{"id":118084,"date":"2026-10-26T06:18:25","date_gmt":"2026-10-25T22:18:25","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/118084.html"},"modified":"2026-10-26T06:18:25","modified_gmt":"2026-10-25T22:18:25","slug":"%e3%80%90c%e3%80%91%e4%b8%80%e6%ac%a1%e6%8f%92%e5%85%a5%ef%bc%8c%e5%9b%9b%e5%9c%ba%e6%97%8b%e8%bd%ac%ef%bc%9ac-avl-%e6%a0%91%e7%9a%84%e8%87%aa%e5%b9%b3%e8%a1%a1%e4%b9%8b%e8%b7%af","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/118084.html","title":{"rendered":"\u3010C++\u3011\u4e00\u6b21\u63d2\u5165\uff0c\u56db\u573a\u65cb\u8f6c\uff1aC++ AVL \u6811\u7684\u81ea\u5e73\u8861\u4e4b\u8def"},"content":{"rendered":"

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0\"\"<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0🏆\u6d6e\u4e16\u5c18\u5f26：\u4e2a\u4eba\u4e3b\u9875<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0\u2b50\u4e2a\u4eba\u4e13\u680f：\u300aC\u8bed\u8a00\u300b<\/span>\u3001\u300a\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u300b<\/span>\u3001\u300aC++\u300b<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 💎：\u975e\u6de1\u8584\u65e0\u4ee5\u660e\u5fd7，\u975e\u5b81\u9759\u65e0\u4ee5\u81f4\u8fdc<\/p>\n

\n

\u524d\u8a00<\/h2>\n

\u666e\u901a\u4e8c\u53c9\u641c\u7d22\u6811\u5728\u6570\u636e\u63a5\u8fd1\u6709\u5e8f\u65f6\u5bb9\u6613\u9000\u5316\u6210\u94fe\u8868，\u67e5\u627e\u6548\u7387\u4f1a\u4ece O(log n) \u964d\u5230 O(n)\u3002\u800cAVL\u6811\u901a\u8fc7\u63a7\u5236\u6bcf\u4e2a\u8282\u70b9\u5de6\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee，\u8ba9\u6811\u5728\u63d2\u5165\u540e\u59cb\u7ec8\u4fdd\u6301\u76f8\u5bf9\u5e73\u8861\u3002<\/p>\n

\u672c\u6587\u5148\u7528 C++ \u8ba4\u8bc6 AVL \u6811\u53ca\u5176\u8282\u70b9\u7ed3\u6784，\u518d\u5b8c\u6574\u6a21\u62df\u4e00\u6b21\u63d2\u5165：\u5bfb\u627e\u4f4d\u7f6e\u3001\u63d2\u5165\u8282\u70b9\u3001\u66f4\u65b0\u5e73\u8861\u56e0\u5b50<\/span>\u3002\u968f\u540e\u4f9d\u6b21\u5206\u6790\u53f3\u5355\u65cb\u3001\u5de6\u5355\u65cb\u3001\u5de6\u53f3\u53cc\u65cb\u548c\u53f3\u5de6\u53cc\u65cb\u56db\u79cd\u8c03\u6574\u65b9\u5f0f<\/span>，\u5e76\u5b9e\u73b0\u67e5\u627e\u64cd\u4f5c\u4e0e AVL \u6811\u5224\u5b9a\u3002<\/p>\n

\u6574\u4e2a\u8fc7\u7a0b\u6cbf\u7740\u201c\u63d2\u5165\u3001\u5931\u8861\u3001\u65cb\u8f6c\u3001\u6062\u590d\u5e73\u8861\u201d\u7684\u8def\u5f84\u5c55\u5f00，\u4e0d\u6025\u4e8e\u5806\u780c\u4ee3\u7801，\u800c\u662f\u5f04\u6e05\u6bcf\u4e00\u6b65\u4e3a\u4f55\u53d1\u751f\u3001\u4e3a\u4ec0\u4e48\u9009\u62e9\u8fd9\u79cd\u8c03\u6574\u3002<\/p>\n

\u8ba9\u6211\u4eec\u5f00\u59cb\u4eca\u5929\u7684\u5b66\u4e60\u5427！<\/p>\n

\"\"<\/p>\n

\u76ee\u5f55<\/p>\n

\u524d\u8a00<\/p>\n

\u4e00，\u4ecb\u7ecdAVL\u6811<\/p>\n

\u4e8c，\u6a21\u62df\u5b9e\u73b0AVL\u6811<\/p>\n

1，AVL\u6811\u8282\u70b9<\/p>\n

2，AVL\u6811\u7684\u63d2\u5165<\/p>\n

1，\u5bfb\u627e\u63d2\u5165\u4f4d\u7f6e\u5e76\u63d2\u5165<\/p>\n

2，\u66f4\u65b0\u5e73\u8861\u56e0\u5b50<\/p>\n

3，\u65cb\u8f6c<\/p>\n

1，\u53f3\u5355\u65cb<\/p>\n

2，\u5de6\u5355\u65cb<\/p>\n

3，\u5de6\u53f3\u53cc\u65cb<\/p>\n

4，\u53f3\u5de6\u53cc\u65cb<\/p>\n

4，AVL\u6811\u7684\u67e5\u627e<\/p>\n

5，\u5224\u65ad\u662f\u5426\u662fAVL\u6811<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u7ed3\u5c3e<\/p>\n

\n

\u4e00，\u4ecb\u7ecdAVL\u6811<\/h2>\n

AVL\u6811\u662f\u6700\u5148\u88ab\u53d1\u660e\u7684\u81ea\u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811，AVL\u6811\u8981\u4e48\u662f\u4e00\u4e2a\u7a7a\u6811，\u8981\u4e48\u5177\u6709\u4ee5\u4e0b\u7279\u70b9：<\/p>\n

\u5de6\u53f3\u5b50\u6811\u90fd\u662fAVL\u6811，\u4e14\u6bcf\u4e2a\u8282\u70b9\u7684\u5de6\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u90fd\u4e0d\u8d85\u8fc71<\/span><\/p>\n

\u6838\u5fc3\u6982\u5ff5：\u5e73\u8861\u56e0\u5b50（bf）<\/p>\n

\u6bcf\u4e2a\u8282\u70b9\u90fd\u6709\u4e00\u4e2a\u5e73\u8861\u56e0\u5b50，\u7528\u6765\u8bb0\u5f55\u5de6\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee\u3002<\/p>\n

\u9ad8\u5ea6\u5dee\u5408\u7406\u53d6\u503c：-1,0,1<\/span>\u00a0 \u00a0\u5982\u679c\u5e73\u8861\u56e0\u5b50\u7684\u503c\u4e3a2，-2，\u8868\u660e\u8fd9\u68f5\u6811\u4e0d\u5e73\u8861\u9700\u8981\u8fdb\u884c\u8c03\u6574（\u65cb\u8f6c）<\/span><\/p>\n

AVL\u6811\u7684\u7ed3\u6784\u548c\u5b8c\u5168\u4e8c\u53c9\u6811\u7c7b\u4f3c，\u9ad8\u5ea6\u5927\u7ea6\u5728logN,\u76f8\u8f83\u4e8e\u4e8c\u53c9\u641c\u7d22\u6811\u589e\u5220\u67e5\u6539\u5e73\u5747\u4e3aO(N),\u6700\u597dO(logN).AVL\u589e\u5220\u67e5\u6539\u7684\u6548\u7387\u4e25\u683c\u4e3aO(logN)，\u6548\u7387\u8f83\u9ad8\u3002<\/span><\/p>\n

\"\"<\/p>\n

\u4e8c，\u6a21\u62df\u5b9e\u73b0AVL\u6811<\/h2>\n

1，AVL\u6811\u8282\u70b9<\/h3>\n

AVL\u6811\u7684\u8282\u70b9\u7531\u4e94\u90e8\u5206\u6784\u6210：1，\u5173\u952e\u5b57key，\u4e5f\u53ef\u4ee5\u4e3apair\u7c7b\u578b\u30022，\u6307\u5411\u5de6\u5b50\u6811\u7684\u6307\u9488：left<\/p>\n

3,\u6307\u5411\u53f3\u5b50\u6811\u7684\u6307\u9488：right 4，\u6307\u5411\u7236\u4eb2\u8282\u70b9\u7684\u6307\u9488 5，\u5e73\u8861\u56e0\u5b50bf<\/p>\n

template <class K,class V>
\n\/\/AVL\u6570\u8282\u70b9
\nstruct AVLTreeNode
\n{
\n\/\/struct\u9ed8\u8ba4\u4e3a\u516c\u6709
\npair<K, V> kv;
\nAVLTreeNode* left;
\nAVLTreeNode* right;
\nAVLTreeNode* parent;
\nint bf;\/\/\u5e73\u8861\u56e0\u5b50
\nAVLTreeNode(const pair<K, V>& p)
\n:kv(p)
\n, left(nullptr)
\n, right(nullptr)
\n,parent(nullptr)
\n,bf(0)
\n{}
\n}; <\/p>\n

2，AVL\u6811\u7684\u63d2\u5165<\/h3>\n

\u63d2\u5165\u6b65\u9aa4：<\/span><\/p>\n

1，\u5bfb\u627e\u63d2\u5165\u4f4d\u7f6e\u5e76\u63d2\u5165<\/h4>\n

\u5bfb\u627e\u4f4d\u7f6e\u548c\u63d2\u5165\u7684\u89c4\u5219\u548c\u5e73\u8861\u4e8c\u53c9\u6811\u63d2\u5165\u503c\u7684\u8fc7\u7a0b\u4e00\u6837\u3002<\/p>\n

\u4ece\u6839\u8282\u70b9\u4f4d\u7f6e\u5f00\u59cb，\u6bd4\u8f83\u8282\u70b9\u503c\u7684\u5927\u5c0f\u3002\u8d70\u5411\u5de6\u5b50\u6811\u6216\u8005\u53f3\u5b50\u6811\u3002\u77e5\u9053\u627e\u5230\u63d2\u5165\u4f4d\u7f6e\u3002<\/span><\/p>\n

\u6ce8\u610f:\u8981\u63d0\u524d\u8bbe\u8ba1\u4e00\u4e2a\u7236\u4eb2\u8282\u70b9，\u63d0\u524d\u8bb0\u5f55\u4f4d\u7f6e，\u65b9\u4fbf\u63d2\u5165\u3002<\/span><\/p>\n

template <class K,class V>
\nclass AVLTree
\n{
\ntypedef AVLTreeNode<K, V> Node;
\npublic:
\n\/\/\u63d2\u5165
\nbool Insert(pair<K, V> p1)
\n{
\n\/\/\u6839\u8282\u70b9\u4e3a\u7a7a
\nif (root == nullptr)
\n{
\nroot = new Node(p1);
\nreturn true;
\n}
\n\/\/\u6839\u8282\u70b9\u4e0d\u4e3a\u7a7a，\u627e\u5230\u8981\u63d2\u5165\u7684\u4f4d\u7f6e
\nNode* cur = root;
\nNode* parent = nullptr;
\nwhile (cur)
\n{
\nif (p1.first > cur->kv.first)
\n{
\nparent = cur;
\ncur = cur->right;
\n}
\nelse if (p1.first < cur->kv.first)
\n{
\nparent = cur;
\ncur = cur->left;
\n}
\nelse \/\/\u4e0d\u80fd\u5b58\u5728\u76f8\u540c\u8282\u70b9
\n{
\nreturn false;
\n}
\n}
\n\/\/\u8fdb\u884c\u63d2\u5165
\ncur = new Node(p1);
\nif (p1.first > parent->kv.first)
\n{
\nparent->right = cur;
\n}
\nelse
\n{
\nparent->left = cur;
\n}
\ncur->parent = parent; <\/p>\n

2，\u66f4\u65b0\u5e73\u8861\u56e0\u5b50 \u2b50<\/h4>\n

\u5e73\u8861\u56e0\u5b50\u7684\u66f4\u65b0\u89c4\u5219：<\/span><\/p>\n

\u5e73\u8861\u56e0\u5b50= \u53f3\u5b50\u6811\u9ad8\u5ea6- \u5de6\u5b50\u6811\u9ad8\u5ea6<\/p>\n

\u53ea\u6709\u5b50\u6811\u9ad8\u5ea6\u53d8\u5316\u624d\u4f1a\u5f71\u54cd\u5f53\u524d\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u3002<\/p>\n

\u63d2\u5165\u8282\u70b9\u4f1a\u5f71\u54cd\u5f53\u524d\u8282\u70b9parent\u7684\u5e73\u8861\u56e0\u5b50，\u63d2\u5165\u5728\u53f3\u8fb9\u5f53\u524d\u5e73\u8861\u56e0\u5b50++，\u63d2\u5165\u5728\u5de6\u8fb9\u5f53\u524d\u5e73\u8861\u56e0\u5b50–\u3002<\/p>\n

parent\u8282\u70b9\u4f4d\u7f6e\u7684\u5e73\u8861\u56e0\u5b50\u662f\u5426\u53d1\u751f\u53d8\u5316\u4f1a\u5f71\u54cd\u662f\u5426\u9700\u8981\u5411\u4e0a\u8fdb\u884c\u66f4\u65b0\u5e73\u8861\u56e0\u5b50\u3002<\/p>\n

\u66f4\u65b0\u5e73\u8861\u56e0\u5b50\u7684\u4e09\u79cd\u60c5\u51b5：<\/span><\/p>\n

1，\u66f4\u65b0\u540eparent\u7684\u5e73\u8861\u56e0\u5b50\u503c\u4e3a0，\u8bf4\u660e\u66f4\u65b0\u524dparent\u7684\u5e73\u8861\u56e0\u5b50\u662f-1\/1<\/span>\u3002<\/p>\n

\u8868\u660e\u63d2\u5165\u524d\u5b50\u6811\u4e00\u8fb9\u9ad8\u4e00\u8fb9\u4f4e，\u800c\u65b0\u63d2\u5165\u7684\u8282\u70b9\u4f4d\u4e8e\u8f83\u4f4e\u7684\u4e00\u4fa7\u3002\u6545\u8be5\u8282\u70b9\u5b50\u6811\u9ad8\u5ea6\u6ca1\u6709\u8fdb\u884c\u53d8\u5316，\u4e0d\u5f71\u54cd\u4e0a\u5c42\u7684\u5e73\u8861\u8282\u70b9\u3002\u6545\u4e0d\u9700\u8981\u5411\u4e0a\u8fdb\u884c\u66f4\u65b0\u3002<\/p>\n<\/p>\n

2，\u66f4\u65b0\u540eparent\u7684\u5e73\u8861\u56e0\u5b50\u503c\u4e3a-1\/1，\u8bf4\u660e\u66f4\u65b0\u524dparent\u7684\u5e73\u8861\u56e0\u5b50\u662f0<\/span>\u3002<\/p>\n

\u8868\u660e\u63d2\u5165\u524d\u5b50\u6811\u662f\u5e73\u8861\u7684，\u800c\u65b0\u63d2\u5165\u4e00\u4e2a\u8282\u70b9\u5bfc\u81f4\u5b50\u6811\u4e00\u8fb9\u9ad8\u4e00\u8fb9\u4f4e\u3002\u5b50\u6811\u7684\u9ad8\u5ea6\u53d8\u5316\u4e86，\u5f71\u54cd\u4e86\u4e0a\u5c42\u7684\u5e73\u8861\u56e0\u5b50，\u9700\u8981\u5411\u4e0a\u8fdb\u884c\u66f4\u65b0\u3002<\/p>\n

\"\"<\/p>\n

3，\u66f4\u65b0\u540eparent\u7684\u5e73\u8861\u56e0\u5b50\u503c\u4e3a-2\/2，\u8bf4\u660e\u66f4\u65b0\u524dparent\u7684\u5e73\u8861\u56e0\u5b50\u662f-1\/1\u3002<\/p>\n

\u8868\u660e\u63d2\u5165\u524d\u5b50\u6811\u5c31\u662f\u4e00\u8fb9\u9ad8\u4e00\u8fb9\u4f4e，\u800c\u65b0\u63d2\u5165\u7684\u8282\u70b9\u5728\u8f83\u9ad8\u7684\u90a3\u4e00\u4fa7\u3002\u5bfc\u81f4\u9ad8\u7684\u66f4\u9ad8\u3002\u7834\u574f\u4e86AVL\u6811\u7684\u5e73\u8861\u3002\u9700\u8981\u8fdb\u884c\u65cb\u8f6c\u8c03\u6574\u3002\u65cb\u8f6c\u9700\u8981\u5b9e\u73b0\u4e24\u4e2a\u76ee\u6807：1，\u628aparent\u5b50\u6811\u65cb\u8f6c\u5e73\u8861\u30022，\u964d\u4f4eparent\u5b50\u6811\u7684\u9ad8\u5ea6，\u6062\u590d\u5230\u63d2\u5165\u8282\u70b9\u524d\u7684\u9ad8\u5ea6\u3002\u5b8c\u6210\u540e\u4e0d\u9700\u8981\u5411\u4e0a\u66f4\u65b0\u5e73\u8861\u56e0\u5b50，\u5e94\u4e3a\u5b50\u6811\u7684\u9ad8\u5ea6\u6ca1\u6709\u53d8\u5316\u3002<\/p>\n

\"\"<\/p>\n

4，\u6700\u574f\u9700\u8981\u66f4\u65b0\u5230\u6839\u8282\u70b9\u3002<\/p>\n

\u63d2\u5165\u4e2d\u66f4\u65b0\u5e73\u8861\u56e0\u5b50\u90e8\u5206：<\/p>\n

\/\/\u5904\u7406\u5e73\u8861\u56e0\u5b50
\nwhile (parent)
\n{
\nif (cur == parent->left)
\n{
\nparent->bf–;
\n}
\nelse
\n{
\nparent->bf++;
\n}
\nif (parent->bf == 0)
\n{
\nreturn true;
\n}
\nelse if (parent->bf == 1 || parent->bf == -1)\/\/\u5411\u4e0a\u8ddf\u65b0
\n{
\ncur = parent;
\nparent = parent->parent;
\n}
\nelse if (parent->bf == 2 || parent->bf == -2)\/\/\u9700\u8981\u65cb\u8f6c
\n{
\n\/\/\u53f3\u65cb
\nif (cur->bf == -1 && parent->bf == -2)
\n{
\nRotateR(parent);
\n}
\n\/\/\u5de6\u65cb
\nelse if (cur->bf == 1 && parent->bf == 2)
\n{
\nRotateL(parent);
\n}
\n\/\/\u5de6\u53f3\u65cb
\nelse if (cur->bf == 1 && parent->bf == -2)
\n{
\nRotateLR(parent);
\n}
\n\/\/\u53f3\u5de6\u65cb
\nelse if (cur->bf == -1 && parent->bf == 2)
\n{
\nRotateRL(parent);
\n}
\nelse
\n{
\nassert(false);
\n}
\nbreak; \/\/\u65cb\u8f6c\u5b8c\u540e\u8df3\u51fa
\n}
\nelse
\n{
\nassert(false);
\n}
\n}
\nreturn true;
\n} <\/p>\n

3，\u65cb\u8f6c \u2b50<\/h3>\n

\u65cb\u8f6c\u7684\u76ee\u7684：<\/p>\n

1，\u8ba9\u65cb\u8f6c\u7684\u6811\u7531\u4e0d\u5e73\u8861\u8f6c\u5411\u5e73\u8861，\u540c\u65f6\u964d\u4f4e\u65cb\u8f6c\u6811\u7684\u9ad8\u5ea6，\u4e0d\u5f71\u54cd\u4e0a\u5c42\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u3002<\/span><\/p>\n

1，\u53f3\u5355\u65cb<\/h4>\n

\u53f3\u5355\u65cb\u62bd\u8c61\u56fe：<\/p>\n

\"\"<\/p>\n

\u4e0a\u56fe\u4e2d\u768410\u53ef\u80fd\u662f\u6574\u68f5\u6811\u7684\u6839，\u4e5f\u53ef\u80fd\u662f\u4e00\u9897\u5c40\u90e8\u5b50\u6811\u7684\u6839\u3002a,b,c\u662f\u62bd\u8c61\u6210\u9ad8\u5ea6\u4e3ah（h>=0）\u7684\u5b50\u6811，\u62bd\u8c61\u7684\u597d\u5904\u5728\u4e8e：\u4e0d\u9700\u8981\u8003\u8651a\/b\/c\u5185\u90e8\u662f\u4ec0\u4e48\u7ed3\u6784\u3002<\/p>\n

\u65cb\u8f6c\u7684\u6b65\u9aa4：<\/span><\/p>\n

\u90a3\u8fb9\u9ad8\u5c31\u9700\u8981\u5c06\u6839\u8282\u70b9\u671d\u7740\u76f8\u53cd\u7684\u65b9\u5411\u6309\u4e0b\u53bb\u3002<\/p>\n

1，\u5c06parent\u63d2\u5165\u5230subL\u7684\u53f3\u5b50\u6811\u3002<\/span><\/p>\n

2，subLR\u4f5c\u4e3aparent\u7684\u53f3\u5b50\u6811<\/span><\/p>\n

3，\u5982\u679cparent\u4e4b\u524d\u53ea\u662f\u5c40\u90e8\u5b50\u6811\u7684\u6839\u8282\u70b9，\u9700\u8981\u66f4\u65b0\u66f4\u4e0a\u5c42\u8282\u70b9\u7684\u94fe\u63a5subL<\/span><\/p>\n

\u4e0b\u9762\u662fh\u4e0d\u540c\u503c\u7684\u5b9e\u9645\u56fe：<\/p>\n

\u5f53h= 0\u65f6：<\/p>\n

\"\"<\/p>\n

\u5f53h = 1\u65f6：<\/p>\n

\"\"<\/p>\n<\/p>\n

\u5f53h = 2\u65f6：<\/p>\n

\"\"<\/p>\n

\u65cb\u8f6c\u4ee3\u7801\u5b9e\u73b0：<\/p>\n

\/\/\u53f3\u65cb
\nvoid RotateR(Node* p)
\n{
\nNode* subL = p->left;
\nNode* subLR = subL->right;<\/p>\n

p->left = subLR;
\nif (subLR != nullptr)\/\/\u53ef\u80fd\u4e3a\u7a7a\u5904\u7406\u4e00\u4e0b
\nsubLR->parent = p;
\nsubL->right = p;
\nif (p == root)
\n{
\nroot = subL;
\nsubL->parent = nullptr;
\n}
\nelse
\n{
\nNode* pparent = p->parent;
\n\/\/parent\u539f\u6765\u4e0d\u662f\u6839
\nif (pparent->left == p)
\n{
\npparent->left = subL;
\n}
\nelse
\n{
\npparent->right = subL;
\n}
\nsubL->parent = pparent;
\n}
\np->parent = subL;
\np->bf = 0;
\nsubL->bf = 0;
\n} <\/p>\n

2，\u5de6\u5355\u65cb<\/h4>\n

\u5de6\u5355\u65cb\u5c31\u76f8\u5f53\u4e8e\u53f3\u65cb\u7684\u53cd\u9762，\u5341\u5206\u7c7b\u4f3c，\u4e0b\u9762\u7b80\u5355\u89e3\u91ca\u4e00\u4e0b：<\/p>\n

\u5de6\u5355\u65cb\u62bd\u8c61\u56fe：<\/p>\n

\"\"<\/p>\n

\u65cb\u8f6c\u7684\u6b65\u9aa4：<\/p>\n

1，\u5c06parent\u90e8\u5206（\u84dd\u8272）\u63d2\u5165\u5230subR\u7684\u5de6\u5b50\u6811\u5904<\/p>\n

2，subRL\u63d2\u5165\u5230parent\u7684\u53f3\u5b50\u6811\u5904<\/p>\n

3，\u5982\u679cparent\u4e4b\u524d\u53ea\u662f\u5c40\u90e8\u5b50\u6811\u7684\u6839\u8282\u70b9，\u9700\u8981\u66f4\u65b0\u66f4\u4e0a\u5c42\u8282\u70b9\u7684\u94fe\u63a5subR<\/p>\n

\u4ee3\u7801\u5b9e\u73b0：<\/p>\n

\/\/\u5de6\u65cb
\nvoid RotateL(Node* p)
\n{
\nNode* subR = p->right;
\nNode* subRL = subR->left;<\/p>\n

p->right = subRL;
\nif (subRL)
\nsubRL->parent = p;
\nsubR->left = p;
\nif (p == root)
\n{
\nroot = subR;
\nsubR->parent = nullptr;
\n}
\nelse \/\/p\u4e0d\u662f\u6839\u8282\u70b9
\n{
\nNode* pparent = p->parent;
\nif (pparent->left == p)
\n{
\npparent->left = subR;
\n}
\nelse
\n{
\npparent->right = subR;
\n}
\nsubR->parent = pparent;
\n}
\np->parent = subR;
\np->bf = subR->bf = 0;
\n} <\/p>\n

3，\u5de6\u53f3\u53cc\u65cb<\/h4>\n

\u5148\u770b\u8fd9\u6837\u4e24\u7ec4\u6848\u4f8b：<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\u5de6\u8fb9\u9ad8，\u4f46\u662f\u65b0\u63d2\u5165\u7684\u8282\u70b9\u5728b\u4f4d\u7f6e，\u4ec5\u4ec5\u8fdb\u884c\u53f3\u5355\u65cb\u662f\u4e0d\u884c\u7684，\u65cb\u8f6c\u540e\u7684\u8fd8\u662f\u4e0d\u5e73\u8861\u3002<\/p>\n

\u6b64\u65f6\u5c06\u4e0a\u9762\u7684\u573a\u666f\u62bd\u8c61\u6210\u4e0b\u9762\u7684\u7ed3\u6784\u56fe：<\/p>\n

\u6839\u636e\u63d2\u5165\u7684\u4f4d\u7f6e\u53ef\u4ee5\u5206\u6210\u4e09\u79cd\u60c5\u666f：<\/p>\n

\"\"<\/p>\n

\u8fd9\u79cd\u60c5\u51b5\u63d2\u5165\u8282\u70b9\u540e，parent\u548csubL，subLR\u7684\u5e73\u8861\u56e0\u5b50\u662f\u5f02\u53f7\u7684<\/span>\u3002\u8fd9\u662f\u548c\u53ea\u5355\u72ec\u65cb\u8f6c\u7684\u4e00\u4e2a\u8f83\u5927\u7684\u533a\u522b\u3002<\/p>\n

\u63d2\u5165\u540e\u9700\u8981\u5148\u5bf9subL\u8fdb\u884c\u5de6\u5355\u65cb，\u7136\u540e\u5bf9\u6574\u4f53parent\u8fdb\u884c\u53f3\u5355\u65cb<\/span>\u3002\u5c31\u53ef\u4ee5\u8fbe\u6210\u5e73\u8861\u3002<\/p>\n

\u5de6\u53f3\u53cc\u65cb\u4ee3\u7801:<\/p>\n

\/\/\u53cc\u65cb-\u5148\u5de6\u540e\u53f3
\nvoid RotateLR(Node* p)
\n{
\nNode* subL = p->left;
\nNode* subLR = subL->right;
\nint _bf = subLR->bf;
\nRotateL(subL);
\nRotateR(p);
\nif (_bf == -1)
\n{
\nsubL->bf = 0;
\nsubLR->bf = 0;
\np->bf = 1;
\n}
\nelse if (_bf == 1)
\n{
\nsubL->bf = -1;
\nsubLR->bf = 0;
\np->bf = 0;
\n}
\nelse if (_bf == 0)
\n{
\nsubL->bf = 0;
\nsubLR->bf = 0;
\np->bf = 0;
\n}
\nelse\/\/\u9632\u5fa1\u6027\u7f16\u7a0b，\u53ef\u4ee5\u4e0d\u5199
\n{
\nassert(false);
\n}
\n} <\/p>\n

4，\u53f3\u5de6\u53cc\u65cb<\/h4>\n

\u53f3\u5de6\u53cc\u65cb\u7684\u60c5\u51b5\u548c\u5de6\u53f3\u53cc\u65cb\u7684\u60c5\u51b5\u7c7b\u4f3c，\u4e0b\u9762\u7b80\u5355\u89e3\u91ca\u4e00\u4e0b<\/p>\n

\u76f4\u63a5\u770b\u62bd\u8c61\u7ed3\u6784\u56fe：<\/p>\n

\u6839\u636e\u63d2\u5165\u7684\u4e0d\u540c\u4f4d\u7f6e\u53ef\u4ee5\u5206\u6210\u4e09\u79cd\u573a\u666f：<\/p>\n

\"\"<\/p>\n

parent\u548csubR\u4ee5\u53casubRL\u7684\u5e73\u8861\u56e0\u5b50\u4f9d\u65e7\u662f\u5f02\u53f7\u7684\u3002<\/p>\n

\u63d2\u5165\u540e\u5148\u5bf9subR\u8fdb\u884c\u53f3\u5355\u65cb，\u518d\u5bf9parent\u8fdb\u884c\u5de6\u5355\u65cb<\/span>，\u5c31\u53ef\u4ee5\u8fbe\u5230\u5e73\u8861\u3002<\/p>\n

\u53f3\u5de6\u53cc\u65cb\u4ee3\u7801：<\/p>\n

\/\/\u53cc\u65cb-\u5148\u53f3\u540e\u5de6
\nvoid RotateRL(Node* p)
\n{
\nNode* subR = p->right;
\nNode* subRL = subR->left;
\nint _bf = subRL->bf;
\nRotateR(subR);
\nRotateL(p);
\nif (_bf == -1)
\n{
\nsubR->bf = 1;
\nsubRL->bf = 0;
\np->bf = 0;
\n}
\nelse if (_bf == 1)
\n{
\nsubR->bf = 0;
\nsubRL->bf = 0;
\np->bf = -1;
\n}
\nelse if (_bf == 0)
\n{
\nsubR->bf = 0;
\nsubRL->bf = 0;
\np->bf = 0;
\n}
\nelse\/\/\u9632\u5fa1\u6027\u7f16\u7a0b
\n{
\nassert(false);
\n}
\n} <\/p>\n

4，AVL\u6811\u7684\u67e5\u627e<\/h3>\n

\u76f4\u63a5\u4ece\u6839\u8282\u70b9\u6839\u636eAVL\u6811\u7684\u89c4\u5219\u5411\u4e0b\u8fdb\u884c\u67e5\u627e\u3002<\/p>\n

AVL\u6811\u67e5\u627e\u4ee3\u7801：<\/p>\n

\/\/\u67e5\u627e
\nNode* Find(const K& k)
\n{
\nNode* cur = root;
\nwhile (cur)
\n{
\nif (k > cur->kv.first)
\n{
\ncur = cur->right;
\n}
\nelse if (k < cur->kv.first)
\n{
\ncur = cur->left;
\n}
\nelse \/\/\u627e\u5230\u4e86
\n{
\nreturn cur;
\n}
\n}
\nreturn nullptr;
\n} <\/p>\n

5，\u5224\u65ad\u662f\u5426\u662fAVL\u6811<\/h3>\n

1，\u5de6\u53f3\u9ad8\u5ea6\u5dee\u4e0d\u8d85\u8fc71，\u540c\u65f6\u5de6\u53f3\u90fd\u662fAVL\u6811<\/p>\n

\/\/\u5224\u65ad\u662f\u5426\u662f\u4e00\u9897AVL\u6811
\nbool _IsAVLTree(Node* root)
\n{
\n\/\/\u7a7a\u6811\u4e5f\u662f\u4e00\u4e2aAVL\u6811
\nif (root == nullptr)
\nreturn true;
\nint leftHeight = _Height(root->left);
\nint rightHeight = _Height(root->right);
\nint d = rightHeight – leftHeight;
\nif (abs(d) >= 2)
\n{
\ncout << "\u9ad8\u5ea6\u5dee\u5f02\u5e38" << endl;
\nreturn false;
\n}
\nif (d != root->bf)\/\/\u5e73\u8861\u56e0\u5b50\u548c\u9ad8\u5ea6\u5dee\u5bf9\u4e0d\u4e0a
\n{
\ncout << "\u5e73\u8861\u56e0\u5b50\u5f02\u5e38" << endl;
\nreturn false;
\n}
\n\/\/\u4fdd\u8bc1\u5de6\u53f3\u5b50\u6811\u90fd\u662fAVL\u6811
\nreturn _IsAVLTree(root->left) && _IsAVLTree(root->right);
\n} <\/p>\n

\u6d4b\u8bd5\u7ed3\u6784\u6392\u5e8f\u4ee3\u7801：<\/p>\n

\"\"<\/p>\n

\u6d4b\u8bd5\u6027\u80fd：<\/p>\n

\/\/ \u63d2\u5165\u4e00\u5806\u968f\u673a\u503c，\u6d4b\u8bd5\u5e73\u8861，\u987a\u4fbf\u6d4b\u8bd5\u4e00\u4e0b\u9ad8\u5ea6\u548c\u6027\u80fd\u7b49
\nvoid TestAVLTree2()
\n{
\nconst int N = 1000000;
\nvector<int> v;
\nv.reserve(N);
\nsrand(time(0));
\nfor (size_t i = 0; i < N; i++)
\n{
\nv.push_back(rand() + i);
\n}
\n\/\/\u63d2\u5165
\nsize_t begin2 = clock();
\nAVLTree<int, int> t;
\nfor (auto e : v)
\n{
\nt.Insert(make_pair(e, e));
\n}
\nsize_t end2 = clock();<\/p>\n

cout << "Insert:" << end2 – begin2 << endl;
\ncout << t.IsAVLTree() << endl;<\/p>\n

cout << "Height:" << t.Height() << endl;
\ncout << "Size:" << t.Size() << endl;<\/p>\n

size_t begin1 = clock();
\n\/\/ \u786e\u5b9a\u5728\u7684\u503c
\nfor (auto e : v)
\n{
\nt.Find(e);
\n}
\nsize_t end1 = clock();
\ncout << "Find:" << end1 – begin1 << endl;
\n}
\nint main()
\n{
\nTestAVLTree2();
\nreturn 0;
\n} <\/p>\n

\u6d4b\u8bd5\u7ed3\u679c：<\/p>\n

\"\"<\/p>\n

\n

\u00a0\u00a0\u00a0\u00a0\u7ed3\u5c3e<\/h2>\n

\u672c\u7bc7\u6587\u7ae0\u4e2d\u6240\u6d89\u53ca\u5230\u7684\u4ee3\u7801：<\/p>\n

gitee\u94fe\u63a5：AVL\u6811\u7684\u5b9e\u73b0<\/p>\n

\u4ee5\u4e0a\u5c31\u662f\u672c\u6587\u7684\u5168\u90e8\u5185\u5bb9\u4e86，\u5982\u679c\u5bf9\u4f60\u6709\u6240\u5e2e\u52a9\u7684\u8bdd，\u8bf7\u5927\u4f6c\u4e0d\u59a8\u7ed9\u535a\u4e3b\u6765\u4e2a\u201c\u4e00\u952e\u4e09\u8fde<\/span>\u201d，\u8fd9\u5bf9\u6211\u662f\u5927\u5927\u7684\u652f\u6301，\u4e5f\u80fd\u8ba9\u535a\u4e3b\u4ea7\u51fa\u66f4\u4f18\u8d28\u7684\u5185\u5bb9\u3002<\/p>\n

\u5f80\u671f\u56de\u987e：<\/p>\n

\u3010C++\u3011\u300a\u624b\u6495\u4e8c\u53c9\u641c\u7d22\u6811：\u5220\u9664\u624d\u662f\u771f\u6b63\u7684\u5206\u6c34\u5cad\u300b<\/span><\/p>\n

\u3010C++\u3011map \u4e0e set \u7684\u5173\u8054\u5f0f\u5bb9\u5668\u5b9e\u8df5<\/p>\n

\u603b\u7ed3：\u672c\u6587\u7cfb\u7edf\u8bb2\u89e3\u4e86AVL\u6811\u7684\u539f\u7406\u4e0e\u6a21\u62df\u5b9e\u73b0，\u6db5\u76d6\u8282\u70b9\u7ed3\u6784\u3001\u63d2\u5165\u64cd\u4f5c\u3001\u5e73\u8861\u56e0\u5b50\u66f4\u65b0\u53ca\u56db\u79cd\u65cb\u8f6c\u673a\u5236（\u53f3\u5355\u65cb\u3001\u5de6\u5355\u65cb\u3001\u5de6\u53f3\u53cc\u65cb\u3001\u53f3\u5de6\u53cc\u65cb），\u786e\u4fdd\u6811\u59cb\u7ec8\u4fdd\u6301\u5e73\u8861\u3002\u901a\u8fc7\u63d2\u5165\u540e\u81ea\u4e0a\u800c\u4e0b\u7684\u5e73\u8861\u56e0\u5b50\u8c03\u6574\u4e0e\u65cb\u8f6c，\u4fdd\u969c\u589e\u5220\u67e5\u6548\u7387\u7a33\u5b9a\u5728O(logN)\u3002\u6587\u7ae0\u8fd8\u5b9e\u73b0\u4e86\u67e5\u627e\u3001\u5224\u65ad\u662f\u5426\u4e3aAVL\u6811\u7b49\u529f\u80fd，\u5e76\u901a\u8fc7\u6027\u80fd\u6d4b\u8bd5\u9a8c\u8bc1\u5176\u9ad8\u6548\u6027，\u9002\u5408\u6df1\u5165\u7406\u89e3\u81ea\u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u5b9e\u73b0\u903b\u8f91\u3002<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u26a1\u628a\u4e0a\u9762\u7684\u5185\u5bb9\u5403\u900f\u5c31\u4f11\u606f\u4e00\u4e0b\u5427\u26a1<\/p>\n<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0\"\"<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"

🏆\u6d6e\u4e16\u5c18\u5f26：\u4e2a\u4eba\u4e3b\u9875 \u2b50\u4e2a\u4eba\u4e13\u680f：\u300aC\u8bed\u8a00\u300b\u3001\u300a\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u300b\u3001\u300aC\u300b 💎：\u975e\u6de1\u8584\u65e0\u4ee5\u660e\u5fd7，\u975e\u5b81\u9759\u65e0\u4ee5\u81f4\u8fdc \u524d\u8a00 \u666e\u901a\u4e8c\u53c9\u641c\u7d22\u6811\u5728\u6570\u636e\u63a5\u8fd1\u6709\u5e8f\u65f6\u5bb9\u6613\u9000\u5316\u6210\u94fe\u8868，\u67e5\u627e\u6548\u7387\u4f1a\u4ece O(log n) \u964d\u5230 O(n)\u3002\u800cAVL\u6811\u901a\u8fc7\u63a7\u5236\u6bcf\u4e2a\u8282\u70b9\u5de6\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee，\u8ba9\u6811\u5728\u63d2\u5165\u540e\u59cb\u7ec8\u4fdd\u6301\u76f8\u5bf9\u5e73\u8861\u3002 \u672c\u6587\u5148\u7528 C \u8ba4\u8bc6 AVL \u6811\u53ca\u5176\u8282\u70b9\u7ed3\u6784，\u518d\u5b8c\u6574\u6a21\u62df\u4e00\u6b21\u63d2\u5165&<\/p>\n","protected":false},"author":2,"featured_media":118067,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[427],"topic":[],"class_list":["post-118084","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-427"],"yoast_head":"\n\u3010C++\u3011\u4e00\u6b21\u63d2\u5165\uff0c\u56db\u573a\u65cb\u8f6c\uff1aC++ AVL \u6811\u7684\u81ea\u5e73\u8861\u4e4b\u8def - \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\/118084.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u3010C++\u3011\u4e00\u6b21\u63d2\u5165\uff0c\u56db\u573a\u65cb\u8f6c\uff1aC++ AVL \u6811\u7684\u81ea\u5e73\u8861\u4e4b\u8def - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"🏆\u6d6e\u4e16\u5c18\u5f26：\u4e2a\u4eba\u4e3b\u9875 \u2b50\u4e2a\u4eba\u4e13\u680f：\u300aC\u8bed\u8a00\u300b\u3001\u300a\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u300b\u3001\u300aC\u300b 💎：\u975e\u6de1\u8584\u65e0\u4ee5\u660e\u5fd7，\u975e\u5b81\u9759\u65e0\u4ee5\u81f4\u8fdc \u524d\u8a00 \u666e\u901a\u4e8c\u53c9\u641c\u7d22\u6811\u5728\u6570\u636e\u63a5\u8fd1\u6709\u5e8f\u65f6\u5bb9\u6613\u9000\u5316\u6210\u94fe\u8868，\u67e5\u627e\u6548\u7387\u4f1a\u4ece O(log n) \u964d\u5230 O(n)\u3002\u800cAVL\u6811\u901a\u8fc7\u63a7\u5236\u6bcf\u4e2a\u8282\u70b9\u5de6\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee，\u8ba9\u6811\u5728\u63d2\u5165\u540e\u59cb\u7ec8\u4fdd\u6301\u76f8\u5bf9\u5e73\u8861\u3002 \u672c\u6587\u5148\u7528 C \u8ba4\u8bc6 AVL \u6811\u53ca\u5176\u8282\u70b9\u7ed3\u6784，\u518d\u5b8c\u6574\u6a21\u62df\u4e00\u6b21\u63d2\u5165&\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/118084.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-10-25T22:18:25+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261025221817-6ade80292c154.png\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/118084.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/118084.html\",\"name\":\"\u3010C++\u3011\u4e00\u6b21\u63d2\u5165\uff0c\u56db\u573a\u65cb\u8f6c\uff1aC++ AVL \u6811\u7684\u81ea\u5e73\u8861\u4e4b\u8def - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2026-10-25T22:18:25+00:00\",\"dateModified\":\"2026-10-25T22:18:25+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/118084.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/118084.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/118084.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u3010C++\u3011\u4e00\u6b21\u63d2\u5165\uff0c\u56db\u573a\u65cb\u8f6c\uff1aC++ AVL \u6811\u7684\u81ea\u5e73\u8861\u4e4b\u8def\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u3010C++\u3011\u4e00\u6b21\u63d2\u5165\uff0c\u56db\u573a\u65cb\u8f6c\uff1aC++ AVL \u6811\u7684\u81ea\u5e73\u8861\u4e4b\u8def - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/118084.html","og_locale":"zh_CN","og_type":"article","og_title":"\u3010C++\u3011\u4e00\u6b21\u63d2\u5165\uff0c\u56db\u573a\u65cb\u8f6c\uff1aC++ AVL \u6811\u7684\u81ea\u5e73\u8861\u4e4b\u8def - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"🏆\u6d6e\u4e16\u5c18\u5f26：\u4e2a\u4eba\u4e3b\u9875 \u2b50\u4e2a\u4eba\u4e13\u680f：\u300aC\u8bed\u8a00\u300b\u3001\u300a\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u300b\u3001\u300aC\u300b 💎：\u975e\u6de1\u8584\u65e0\u4ee5\u660e\u5fd7，\u975e\u5b81\u9759\u65e0\u4ee5\u81f4\u8fdc \u524d\u8a00 \u666e\u901a\u4e8c\u53c9\u641c\u7d22\u6811\u5728\u6570\u636e\u63a5\u8fd1\u6709\u5e8f\u65f6\u5bb9\u6613\u9000\u5316\u6210\u94fe\u8868，\u67e5\u627e\u6548\u7387\u4f1a\u4ece O(log n) \u964d\u5230 O(n)\u3002\u800cAVL\u6811\u901a\u8fc7\u63a7\u5236\u6bcf\u4e2a\u8282\u70b9\u5de6\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee，\u8ba9\u6811\u5728\u63d2\u5165\u540e\u59cb\u7ec8\u4fdd\u6301\u76f8\u5bf9\u5e73\u8861\u3002 \u672c\u6587\u5148\u7528 C \u8ba4\u8bc6 AVL \u6811\u53ca\u5176\u8282\u70b9\u7ed3\u6784，\u518d\u5b8c\u6574\u6a21\u62df\u4e00\u6b21\u63d2\u5165&","og_url":"https:\/\/www.wsisp.com\/helps\/118084.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2026-10-25T22:18:25+00:00","og_image":[{"url":"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261025221817-6ade80292c154.png"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"6 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/118084.html","url":"https:\/\/www.wsisp.com\/helps\/118084.html","name":"\u3010C++\u3011\u4e00\u6b21\u63d2\u5165\uff0c\u56db\u573a\u65cb\u8f6c\uff1aC++ AVL \u6811\u7684\u81ea\u5e73\u8861\u4e4b\u8def - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2026-10-25T22:18:25+00:00","dateModified":"2026-10-25T22:18:25+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/118084.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/118084.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/118084.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"\u3010C++\u3011\u4e00\u6b21\u63d2\u5165\uff0c\u56db\u573a\u65cb\u8f6c\uff1aC++ AVL \u6811\u7684\u81ea\u5e73\u8861\u4e4b\u8def"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/118084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=118084"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/118084\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media\/118067"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=118084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=118084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=118084"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=118084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}