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AVLTree.h
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AVLTree.h
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//
// Created by hpf on 18-6-21.
//
#ifndef AVLTREE_AVLTREE_H
#define AVLTREE_AVLTREE_H
#include <algorithm>
#include <iostream>
#include <vector>
template<typename Key, typename Value>
class AVLTree {
private:
struct Node {
Key key;
Value value;
Node *left;
Node *right;
int height;
Node(Key key, Value value) {
this->key = key;
this->value = value;
this->left = this->right = nullptr;
height = 1;
}
Node(Node *node) {
this->key = node->key;
this->value = node->value;
this->left = node->left;
this->right = node->right;
this->height = node->height;
}
};
Node *root;
int size;
public:
AVLTree() {
root = nullptr;
size = 0;
}
~AVLTree() {
destroy(root);
}
int getSize() {
return size;
}
int isEmpty() {
return size == 0;
}
int getHeight(Node *node) {
if (node == nullptr) {
return 0;
}
return node->height;
}
int getBalanceFactor(Node *node) {
if (node == nullptr) {
return 0;
}
return getHeight(node->left) - getHeight(node->right);
}
bool isBST() {
std::vector<Key> keys;
inOrder(root, keys);
for (int i = 1; i < keys.size(); ++i) {
if (keys.at(i - 1) < keys.at(i)) {
return false;
}
}
return true;
}
bool isBalanced() {
return isBalanced(root);
}
void add(Key key, Value value) {
root = add(root, key, value);
}
bool contains(Key key) {
return getNode(root, key) != nullptr;
}
Value *get(Key key) {
Node *node = getNode(root, key);
return node == nullptr ? nullptr : &(node->value);
}
void set(Key key, Value newValue) {
Node *node = getNode(root, key);
if (node != nullptr) {
node->value = newValue;
}
}
// 从二叉树中删除键值为key的节点
Value *remove(Key key) {
Node *node = getNode(root, key);
if (node != nullptr) {
root = remove(root, key);
return &(node->value);
}
return nullptr;
}
private:
// 向以node为根的二叉搜索树中,插入节点(key, value)
// 返回插入新节点后的二叉搜索树的根
Node *add(Node *node, Key key, Value value) {
if (node == nullptr) {
size++;
return new Node(key, value);
}
if (key == node->key) {
node->value = value;
} else if (key < node->key) {
node->left = add(node->left, key, value);
} else {
node->right = add(node->right, key, value);
}
node->height = 1 + std::max(getHeight(node->left), getHeight(node->right));
int balanceFactor = getBalanceFactor(node);
if (balanceFactor > 1 && getBalanceFactor(node->left) >= 0) {
return rightRotate(node);
}
if (balanceFactor < -1 && getBalanceFactor(node->right) <= 0) {
return leftRotate(node);
}
if (balanceFactor > 1 && getBalanceFactor(node->left) < 0) {
node->left = leftRotate(node->left);
return rightRotate(node);
}
if (balanceFactor < -1 && getBalanceFactor(node->right) > 0) {
node->right = rightRotate(node->right);
return leftRotate(node);
}
return node;
}
// 在以node为根的二叉搜索树中查找key所对应的Node
Node *getNode(Node *node, Key key) {
if (node == nullptr) {
return nullptr;
}
if (key == node->key) {
return node;
} else if (key < node->key) {
return getNode(node->left, key);
} else {
return getNode(node->right, key);
}
}
void destroy(Node *node) {
if (node != nullptr) {
destroy(node->left);
destroy(node->right);
delete node;
size--;
}
}
// 在以node为根的二叉搜索树中,返回最小键值的节点
Node *minimum(Node *node) {
if (node->left == nullptr)
return node;
return minimum(node->left);
}
// 在以node为根的二叉搜索树中,返回最大键值的节点
Node *maximum(Node *node) {
if (node->right == nullptr)
return node;
return maximum(node->right);
}
// 删除掉以node为根的二分搜索树中的最小节点
// 返回删除节点后新的二分搜索树的根
Node *removeMin(Node *node) {
if (node->left == nullptr) {
Node *rightNode = node->right;
delete node;
size--;
return rightNode;
}
node->left = removeMin(node->left);
return node;
}
// 删除掉以node为根的二分搜索树中的最大节点
// 返回删除节点后新的二分搜索树的根
Node *removeMax(Node *node) {
if (node->right == nullptr) {
Node *leftNode = node->left;
delete node;
size--;
return leftNode;
}
node->right = removeMax(node->right);
return node;
}
// 删除掉以node为根的二分搜索树中键值为key的节点
// 返回删除节点后新的二分搜索树的根
Node *remove(Node *node, Key key) {
if (node == nullptr) {
return nullptr;
}
Node *retNode;
if (key < node->key) {
node->left = remove(node->left, key);
retNode = node;
} else if (key > node->key) {
node->right = remove(node->right, key);
retNode = node;
} else {
if (node->left == nullptr) {
Node *rightNode = node->right;
delete node;
size--;
retNode = rightNode;
} else if (node->right == nullptr) {
Node *leftNode = node->left;
delete node;
size--;
retNode = leftNode;
} else {
Node *successor = new Node(minimum(node->right));
size++;
successor->right = remove(node->right, successor->key);
successor->left = node->left;
delete node;
size--;
retNode = successor;
}
}
if (retNode == nullptr) {
return nullptr;
}
retNode->height = 1 + std::max(getHeight(retNode->left), getHeight(retNode->right));
int balanceFactor = getBalanceFactor(retNode);
if (balanceFactor > 1 && getBalanceFactor(retNode->left) >= 0) {
return rightRotate(retNode);
}
if (balanceFactor < -1 && getBalanceFactor(retNode->right) <= 0) {
return leftRotate(retNode);
}
if (balanceFactor > 1 && getBalanceFactor(retNode->left) < 0) {
retNode->left = leftRotate(retNode->left);
return rightRotate(retNode);
}
if (balanceFactor < -1 && getBalanceFactor(retNode->right) > 0) {
retNode->right = rightRotate(retNode->right);
return leftRotate(retNode);
}
return retNode;
}
void inOrder(Node *node, std::vector<Key> keys) {
if (node == nullptr) {
return;
}
inOrder(node->left, keys);
keys.push_back(node->key);
inOrder(node->right, keys);
}
bool isBalanced(Node *node) {
if (node == nullptr) {
return true;
}
int balanceFactor = getBalanceFactor(node);
if (std::abs(balanceFactor) > 1) {
return false;
}
return isBalanced(node->left) && isBalanced(node->right);
}
Node *leftRotate(Node *y) {
Node *x = y->right;
Node *tmp = x->left;
x->left = y;
y->right = tmp;
y->height = std::max(getHeight(y->left), getHeight(y->right)) + 1;
x->height = std::max(getHeight(x->left), getHeight(x->right)) + 1;
return x;
}
Node *rightRotate(Node *y) {
Node *x = y->left;
Node *tmp = x->right;
x->right = y;
y->left = tmp;
y->height = std::max(getHeight(y->left), getHeight(y->right)) + 1;
x->height = std::max(getHeight(x->left), getHeight(x->right)) + 1;
return x;
}
};
#endif //AVLTREE_AVLTREE_H