/** * File: avl_tree.cpp * Created Time: 2022-12-2 * Author: mgisr (maguagua0706@gmail.com) */ #include "../include/include.hpp" class AvlTree { private: TreeNode *root{}; static bool isBalance(const TreeNode *p); static int getBalanceFactor(const TreeNode *p); static void updateHeight(TreeNode *p); void fixBalance(TreeNode *p); static bool isLeftChild(const TreeNode *p); static TreeNode *&fromParentTo(TreeNode *node); public: AvlTree() = default; AvlTree(const AvlTree &p) = default; const TreeNode *search(int val); bool insert(int val); bool remove(int val); void printTree(); }; // 判断该结点是否平衡 bool AvlTree::isBalance(const TreeNode *p) { int balance_factor = getBalanceFactor(p); if (-1 <= balance_factor && balance_factor <= 1) { return true; } else { return false; } } // 获取当前结点的平衡因子 int AvlTree::getBalanceFactor(const TreeNode *p) { if (p->left == nullptr && p->right == nullptr) { return 0; } else if (p->left == nullptr) { return (-1 - p->right->height); } else if (p->right == nullptr) { return p->left->height + 1; } else { return p->left->height - p->right->height; } } // 更新结点高度 void AvlTree::updateHeight(TreeNode *p) { if (p->left == nullptr && p->right == nullptr) { p->height = 0; } else if (p->left == nullptr) { p->height = p->right->height + 1; } else if (p->right == nullptr) { p->height = p->left->height + 1; } else { p->height = std::max(p->left->height, p->right->height) + 1; } } void AvlTree::fixBalance(TreeNode *p) { // 左旋操作 auto rotate_left = [&](TreeNode *node) -> TreeNode * { TreeNode *temp = node->right; temp->parent = p->parent; node->right = temp->left; if (temp->left != nullptr) { temp->left->parent = node; } temp->left = node; node->parent = temp; updateHeight(node); updateHeight(temp); return temp; }; // 右旋操作 auto rotate_right = [&](TreeNode *node) -> TreeNode * { TreeNode *temp = node->left; temp->parent = p->parent; node->left = temp->right; if (temp->right != nullptr) { temp->right->parent = node; } temp->right = node; node->parent = temp; updateHeight(node); updateHeight(temp); return temp; }; // 根据规则选取旋转方式 if (getBalanceFactor(p) > 1) { if (getBalanceFactor(p->left) > 0) { if (p->parent == nullptr) { root = rotate_right(p); } else { fromParentTo(p) = rotate_right(p); } } else { p->left = rotate_left(p->left); if (p->parent == nullptr) { root = rotate_right(p); } else { fromParentTo(p) = rotate_right(p); } } } else { if (getBalanceFactor(p->right) < 0) { if (p->parent == nullptr) { root = rotate_left(p); } else { fromParentTo(p) = rotate_left(p); } } else { p->right = rotate_right(p->right); if (p->parent == nullptr) { root = rotate_left(p); } else { fromParentTo(p) = rotate_left(p); } } } } // 判断当前结点是否为其父节点的左孩子 bool AvlTree::isLeftChild(const TreeNode *p) { if (p->parent == nullptr) { return false; } return (p->parent->left == p); } // 返回父节点指向当前结点指针的引用 TreeNode *&AvlTree::fromParentTo(TreeNode *node) { if (isLeftChild(node)) { return node->parent->left; } else { return node->parent->right; } } const TreeNode *AvlTree::search(int val) { TreeNode *p = root; while (p != nullptr) { if (p->val == val) { return p; } else if (p->val > val) { p = p->left; } else { p = p->right; } } return nullptr; } bool AvlTree::insert(int val) { TreeNode *p = root; if (p == nullptr) { root = new TreeNode(val); return true; } for (;;) { if (p->val == val) { return false; } else if (p->val > val) { if (p->left == nullptr) { p->left = new TreeNode(val, p); break; } else { p = p->left; } } else { if (p->right == nullptr) { p->right = new TreeNode(val, p); break; } else { p = p->right; } } } for (; p != nullptr; p = p->parent) { if (!isBalance(p)) { fixBalance(p); break; } else { updateHeight(p); } } return true; } bool AvlTree::remove(int val) { TreeNode *p = root; if (p == nullptr) { return false; } while (p != nullptr) { if (p->val == val) { TreeNode *real_delete_node = p; TreeNode *next_node; if (p->left == nullptr) { next_node = p->right; if (p->parent == nullptr) { root = next_node; } else { fromParentTo(p) = next_node; } } else if (p->right == nullptr) { next_node = p->left; if (p->parent == nullptr) { root = next_node; } else { fromParentTo(p) = next_node; } } else { while (real_delete_node->left != nullptr) { real_delete_node = real_delete_node->left; } std::swap(p->val, real_delete_node->val); next_node = real_delete_node->right; if (real_delete_node->parent == p) { p->right = next_node; } else { real_delete_node->parent->left = next_node; } } if (next_node != nullptr) { next_node->parent = real_delete_node->parent; } for (p = real_delete_node; p != nullptr; p = p->parent) { if (!isBalance(p)) { fixBalance(p); } updateHeight(p); } delete real_delete_node; return true; } else if (p->val > val) { p = p->left; } else { p = p->right; } } return false; } void inOrder(const TreeNode *root) { if (root == nullptr) return; inOrder(root->left); cout << root->val << ' '; inOrder(root->right); } void AvlTree::printTree() { inOrder(root); cout << endl; } int main() { AvlTree tree = AvlTree(); // tree.insert(13); // tree.insert(24); // tree.insert(37); // tree.insert(90); // tree.insert(53); tree.insert(53); tree.insert(90); tree.insert(37); tree.insert(24); tree.insert(13); tree.remove(90); tree.printTree(); const TreeNode *p = tree.search(37); cout << p->val; return 0; }