{"id":120976,"date":"2026-11-01T21:57:06","date_gmt":"2026-11-01T13:57:06","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/120976.html"},"modified":"2026-11-01T21:57:06","modified_gmt":"2026-11-01T13:57:06","slug":"%e3%80%90c%e3%80%91avl-%e6%a0%91","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/120976.html","title":{"rendered":"\u3010C++\u3011AVL \u6811"},"content":{"rendered":"

\u76ee\u5f55<\/p>\n

1. AVL\u7684\u6982\u5ff5\u200b\u7f16\u8f91<\/p>\n

2. AVL \u6811\u7684\u5b9e\u73b0<\/p>\n

2.1 AVL \u6811\u7684\u7ed3\u6784<\/p>\n

2.2 AVL \u6811\u7684\u63d2\u5165<\/p>\n

2.3 \u65cb\u8f6c<\/p>\n

2.4 AVL \u6811\u7684\u67e5\u627e<\/p>\n

2.5 AVL \u6811\u7684\u5e73\u8861\u68c0\u67e5<\/p>\n

2.6 AVL\u6811\u7684\u5220\u9664<\/p>\n

\n

1. AVL\u7684\u6982\u5ff5<\/span>\"\"<\/h2>\n

AVL \u6811\u7531\u524d\u82cf\u8054\u6570\u5b66\u5bb6 G.M. Adelson-Velsky（\u963f\u5fb7\u5c14\u68ee – \u97e6\u5c14\u65af\u57fa） \u548c E.M. Landis（\u5170\u8fea\u65af） \u5728 1962 \u5e74\u63d0\u51fa\u5e76\u53d1\u8868\u8bba\u6587，\u5b83\u4e5f\u662f\u4e16\u754c\u4e0a\u7b2c\u4e00\u4e2a\u81ea\u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811\u3002<\/p>\n

AVL \u548c\u666e\u901a\u4e8c\u53c9\u641c\u7d22\u6811（BST）\u6700\u5927\u533a\u522b<\/p>\n

AVL \u672c\u8d28\u4e0a\u4f9d\u7136\u662f\u4e00\u68f5\u4e8c\u53c9\u641c\u7d22\u6811，\u4fdd\u7559 BST \u7684\u6709\u5e8f\u6027\u8d28；\u989d\u5916\u589e\u52a0\u4e00\u6761\u5e73\u8861\u7ea6\u675f：\u6811\u4e2d\u4efb\u610f\u8282\u70b9，\u5de6\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc7 1（\u5e73\u8861\u56e0\u5b50 \u2208 {-1,0,1}）\u3002\u4e00\u65e6\u63d2\u5165\u3001\u5220\u9664\u9020\u6210\u5931\u8861，\u4f1a\u901a\u8fc7\u65cb\u8f6c\u81ea\u52a8\u8c03\u6574\u7ed3\u6784\u3001\u6062\u590d\u5e73\u8861；\u666e\u901a BST \u6ca1\u6709\u8fd9\u4e2a\u81ea\u52a8\u5e73\u8861\u673a\u5236，\u6811\u5f62\u6001\u5b8c\u5168\u7531\u63d2\u5165\u987a\u5e8f\u51b3\u5b9a\u3002<\/p>\n

AVL \u6811\u8fdb\u6b65\u7684\u5730\u65b9<\/p>\n

  • \u64cd\u4f5c\u590d\u6742\u5ea6\u7a33\u5b9a：\u67e5\u627e\u3001\u63d2\u5165\u3001\u5220\u9664\u6700\u574f\u65f6\u95f4\u590d\u6742\u5ea6\u7a33\u5b9a \\\\(O(\\\\log n)\\\\)，\u4e0d\u4f1a\u9000\u5316\u6210\u94fe\u8868，\u6d88\u9664\u4e86 BST \u6700\u574f \\\\(O(n)\\\\) \u7684\u98ce\u9669\u3002<\/li>\n
  • \u6811\u9ad8\u88ab\u4e25\u683c\u9650\u5236，\u6811\u66f4 \u201c\u77ee\u201d，\u67e5\u627e\u901f\u5ea6\u5f88\u5feb，\u9002\u5408\u8bfb\u591a\u5199\u5c11\u7684\u573a\u666f\u3002<\/li>\n
  • \u81ea\u5e73\u8861\u673a\u5236：\u589e\u5220\u540e\u81ea\u52a8\u65cb\u8f6c\u4fee\u590d\u5e73\u8861，\u4e0d\u9700\u8981\u4eba\u5de5\u91cd\u6784\u6574\u68f5\u6811\u3002<\/li>\n

    AVL \u6811\u7684\u7f3a\u70b9<\/p>\n

  • \u5e73\u8861\u6761\u4ef6\u5f88\u4e25\u683c，\u63d2\u5165\u3001\u5220\u9664\u5f88\u5bb9\u6613\u89e6\u53d1\u65cb\u8f6c，\u5c24\u5176\u662f\u5220\u9664\u64cd\u4f5c，\u53ef\u80fd\u9700\u8981\u6cbf\u7740\u8def\u5f84\u5411\u4e0a\u591a\u6b21\u65cb\u8f6c，\u8c03\u6574\u5f00\u9500\u5927\u3001\u5199\u64cd\u4f5c\u4ee3\u4ef7\u9ad8\u3002<\/li>\n
  • \u6bcf\u4e2a\u8282\u70b9\u9700\u8981\u989d\u5916\u8bb0\u5f55\u5b50\u6811\u9ad8\u5ea6（\u6216\u8005\u5e73\u8861\u56e0\u5b50），\u5360\u7528\u989d\u5916\u5b58\u50a8\u7a7a\u95f4\u3002<\/li>\n
  • \u65cb\u8f6c\u903b\u8f91\u591a（LL\u3001RR\u3001LR\u3001RL \u56db\u79cd\u60c5\u51b5），\u4ee3\u7801\u5b9e\u73b0\u3001\u8c03\u8bd5\u66f4\u590d\u6742\u3002<\/li>\n
  • \u5199\u5bc6\u96c6\u573a\u666f\u4e0d\u5982\u7ea2\u9ed1\u6811\u5408\u9002，\u6240\u4ee5\u5de5\u7a0b\u91cc C++ map \u7b49\u5bb9\u5668\u5e95\u5c42\u9009\u7528\u7ea2\u9ed1\u6811\u800c\u4e0d\u662f AVL\u3002<\/li>\n

    2. AVL \u6811\u7684\u5b9e\u73b0<\/h2>\n

    2.1 AVL \u6811\u7684\u7ed3\u6784<\/h3>\n

    using namespace std;
    \ntemplate<class T>
    \nstruct AVLTreeNode
    \n{
    \nAVLTreeNode(const T& data = T())
    \n: _pLeft(nullptr)
    \n, _pRight(nullptr)
    \n, _pParent(nullptr)
    \n, _data(data)
    \n, _bf(0)
    \n{
    \n}<\/p>\n

    AVLTreeNode<T>* _pLeft;
    \nAVLTreeNode<T>* _pRight;
    \nAVLTreeNode<T>* _pParent;
    \nT _data;
    \nint _bf; \/\/ \u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50
    \n};<\/p>\n

    \/\/ \u5de6\u52a0 \u53f3\u51cf
    \n\/\/ AVL: \u4e8c\u53c9\u641c\u7d22\u6811 + \u5e73\u8861\u56e0\u5b50\u7684\u9650\u5236
    \ntemplate<class T>
    \nclass AVLTree
    \n{
    \ntypedef AVLTreeNode<T> Node;
    \npublic:
    \n\/\/ \u521d\u59cb\u9ed8\u8ba4\u6784\u9020
    \nAVLTree()
    \n: _pRoot(nullptr)
    \n{<\/p>\n

    }<\/p>\n

    private:
    \nNode* _pRoot;
    \n}; <\/p>\n

    2.2 AVL \u6811\u7684\u63d2\u5165<\/h3>\n

    2.2.1 AVL \u63d2\u5165\u7684\u5927\u6982\u8fc7\u7a0b<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5411 AVL \u6811\u63d2\u5165\u8282\u70b9\u65f6，\u9996\u5148\u6309\u7167\u666e\u901a\u4e8c\u53c9\u641c\u7d22\u6811\u89c4\u5219\u627e\u5230\u7a7a\u4f4d\u63d2\u5165\u65b0\u8282\u70b9\u3002\u63d2\u5165\u5b8c\u6210\u540e，\u4ece\u65b0\u8282\u70b9\u5411\u4e0a\u56de\u6eaf，\u4f9d\u6b21\u66f4\u65b0\u6cbf\u9014\u6bcf\u4e2a\u7956\u5148\u8282\u70b9\u7684\u9ad8\u5ea6，\u8ba1\u7b97\u5e73\u8861\u56e0\u5b50\u3002<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u82e5\u6240\u6709\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u7edd\u5bf9\u503c\u90fd\u4e0d\u5927\u4e8e 1，\u6811\u4fdd\u6301\u5e73\u8861，\u63d2\u5165\u7ed3\u675f\u3002<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5982\u679c\u67d0\u4e2a\u8282\u70b9\u5e73\u8861\u56e0\u5b50\u8d85\u51fa\u8303\u56f4，\u8bf4\u660e\u53d1\u751f\u5931\u8861，\u9700\u8981\u5224\u65ad\u5931\u8861\u7c7b\u578b：LL\u3001RR\u3001LR\u3001RL，\u5bf9\u5e94\u6267\u884c\u5355\u65cb\u8f6c\u6216\u8005\u53cc\u65cb\u8f6c\u8c03\u6574\u7ed3\u6784，\u8ba9\u8be5\u5b50\u6811\u6062\u590d\u5e73\u8861\u3002\u65cb\u8f6c\u5b8c\u6210\u540e，\u7ee7\u7eed\u5411\u4e0a\u68c0\u67e5\u4e0a\u5c42\u8282\u70b9\u662f\u5426\u5931\u8861，\u76f4\u5230\u6839\u8282\u70b9\u3002AVL \u4f9d\u9760\u65cb\u8f6c\u4fdd\u8bc1\u4efb\u610f\u8282\u70b9\u5de6\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u4e0d\u8d85\u8fc7 1，\u7ef4\u6301\u6811\u9ad8\u4e3a\u5bf9\u6570\u7ea7\u522b，\u4fdd\u8bc1\u67e5\u627e\u6548\u7387\u7a33\u5b9a\u3002<\/p>\n

    2.2.2 \u5e73\u8861\u56e0\u5b50\u7684\u66f4\u65b0<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 \u2212 \u53f3\u5b50\u6811\u9ad8\u5ea6\u3002 \u63d2\u5165\u65b0\u8282\u70b9\u540e，\u4ece\u65b0\u8282\u70b9\u7684\u7236\u8282\u70b9\u5f00\u59cb\u5f80\u6839\u65b9\u5411\u56de\u6eaf：\u5148\u66f4\u65b0\u5f53\u524d\u8282\u70b9\u7684\u9ad8\u5ea6，\u518d\u91cd\u65b0\u8ba1\u7b97\u5b83\u7684\u5e73\u8861\u56e0\u5b50\u3002<\/p>\n

      \n
    • \u5e73\u8861\u56e0\u5b50\u7edd\u5bf9\u503c\u22641：\u8be5\u8282\u70b9\u5e73\u8861，\u7ee7\u7eed\u5411\u4e0a\u68c0\u67e5\u7956\u5148；<\/li>\n
    • \u5e73\u8861\u56e0\u5b50\u7edd\u5bf9\u503c＞1：\u8282\u70b9\u5931\u8861，\u8fdb\u884c\u65cb\u8f6c\u8c03\u6574；\u65cb\u8f6c\u5b8c\u6210\u540e，\u66f4\u65b0\u65cb\u8f6c\u6d89\u53ca\u8282\u70b9\u7684\u9ad8\u5ea6\u4e0e\u5e73\u8861\u56e0\u5b50，\u518d\u7ee7\u7eed\u5411\u4e0a\u5224\u65ad\u4e0a\u5c42\u8282\u70b9\u3002 \u5220\u9664\u8282\u70b9\u65f6\u53d8\u5316\u66f4\u5927，\u5220\u9664\u53ef\u80fd\u8ba9\u7956\u5148\u9ad8\u5ea6\u6301\u7eed\u53d8\u5316，\u9700\u8981\u4e00\u8def\u5411\u4e0a\u66f4\u65b0\u9ad8\u5ea6\u3001\u91cd\u7b97\u5e73\u8861\u56e0\u5b50，\u591a\u6b21\u89e6\u53d1\u8c03\u6574\u3002<\/li>\n<\/ul>\n

      size_t _Height(Node* pRoot)
      \n{
      \nif (pRoot == nullptr)
      \n{
      \nreturn 0;
      \n}
      \n\/\/ max \u627e\u51fa\u4e24\u6570\u6700\u5927\u6570\u503c
      \nsize_t left = _Height(pRoot->_pLeft);
      \nsize_t right = _Height(pRoot->_pRight);
      \nreturn max(left,right) + 1;
      \n}
      \n\/\/ Bf \u8c03\u6574
      \nvoid Bf(Node* root)
      \n{
      \nif (root == nullptr)
      \nreturn;
      \nint left = root->_pLeft ? _Height(root->_pLeft) : 0;
      \nint right = root->_pRight ? _Height(root->_pRight) : 0;
      \nroot->_bf = left – right;
      \n} <\/p>\n

      2.2.2 \u63d2\u5165\u8282\u70b9\u7684\u66f4\u65b0\u5e73\u8861\u97f3\u7cfb\u7684\u4ee3\u7801\u5b9e\u73b0<\/p>\n

      \/\/ \u5728AVL\u6811\u4e2d\u63d2\u5165\u503c\u4e3adata\u7684\u8282\u70b9
      \nbool Insert(const T& data)
      \n{
      \nif (_pRoot == nullptr)
      \n{
      \n_pRoot = new Node(data);
      \nreturn true;
      \n}
      \nelse
      \n{
      \nNode* dest = _pRoot, *cur = nullptr;
      \nwhile (dest)
      \n{
      \nif (data < dest->_data)
      \n{
      \ncur = dest;
      \ndest = dest->_pLeft;
      \n}
      \nelse if (dest->_data < data)
      \n{
      \ncur = dest;
      \ndest = dest->_pRight;
      \n}
      \nelse
      \n{
      \nreturn false;
      \n}
      \n}
      \ndest = new Node(data);
      \nif (data < cur->_data)
      \n{
      \ncur->_pLeft = dest;
      \n}
      \nelse if (cur->_data < data)
      \n{
      \ncur->_pRight = dest;
      \n}
      \ndest->_pParent = cur;
      \n\/\/ \u5411\u4e0a\u8c03\u6574\u5e73\u8861\u6570
      \nBf(cur);
      \nwhile (cur != nullptr && abs(cur->_bf) < 2)
      \n{
      \ncur = cur->_pParent;
      \nBf(cur);
      \n}
      \n\/\/ \u5982\u679c\u6ca1\u6709\u95ee\u9898\u76f4\u63a5\u9000\u51fa\u6709\u5e73\u8861\u5931\u8861\u7684\u60c5\u51b5\u5c31\u8fdb\u884c\u65cb\u8f6c
      \n if (cur == nullptr)
      \nreturn true;
      \nelse if (cur->_bf == 2)
      \n{
      \nif (cur->_pLeft->_bf == 1)
      \n{
      \nRotateR(cur);
      \n}
      \nelse if(cur->_pLeft->_bf == -1)
      \n{
      \nRotateLR(cur);
      \n}
      \n}
      \nelse if (cur->_bf == -2)
      \n{
      \nif (cur->_pRight->_bf == 1)
      \n{
      \nRotateRL(cur);
      \n}
      \nelse if (cur->_pRight->_bf == -1)
      \n{
      \nRotateL(cur);
      \n}
      \n}
      \nelse
      \n{
      \nassert(false);
      \n}
      \nreturn true;
      \n}<\/p>\n

      } <\/p>\n

      2.3 \u65cb\u8f6c<\/h3>\n

      2.3.1 \u65cb\u8f6c\u7684\u539f\u5219<\/p>\n

      \u65cb\u8f6c\u6838\u5fc3\u539f\u5219：\u4e0d\u7834\u574f\u4e8c\u53c9\u641c\u7d22\u6811\u6709\u5e8f\u6027，\u540c\u65f6\u4fee\u6b63\u5931\u8861，\u8c03\u6574\u5b50\u6811\u9ad8\u5ea6\u3001\u66f4\u65b0\u5e73\u8861\u56e0\u5b50\u3002<\/p>\n

    • \u4fdd\u6301 BST \u6027\u8d28：\u65cb\u8f6c\u540e\u4f9d\u65e7\u6ee1\u8db3\u5de6\u5b50\u6811\u503c < \u6839 < \u53f3\u5b50\u6811\u503c，\u4e2d\u5e8f\u904d\u5386\u7ed3\u679c\u4e0d\u53d8\u3002<\/li>\n
    • \u8f6c\u79fb\u5b50\u6811：\u65cb\u8f6c\u65f6\u628a\u4e2d\u95f4\u90a3\u68f5\u5b50\u6811（\u88ab\u6324\u51fa\u6765\u7684\u5b50\u6811）\u63a5\u5230\u5408\u9002\u4f4d\u7f6e，\u907f\u514d\u4e22\u5931\u8282\u70b9\u3002<\/li>\n
    • \u4f18\u5148\u5904\u7406\u6700\u6df1\u5931\u8861\u8282\u70b9：\u4ece\u4e0b\u5f80\u4e0a\u627e\u5230\u7b2c\u4e00\u4e2a\u5931\u8861\u8282\u70b9，\u4ee5\u5b83\u4e3a\u65cb\u8f6c\u4e2d\u5fc3\u8c03\u6574\u3002<\/li>\n
    • \u65cb\u8f6c\u5b8c\u6210\u540e，\u53ca\u65f6\u66f4\u65b0\u88ab\u6539\u52a8\u8282\u70b9\u7684\u9ad8\u5ea6\u548c\u5e73\u8861\u56e0\u5b50，\u518d\u7ee7\u7eed\u5411\u4e0a\u6821\u9a8c\u3002<\/li>\n
    • \u65cb\u8f6c\u53ea\u6539\u53d8\u6307\u9488\u5173\u7cfb，\u4e0d\u6539\u53d8\u8282\u70b9\u76f8\u5bf9\u5927\u5c0f；\u5355\u65cb\u5904\u7406 LL\u3001RR，\u53cc\u65cb\u5904\u7406 LR\u3001RL\u3002<\/li>\n

      2.3.2 \u53f3\u5355\u65cb<\/p>\n

      \"\"<\/p>\n

      \/\/ \u8003\u8651\u95ee\u9898:
      \n\/\/ 1,\u662f\u5426\u6709 Chlid \u7684 \u5de6\u53f3\u8282\u70b9\u662f\u5426\u4e3a\u7a7a(\u4f46\u5176\u5b9e\u53f3\u65cb\u65f6\u5c31R \u53ef\u80fd\u5c31\u662f\u4e3a\u7a7a\u51fa\u73b0\u7684\u53ef\u80fd\u6bd4\u8f83\u5c0f,\u51fa\u73b0\u7684\u8bdd\u5c31\u5df2\u7ecf\u88ab\u5224\u65ad\u9700\u8981\u53cc\u65cb\u4e86)
      \n\/\/ 2,\u8003\u8651\u662f\u5426\u6709 GrandParent \u6709\u9700\u8981\u8fdb\u884c\u4e24\u7ebf\u5bf9\u63a5，\u6ca1\u6709\u5c31\u9700\u8981\u8fdb\u884c\u63d0\u4e0a\u6765\u7684 Child \u7684 Parent \u4e3a\u7a7a
      \n\/\/ \u53f3\u5355\u65cb
      \nvoid RotateR(Node* pParent)
      \n{ \/\/ G G
      \n\/\/ P C
      \n\/\/ C -> L P
      \n\/\/ L R R
      \n\/\/
      \n\/\/ pParent -> P
      \n\/\/
      \n\/\/ \u6700\u6709\u53ef\u80fd\u53d1\u751f_pRoot \u4f4d\u7f6e\u5c31\u662f P \u548c G ，\u5176\u4e2d G \u6539\u53d8\u53ea\u662f\u5176\u4e2d\u4e2a\u522b\u4f4d\u7f6e，\u5bf9_pRoot \u6ca1\u6709\u5f71\u54cd\u4e0b
      \n\/\/ \u5176\u4e2d\u8981\u5173\u6ce8\u5c31\u662f _pRoot \u7684 P \u4f4d\u7f6e \u548c C \u4f4d\u7f6e<\/p>\n

      Node* Child = pParent->_pLeft;\/\/C
      \nNode* Parent = pParent;\/\/P
      \nNode* GrandParent = pParent->_pParent;\/\/G<\/p>\n

      \/\/ 4 \u6bb5\u4ee3\u7801\u7ef4\u62a4
      \n\/\/ P->C = P->R
      \nParent->_pLeft = Child->_pRight;
      \n\/\/ R->P = R->P
      \nif (Child->_pRight != nullptr)
      \n{
      \nChild->_pRight->_pParent = Parent;
      \n}
      \n\/\/ C->R = C->P
      \nChild->_pRight = Parent;
      \n\/\/ P->G = P->C
      \nParent->_pParent = Child;
      \n\/\/ G->P = G->C
      \nif (GrandParent != nullptr)
      \n{
      \nGrandParent->_pLeft == Parent ? GrandParent->_pLeft = Child : GrandParent->_pRight = Child;
      \n\/\/ C->P = C->G
      \nChild->_pParent = GrandParent;
      \n}
      \nelse
      \n{
      \n\/\/ C->P = C->nullptr
      \nChild->_pParent = nullptr;
      \n_pRoot = Child;
      \n}
      \n\/\/ \u8c03\u6574\u5e73\u8861
      \nBf(Parent);
      \nBf(Child);
      \n}<\/p>\n

      2.3.3 \u5de6\u5355\u65cb<\/p>\n

      \"\"<\/p>\n

      \/\/ \u5de6\u5355\u65cb
      \nvoid RotateL(Node* pParent)
      \n{ \/\/ G G
      \n\/\/ P C
      \n\/\/ C -> P R
      \n\/\/ L R L
      \n\/\/ pParent -> P
      \n\/\/ \u6700\u6709\u53ef\u80fd\u53d1\u751f_pRoot \u4f4d\u7f6e\u5c31\u662f P \u548c G ，\u5176\u4e2d G \u6539\u53d8\u53ea\u662f\u5176\u4e2d\u4e2a\u522b\u4f4d\u7f6e，\u5bf9_pRoot \u6ca1\u6709\u5f71\u54cd\u4e0b
      \n\/\/ \u5176\u4e2d\u8981\u5173\u6ce8\u5c31\u662f _pRoot \u7684 P \u4f4d\u7f6e \u548c C \u4f4d\u7f6e
      \n\/\/ 4 \u6bb5\u4ee3\u7801\u7ef4\u62a4
      \n\/\/ P->C = P->L<\/p>\n

      Node* Child = pParent->_pRight;\/\/C
      \nNode* Parent = pParent;\/\/P
      \nNode* GrandParent = pParent->_pParent;\/\/G
      \n\/\/ 4 \u6bb5\u4ee3\u7801\u7ef4\u62a4
      \n\/\/ P->C = P->L
      \nParent->_pRight = Child->_pLeft;
      \n\/\/ L->C = L->P
      \nif (Child->_pLeft != nullptr)
      \n{
      \nChild->_pLeft->_pParent = Parent;
      \n}
      \n\/\/ C->L = C->P
      \nChild->_pLeft = Parent;
      \n\/\/ P->G = P->C
      \nParent->_pParent = Child;
      \nif (GrandParent != nullptr)
      \n{
      \n\/\/ G->P = G->C
      \nGrandParent->_pLeft == Parent ? GrandParent->_pLeft = Child : GrandParent->_pRight = Child;
      \n\/\/ C->P = C->G
      \nChild->_pParent = GrandParent;
      \n}
      \nelse
      \n{
      \n\/\/ C->P = C->nullptr
      \nChild->_pParent = nullptr;
      \n_pRoot = Child;
      \n}
      \n\/\/ \u8c03\u6574\u5e73\u8861
      \nBf(Parent);
      \nBf(Child);
      \n} <\/p>\n

      2.3.4 \u5de6\u53f3\u53cc\u65cb<\/p>\n

      \u5728\u90e8\u5206\u60c5\u51b5\u79cd\u5355\u65cb\u5df2\u7ecf\u6ca1\u6709\u529e\u6cd5\u6ee1\u8db3\u4e86\u6240\u6709\u9700\u8981\u53cc\u65cb\u6765\u6ee1\u8db3，\u7b2c\u4e00\u6b21\u65cb\u8f6c\u662f\u4e3a\u4e86\u7ed3\u6784\u53d8\u6210，\u7b26\u5408\u5de6\u53f3\u5355\u65cb\u7684\u7ed3\u6784\u3002\u5176\u6b21\u53cc\u65cb\u53ef\u4ee5\u590d\u7528\u524d\u9762\u7684\u4ee3\u7801，\u4ee5\u4fbf\u4e8e\u7406\u89e3\u4e5f\u53ef\u4ee5\u4e0d\u7528\u5199\u592a\u591a\u4ee3\u7801\u3002<\/p>\n

      \"\"<\/p>\n

      \/\/ \u5de6\u53f3\u53cc\u65cb
      \n void RotateLR(Node* pParent)
      \n{
      \n\/*
      \n a a c
      \n b -> c-> b a
      \n c b
      \nb->pParent
      \n\u4f18\u5148 c \u8fdb\u884c \u5de6\u65cb
      \n\u56e0\u4e3a c \u8fdb\u884c \u53f3\u65cb
      \n*\/
      \nRotateL(pParent->_pLeft);
      \nRotateR(pParent);
      \n} <\/p>\n

      2.3.5 \u53f3\u5de6\u53cc\u65cb\"\"<\/p>\n

      \/\/ \u53f3\u5de6\u53cc\u65cb
      \nvoid RotateRL(Node* pParent)
      \n{\/\/ pParent -> a
      \n\/*
      \na a c
      \n b -> c-> b a
      \n c b
      \nb->pParent
      \n\u4f18\u5148 c \u8fdb\u884c \u53f3\u65cb
      \n\u56e0\u4e3a c \u8fdb\u884c \u5de6\u65cb
      \n*\/
      \nRotateR(pParent->_pRight);
      \nRotateL(pParent);
      \n} <\/p>\n

      2.4 AVL \u6811\u7684\u67e5\u627e<\/h3>\n

      AVL \u6811\u7684\u67e5\u627e\u8fc7\u7a0b\u548c\u666e\u901a\u4e8c\u53c9\u641c\u7d22\u6811\u67e5\u627e\u903b\u8f91\u4e00\u81f4\u3002\u4ece\u6839\u8282\u70b9\u51fa\u53d1，\u62ff\u76ee\u6807\u503c\u548c\u5f53\u524d\u8282\u70b9\u6bd4\u8f83：\u76ee\u6807\u66f4\u5c0f\u5c31\u53bb\u5f80\u5de6\u5b50\u6811\u67e5\u627e，\u76ee\u6807\u66f4\u5927\u5c31\u53bb\u5f80\u53f3\u5b50\u6811\u67e5\u627e，\u76f8\u7b49\u5219\u67e5\u627e\u6210\u529f\u3002\u5982\u679c\u8d70\u5230\u7a7a\u8282\u70b9，\u4ee3\u8868\u67e5\u627e\u5931\u8d25\u3002 \u533a\u522b\u5728\u4e8e AVL \u6811\u53d7\u5e73\u8861\u7ea6\u675f\u9650\u5236，\u6811\u9ad8\u7a33\u5b9a\u4e3a logn，\u67e5\u627e\u6700\u574f\u65f6\u95f4\u590d\u6742\u5ea6\u662f O (log n)，\u4e0d\u4f1a\u50cf\u666e\u901a BST \u90a3\u6837\u9000\u5316\u6210 O (n)\u3002\u67e5\u627e\u8fc7\u7a0b\u4e0d\u4f1a\u4fee\u6539\u6811\u7ed3\u6784\u3001\u4e0d\u6539\u52a8\u9ad8\u5ea6\u548c\u5e73\u8861\u56e0\u5b50，\u4e5f\u4e0d\u4f1a\u89e6\u53d1\u65cb\u8f6c\u3002<\/p>\n

      2.5 AVL \u6811\u7684\u5e73\u8861\u68c0\u67e5<\/h3>\n

      \/\/ AVL\u6811\u7684\u9a8c\u8bc1
      \nbool IsAVLTree()
      \n{
      \nreturn _IsAVLTree(_pRoot);
      \n}
      \nprivate:
      \n \/\/ \u6839\u636eAVL\u6811\u7684\u6982\u5ff5\u9a8c\u8bc1pRoot\u662f\u5426\u4e3a\u6709\u6548\u7684AVL\u6811
      \nbool _IsAVLTree(Node* pRoot)
      \n{
      \nif (pRoot == nullptr)
      \n{
      \nreturn true;
      \n}
      \nbool put = _IsAVLTree(pRoot->_pLeft);
      \nif (put == false || abs(pRoot->_bf) >= 2)
      \n{
      \ncout << "\u8282\u70b9\u5e73\u8861\u5f02\u5e38" << endl;<\/p>\n

      return false;
      \n}
      \nput = _IsAVLTree(pRoot->_pRight);
      \nreturn put;
      \n} <\/p>\n

      2.6 AVL\u6811\u7684\u5220\u9664<\/h3>\n

      \"\"<\/p>\n

      \u5220\u9664\u7684\u539f\u7406\u5176\u5b9e\u4e0e\u63d2\u5165\u7684\u539f\u7406\u4e00\u81f4，\u7531\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u5220\u9664\u539f\u7406，\u5728\u52a0\u4e0a\u5bf9\u5e94\u4f4d\u7f6e\u65cb\u8f6c\u64cd\u4f5c\u5373\u53ef\u3002<\/p>\n

      AVLTree \u00b7 \u6d6a\u5b50\u00b7\u60a0\u4ec1\/C++ \u77e5\u8bc6\u5e93 – \u7801\u4e91 – \u5f00\u6e90\u4e2d\u56fd<\/p>\n

      \n

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

      \u76ee\u5f55
      \n1. AVL\u7684\u6982\u5ff5\u200b\u7f16\u8f91
      \n2. AVL \u6811\u7684\u5b9e\u73b0
      \n2.1 AVL \u6811\u7684\u7ed3\u6784
      \n2.2 AVL \u6811\u7684\u63d2\u5165
      \n2.3 \u65cb\u8f6c
      \n2.4 AVL \u6811\u7684\u67e5\u627e
      \n2.5 AVL \u6811\u7684\u5e73\u8861\u68c0\u67e5
      \n2.6 AVL\u6811\u7684\u5220\u9664 1. AVL\u7684\u6982\u5ff5
      \nAVL \u6811\u7531\u524d\u82cf\u8054\u6570\u5b66\u5bb6 G.M. Adelson-Velsky（\u963f\u5fb7\u5c14\u68ee – \u97e6\u5c14\u65af\u57fa） \u548c E.M. Landis（\u5170\u8fea\u65af） \u5728 1962 \u5e74\u63d0\u51fa\u5e76\u53d1\u8868\u8bba\u6587，\u5b83\u4e5f\u662f\u4e16<\/p>\n","protected":false},"author":2,"featured_media":120969,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[55],"topic":[],"class_list":["post-120976","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-c"],"yoast_head":"\n\u3010C++\u3011AVL \u6811 - \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\/120976.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u3010C++\u3011AVL \u6811 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u76ee\u5f55 1. AVL\u7684\u6982\u5ff5\u200b\u7f16\u8f91 2. AVL \u6811\u7684\u5b9e\u73b0 2.1 AVL \u6811\u7684\u7ed3\u6784 2.2 AVL \u6811\u7684\u63d2\u5165 2.3 \u65cb\u8f6c 2.4 AVL \u6811\u7684\u67e5\u627e 2.5 AVL \u6811\u7684\u5e73\u8861\u68c0\u67e5 2.6 AVL\u6811\u7684\u5220\u9664 1. AVL\u7684\u6982\u5ff5 AVL \u6811\u7531\u524d\u82cf\u8054\u6570\u5b66\u5bb6 G.M. Adelson-Velsky（\u963f\u5fb7\u5c14\u68ee - \u97e6\u5c14\u65af\u57fa） \u548c E.M. 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AVL\u7684\u6982\u5ff5\u200b\u7f16\u8f91 2. AVL \u6811\u7684\u5b9e\u73b0 2.1 AVL \u6811\u7684\u7ed3\u6784 2.2 AVL \u6811\u7684\u63d2\u5165 2.3 \u65cb\u8f6c 2.4 AVL \u6811\u7684\u67e5\u627e 2.5 AVL \u6811\u7684\u5e73\u8861\u68c0\u67e5 2.6 AVL\u6811\u7684\u5220\u9664 1. AVL\u7684\u6982\u5ff5 AVL \u6811\u7531\u524d\u82cf\u8054\u6570\u5b66\u5bb6 G.M. Adelson-Velsky（\u963f\u5fb7\u5c14\u68ee - \u97e6\u5c14\u65af\u57fa） \u548c E.M. 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