, 2, 4, 6, 1, 3]<\/td>\n\n

    \u7b2c1\u4e2a\u5143\u7d20\u89c6\u4e3a\u5df2\u6392\u5e8f<\/p>\n<\/td>\n<\/tr>\n

    \n

    i=1<\/p>\n<\/td>\n

    		[2, 5, 4, 6, 1, 3]<\/td>\n\n

    \u5c062\u63d2\u5165\u52305\u524d\u9762<\/p>\n<\/td>\n<\/tr>\n

    \n

    i=2<\/p>\n<\/td>\n

    		[2, 4, 5, 6, 1, 3]<\/td>\n\n

    \u5c064\u63d2\u5165\u52302\u548c5\u4e4b\u95f4<\/p>\n<\/td>\n<\/tr>\n

    \n

    i=3<\/p>\n<\/td>\n

    		[2, 4, 5, 6, 1, 3]<\/td>\n\n

    6\u5df2\u5728\u6b63\u786e\u4f4d\u7f6e，\u65e0\u9700\u79fb\u52a8<\/p>\n<\/td>\n<\/tr>\n

    \n

    i=4<\/p>\n<\/td>\n

    		[1, 2, 4, 5, 6, 3]<\/td>\n\n

    \u5c061\u63d2\u5165\u5230\u6700\u524d\u9762<\/p>\n<\/td>\n<\/tr>\n

    \n

    i=5<\/p>\n<\/td>\n

    		[1, 2, 3, 4, 5, 6]<\/td>\n\n

    \u5c063\u63d2\u5165\u52302\u548c4\u4e4b\u95f4<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u2705\u00a0\u6bcf\u4e00\u6b65\u90fd\u4fdd\u8bc1\u5de6\u4fa7\u662f\u6709\u5e8f\u7684，\u6700\u7ec8\u6574\u4e2a\u6570\u7ec4\u6709\u5e8f！<\/p>\n

    \n

    💻 C\u8bed\u8a00\u5b9e\u73b0（\u6807\u51c6\u7248）<\/h3>\n

    void\u00a0insertionSort(int\u00a0arr[],\u00a0int\u00a0n)\u00a0{
    \n\u00a0 \u00a0\u00a0for\u00a0(int\u00a0i =\u00a01; i < n; i++) {
    \n\u00a0 \u00a0 \u00a0 \u00a0\u00a0int\u00a0key = arr[i];
    \n\u00a0 \u00a0 \u00a0 \u00a0\u00a0int\u00a0j = i –\u00a01;
    \n\u00a0 \u00a0 \u00a0 \u00a0\u00a0while\u00a0(j >=\u00a00\u00a0&& arr[j] > key) {
    \n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 arr[j +\u00a01] = arr[j];
    \n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 j–;
    \n\u00a0 \u00a0 \u00a0 \u00a0 }
    \n\u00a0 \u00a0 \u00a0 \u00a0 arr[j +\u00a01] = key;
    \n\u00a0 \u00a0 }
    \n}<\/p>\n

    \n

    \u26a1 \u4f18\u5316\u7248：\u6298\u534a\u63d2\u5165\u6392\u5e8f（Binary Insertion Sort）<\/h3>\n

    \u5728\u6807\u51c6\u63d2\u5165\u6392\u5e8f\u4e2d，\u6211\u4eec\u901a\u8fc7\u7ebf\u6027\u626b\u63cf\u627e\u63d2\u5165\u4f4d\u7f6e，\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\u3002\u4f46\u65e2\u7136\u201c\u5df2\u6392\u5e8f\u533a\u201d\u662f\u6709\u5e8f\u7684，\u4e3a\u4f55\u4e0d\u7528\u4e8c\u5206\u67e5\u627e\u6765\u52a0\u901f\u5b9a\u4f4d？<\/p>\n

    \u8fd9\u5c31\u662f\u6298\u534a\u63d2\u5165\u6392\u5e8f\u7684\u6838\u5fc3\u601d\u60f3！<\/p>\n

    \u2705 \u4f18\u70b9：<\/h4>\n
      \n
    • \n

      \u51cf\u5c11\u6bd4\u8f83\u6b21\u6570（\u4ece O(n) \u964d\u5230 O(log n)）<\/p>\n<\/li>\n

    • \n

      \u79fb\u52a8\u5143\u7d20\u6b21\u6570\u4e0d\u53d8（\u4ecd\u9700 O(n) \u65f6\u95f4\u79fb\u52a8）<\/p>\n<\/li>\n<\/ul>\n

      💻 C\u8bed\u8a00\u5b9e\u73b0（\u6298\u534a\u7248）：<\/h4>\n

      #include\u00a0<stdio.h><\/p>\n

      void\u00a0binaryInsertionSort(int\u00a0arr[],\u00a0int\u00a0n)\u00a0{
      \n\u00a0 \u00a0\u00a0for\u00a0(int\u00a0i =\u00a01; i < n; i++) {
      \n\u00a0 \u00a0 \u00a0 \u00a0\u00a0int\u00a0key = arr[i];
      \n\u00a0 \u00a0 \u00a0 \u00a0\u00a0int\u00a0left =\u00a00, right = i;<\/p>\n

      \u00a0 \u00a0 \u00a0 \u00a0\u00a0\/\/ \u4e8c\u5206\u67e5\u627e\u63d2\u5165\u4f4d\u7f6e
      \n\u00a0 \u00a0 \u00a0 \u00a0\u00a0while\u00a0(left < right) {
      \n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0int\u00a0mid = (left + right) \/\u00a02;
      \n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0if\u00a0(arr[mid] > key)
      \n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 right = mid;
      \n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0else
      \n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 left = mid +\u00a01;
      \n\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n

      \u00a0 \u00a0 \u00a0 \u00a0\u00a0\/\/ \u5c06 arr[left..i-1] \u540e\u79fb\u4e00\u4f4d
      \n\u00a0 \u00a0 \u00a0 \u00a0\u00a0for\u00a0(int\u00a0j = i; j > left; j–) {
      \n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 arr[j] = arr[j –\u00a01];
      \n\u00a0 \u00a0 \u00a0 \u00a0 }
      \n\u00a0 \u00a0 \u00a0 \u00a0 arr[left] = key;
      \n\u00a0 \u00a0 }
      \n}<\/p>\n

      📌 \u6ce8\u610f：\u867d\u7136\u6bd4\u8f83\u6b21\u6570\u51cf\u5c11，\u4f46\u6574\u4f53\u65f6\u95f4\u590d\u6742\u5ea6\u4ecd\u662f O(n\u00b2) ，\u56e0\u4e3a\u5143\u7d20\u79fb\u52a8\u4ecd\u9700\u7ebf\u6027\u65f6\u95f4\u3002\u4f46\u5728\u5b9e\u9645\u8fd0\u884c\u4e2d，\u5c24\u5176\u5f53\u6bd4\u8f83\u64cd\u4f5c\u4ee3\u4ef7\u9ad8\u65f6，\u6298\u534a\u63d2\u5165\u6392\u5e8f\u4f1a\u66f4\u5feb\u3002<\/p>\n

      \n

      🧪 \u7b97\u6cd5\u7a33\u5b9a\u6027\u8be6\u89e3（\u9644\u5b9e\u4f8b）<\/h3>\n

      \u4ec0\u4e48\u662f\u7a33\u5b9a\u6027？
      \n\u5982\u679c\u6392\u5e8f\u540e，\u76f8\u7b49\u5143\u7d20\u7684\u76f8\u5bf9\u987a\u5e8f\u6ca1\u6709\u6539\u53d8，\u5219\u79f0\u8be5\u6392\u5e8f\u7b97\u6cd5\u662f\u7a33\u5b9a\u7684\u3002<\/p>\n

      \u2705 \u63d2\u5165\u6392\u5e8f\u662f\u7a33\u5b9a\u7684！<\/h4>\n

      \u4e3e\u4e2a\u4f8b\u5b50：<\/h5>\n

      \u5047\u8bbe\u6211\u4eec\u5bf9\u4ee5\u4e0b\u5e26\u201c\u989c\u8272\u6807\u7b7e\u201d\u7684\u6570\u7ec4\u6392\u5e8f（\u6570\u5b57\u76f8\u540c\u4f46\u6765\u6e90\u4e0d\u540c）：<\/p>\n

      \u539f\u59cb\u6570\u7ec4（\u683c\u5f0f：\u503c\/\u6807\u7b7e）：
      \n[ (3,\u7ea2), (1,\u84dd), (3,\u7eff), (2,\u9ec4) ]<\/p>\n

      \u6211\u4eec\u53ea\u6309\u6570\u503c\u6392\u5e8f，\u4e0d\u8003\u8651\u6807\u7b7e\u3002<\/p>\n

      \u4f7f\u7528\u63d2\u5165\u6392\u5e8f\u8fc7\u7a0b\u5982\u4e0b：<\/p>\n

    • \n

      i=1：\u63d2\u5165 (1,\u84dd) \u2192\u00a0[ (1,\u84dd), (3,\u7ea2), (3,\u7eff), (2,\u9ec4) ]<\/p>\n<\/li>\n

    • \n

      i=2：(3,\u7eff) \u4e0e (3,\u7ea2) \u6bd4\u8f83，\u56e0\u00a03 > 3\u00a0\u4e0d\u6210\u7acb（\u6761\u4ef6\u4e3a\u00a0arr[j] > key），\u4e0d\u79fb\u52a8\u00a0\u2192 \u4fdd\u6301\u00a0(3,\u7ea2)\u00a0\u5728\u00a0(3,\u7eff)\u00a0\u524d\u9762<\/p>\n<\/li>\n

    • \n

      i=3：\u63d2\u5165 (2,\u9ec4) \u2192 \u6700\u7ec8\u7ed3\u679c：
      \n[ (1,\u84dd), (2,\u9ec4), (3,\u7ea2), (3,\u7eff) ]<\/p>\n<\/li>\n

      \u2705 \u53ef\u89c1，\u4e24\u4e2a\u00a03\u00a0\u7684\u76f8\u5bf9\u987a\u5e8f（\u7ea2\u2192\u7eff）\u6ca1\u6709\u6539\u53d8，\u56e0\u6b64\u63d2\u5165\u6392\u5e8f\u662f\u7a33\u5b9a\u7684！<\/p>\n

      🔍 \u5173\u952e\u70b9：\u4ee3\u7801\u4e2d\u5224\u65ad\u6761\u4ef6\u662f\u00a0arr[j] > key，**\u4e0d\u662f\u00a0>=**\u3002\u82e5\u5199\u6210\u00a0>=，\u5c31\u4f1a\u7834\u574f\u7a33\u5b9a\u6027！<\/p>\n

      \n

      📊 \u6027\u80fd\u603b\u7ed3<\/h3>\n\n\n

      \u7279\u6027<\/p>\n

      \u6807\u51c6\u63d2\u5165\u6392\u5e8f<\/p>\n

      \u6298\u534a\u63d2\u5165\u6392\u5e8f<\/p>\n<\/tr>\n

      \n\n\n\n\n\n\n
      \n

      \u65f6\u95f4\u590d\u6742\u5ea6（\u5e73\u5747\/\u6700\u574f）<\/p>\n<\/td>\n

      		\n

      O(n\u00b2)<\/p>\n<\/td>\n

      		\n

      O(n\u00b2)<\/p>\n<\/td>\n<\/tr>\n

      \n

      \u6bd4\u8f83\u6b21\u6570<\/p>\n<\/td>\n

      		\n

      O(n\u00b2)<\/p>\n<\/td>\n

      		\n

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

      \n

      \u79fb\u52a8\u6b21\u6570<\/p>\n<\/td>\n

      		\n

      O(n\u00b2)<\/p>\n<\/td>\n

      		\n

      O(n\u00b2)<\/p>\n<\/td>\n<\/tr>\n

      \n

      \u7a7a\u95f4\u590d\u6742\u5ea6<\/p>\n<\/td>\n

      		\n

      O(1)<\/p>\n<\/td>\n

      		\n

      O(1)<\/p>\n<\/td>\n<\/tr>\n

      \n

      \u7a33\u5b9a\u6027<\/p>\n<\/td>\n

      		\n

      \u2705 \u7a33\u5b9a<\/p>\n<\/td>\n

      		\n

      \u2705 \u7a33\u5b9a（\u53ea\u8981\u4e8c\u5206\u903b\u8f91\u6b63\u786e）<\/p>\n<\/td>\n<\/tr>\n

      \n

      \u9002\u7528\u573a\u666f<\/p>\n<\/td>\n

      		\n

      \u5c0f\u89c4\u6a21\u3001\u8fd1\u4f3c\u6709\u5e8f\u6570\u636e<\/p>\n<\/td>\n

      		\n

      \u6bd4\u8f83\u64cd\u4f5c\u6602\u8d35\u65f6\u66f4\u4f18<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \n

      \u2705 \u5c0f\u7ed3<\/h3>\n

      \u63d2\u5165\u6392\u5e8f\u867d\u7b80\u5355，\u5374\u8574\u542b\u6df1\u523b\u601d\u60f3：<\/p>\n

        \n
      • \n

        \u76f4\u89c2\u5982\u7406\u724c，\u6613\u4e8e\u7406\u89e3\u548c\u5b9e\u73b0；<\/p>\n<\/li>\n

      • \n

        \u7a33\u5b9a\u53ef\u9760，\u9002\u5408\u5bf9\u76f8\u7b49\u5143\u7d20\u6709\u987a\u5e8f\u8981\u6c42\u7684\u573a\u666f；<\/p>\n<\/li>\n

      • \n

        \u53ef\u4f18\u5316，\u901a\u8fc7\u4e8c\u5206\u67e5\u627e\u63d0\u5347\u6548\u7387；<\/p>\n<\/li>\n

      • \n

        \u662f\u9ad8\u7ea7\u7b97\u6cd5\u7684\u57fa\u77f3（\u5982\u5e0c\u5c14\u6392\u5e8f\u3001Timsort \u7684\u5e95\u5c42\u7ec4\u4ef6）\u3002<\/p>\n<\/li>\n<\/ul>\n

        \u201c\u770b\u4f3c\u5e73\u51e1\u7684\u7b97\u6cd5，\u5f80\u5f80\u85cf\u7740\u4e0d\u5e73\u51e1\u7684\u667a\u6167\u3002\u201d<\/p>\n

        \n

        \u5982\u679c\u4f60\u89c9\u5f97\u8fd9\u7bc7\u6587\u7ae0\u6709\u5e2e\u52a9，\u6b22\u8fce\u70b9\u8d5e\u3001\u5728\u770b\u3001\u8f6c\u53d1\u7ed9\u66f4\u591a\u670b\u53cb！
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