HolyAVLTree

BinaryTree/BalanceTree/AVLTree/CMakeLists.txt

@@ -0,0 +1,6 @@
+cmake_minimum_required(VERSION 3.31)
+project(AVLTree)
+
+set(CMAKE_CXX_STANDARD 20)
+
+add_executable(AVLTree main.cpp)

BinaryTree/BalanceTree/AVLTree/README.MD

@@ -1,2 +1,4 @@
 # 旋转的本质：不能改变BST的属性
 左旋，是指把本节点移动到本节点右节点的左节点上； 右旋，是指把本节点移动到本节点左节点的右节点上
+LR的情况：先把LR的左节点左旋，形成LL，然后再按照LL的方式处理
+RL同理

BinaryTree/BalanceTree/AVLTree/avl.h

@@ -0,0 +1,263 @@
+//
+// Created by PC on 25-8-17.
+//
+
+#ifndef AVL_H
+#define AVL_H
+#include <iostream>
+
+#include "TreeNode.h"
+#include <iostream>
+#include <deque>
+template <class T>
+class AVL {
+private:
+    TreeNode<T>* root;
+    int totalHeight;
+
+    void insert(TreeNode<T>* &r, T element);
+    void erase(TreeNode<T>* &r, T element);
+    void inOrder(TreeNode<T>* r);
+
+public:
+    //构造函数
+    AVL(): root(nullptr), totalHeight(0) {}
+    explicit AVL(TreeNode<T>* root): root(root), totalHeight(1) {}
+    AVL(TreeNode<T>* root, int height): root(root), totalHeight(height) {}
+    AVL(const AVL<T> &other) {/*深拷贝*/}
+    ~AVL() {
+        dispose(root);
+        root = nullptr;
+    }
+    //返回
+    int getTotalHeight() const { return totalHeight; }
+    int getHeight(TreeNode<T>* node) const {
+            return node ? node->height : 0;
+    }
+    int getBalance(TreeNode<T>* node) const {
+        return getHeight(node->left) - getHeight(node->right);
+    }
+    TreeNode<T>* getRoot() { return root; }
+
+    //4种旋转，关注返回值（递归）
+    TreeNode<T>* LL(TreeNode<T>* &node);
+    TreeNode<T>* RR(TreeNode<T>* &node);
+    TreeNode<T>* LR(TreeNode<T>* &node);
+    TreeNode<T>* RL(TreeNode<T>* &node);
+
+    //中序遍历//删除节点
+    void display() {
+        std::cout << "Root is: " << root->element << std::endl;
+        inOrder(root);
+        std::cout << std::endl;
+    }
+    void dispose(TreeNode<T>* r);
+
+    //功能
+    void insert(T element);
+    void erase(T element);
+    void outputTree(int n);
+};
+
+template<class T>
+TreeNode<T> * AVL<T>::LL(TreeNode<T> *&node) {
+    TreeNode<T>* left = node->left;
+    TreeNode<T>* right = left->right;
+    node->left = right;
+    left->right = node;
+    //调整高度，已更新
+    node->height = std::max(getHeight(node->right), getHeight(node->left)) + 1;
+    left->height = std::max(getHeight(left->left), getHeight(left->right)) + 1;
+    return left;
+}
+
+template<class T>
+TreeNode<T>* AVL<T>::RR(TreeNode<T> *&node) {
+    TreeNode<T>* right = node->right;
+    TreeNode<T>* left = right->left;
+    right->left = node;
+    node->right = left;
+    //调整高度
+    node->height = std::max(getHeight(node->right), getHeight(node->left)) + 1;
+    right->height = std::max(getHeight(right->left), getHeight(right->right)) +1;
+    return right;
+}
+
+template<class T>
+TreeNode<T> * AVL<T>::LR(TreeNode<T> *&node) {
+    node->left = RR(node->left);
+    node = LL(node);
+    //不用再调整高度，组合技
+    return node;
+}
+
+template<class T>
+TreeNode<T> * AVL<T>::RL(TreeNode<T> *&node) {
+    node->right = LL(node->right);
+    node = RR(node);
+    return node;
+}
+
+template<class T>
+void AVL<T>::inOrder(TreeNode<T> *r) {
+        if (r != nullptr) {
+            inOrder(r->left);
+            std::cout << r->element << " ";
+            inOrder(r->right);
+        }
+}
+
+template<class T>
+void AVL<T>::dispose(TreeNode<T> *r) {
+    if (r != nullptr) {
+        dispose(r->left);
+        dispose(r->right);
+        delete r;
+    }
+}
+
+template<class T>
+void AVL<T>::insert(T element) {
+    insert(root, element);
+}
+
+template<class T>
+void AVL<T>::erase(T element) {
+    erase(root, element);
+}
+
+//n是输入的max
+template<class T>
+void AVL<T>::outputTree(int n) {
+    int index = 0;
+    std::deque<TreeNode<T> *> q;
+    q.push_back(root);
+    while (true) {
+        if (q[index] != nullptr && q[index]->element == n) {break;}
+        if (q[index]->left) q.push_back(q[index]->left);
+        if (q[index]->right) q.push_back(q[index]->right);
+        index++;
+    }
+    int cnt = 1;
+    int jmp = 1;
+    for (int i = 0; i <= index; i++) {
+        cnt--;
+        q[i] != nullptr ? std::cout << q[i]->element << " " : std::cout << "-1" << " ";
+        if (cnt == 0) {
+            jmp *= 2;
+            cnt = jmp;
+            std::cout << std::endl;
+        }
+    }
+    std::cout << std::endl;
+}
+
+template<class T>
+void AVL<T>::insert(TreeNode<T>* &r, T element) {
+    //BST插入
+    if (r == nullptr) {
+        r = new TreeNode<T>(element);
+        return ;
+    }
+
+    if (element < r->element) {
+        insert(r->left, element);
+    }
+    else if (element > r->element) {
+        insert(r->right, element);
+    }
+    //更新高度，注意在回溯的时候，已经更新了每个父节点的height，不需要再调整（中序遍历一遍）
+    r->height = std::max(getHeight(r->left), getHeight(r->right)) + 1;
+
+    //旋转-关注四个条件
+    int balance = getBalance(r);
+
+    if (balance > 1 && element < r->left->element) {
+        //LL
+        r = LL(r);
+    }
+    else if (balance < -1 && element > r->right->element) {
+        //RR
+        r = RR(r);
+    }
+    else if (balance > 1 && element > r->left->element) {
+        //LR
+        r->left = RR(r->left);
+        r = LL(r);
+    }
+    else if (balance < -1 && element < r->right->element) {
+        //RL
+        r->right = LL(r->right);
+        r = RR(r);
+    }
+}
+
+template<class T>
+void AVL<T>::erase(TreeNode<T> *&r, T element) {
+    /*
+    先按照二叉搜索树的规则删除节点：若删除节点没有孩子 → 直接删除 。
+    若只有一个孩子 → 让孩子接替它 。
+    若有两个孩子 → 找 中序后继（右子树最小） 或 中序前驱（左子树最大），替换值，再递归删除.
+    */
+    if (r == nullptr) {
+        return;
+    }
+    TreeNode<T> *tmp = r;
+    if (element < r->element) {
+        erase(r->left, element);
+    }
+    else if (element > r->element) {
+        erase(r->right, element);
+    }
+    else {
+        //p = 0 or 1
+        if (r->left == nullptr || r->right == nullptr) {
+            tmp = r->left ? r->left : r->right;
+            if (!tmp) {
+                tmp = r;
+                r = nullptr;
+            }
+            else {
+                *r = *tmp;
+            }
+            delete tmp;
+        }
+        //p = 2
+        else if (r->left != nullptr && r->right != nullptr) {
+            //right-min或left-max，提到最上
+            TreeNode<T> *min = r->right;
+            while (min->left != nullptr) {
+                min = min->left;
+            }
+            r->element = min->element;
+            erase(r->right, min->element);
+        }
+    }
+    if (!r) return;
+
+    //这里再对每个节点进行操作，旋转；回溯的时候会将父/祖父节点都旋转
+    //更新高度
+    r->height = std::max(getHeight(r->left), getHeight(r->right)) + 1;
+    //检查左右孩子
+    int balance = getBalance(r);
+    //关注和insert的区别
+    if (balance > 1 && getBalance(r->left) >= 0) {
+        //LL
+        r = LL(r);
+    }
+    else if (balance < -1 && getBalance(r->right) <= 0) {
+        //RR
+        r = RR(r);
+    }
+    else if (balance > 1 && getBalance(r->left) < 0) {
+        //LR
+        r->left = RR(r->left);
+        r = LL(r);
+    }
+    else if (balance < -1 && getBalance(r->right) > 0) {
+        //RL
+        r->right = LL(r->right);
+        r = RR(r);
+    }
+}
+#endif //AVL_H

BinaryTree/BalanceTree/AVLTree/main.cpp

@@ -0,0 +1,97 @@
+#include <iostream>
+#include "avl.h"
+using namespace std;
+int main() {
+    AVL<int> tree;
+    tree.insert(10);
+    tree.display();
+    tree.outputTree(10);
+    tree.insert(20);
+    tree.display();
+    tree.outputTree(20);
+    tree.insert(30);
+    tree.display();
+    tree.outputTree(30);
+    tree.insert(100);
+    tree.display();
+    tree.outputTree(100);
+    tree.insert(50);
+    tree.display();
+    tree.outputTree(50);
+    tree.insert(70);
+    tree.display();
+    tree.outputTree(70);
+    tree.insert(80);
+    tree.display();
+    tree.outputTree(80);
+    tree.insert(60);
+    tree.display();
+    tree.outputTree(60);
+    cout << endl << endl << endl;
+    cout << "To erase: " << endl;
+    tree.erase(60);
+    tree.display();
+    tree.outputTree(100);
+    tree.erase(100);
+    tree.display();
+    tree.outputTree(80);
+
+    return 0;
+}
+/*
+OutputTree写的不好
+Root is: 10
+10
+10
+
+Root is: 10
+10 20
+10
+20
+
+Root is: 20
+10 20 30
+20
+10 30
+
+Root is: 20
+10 20 30 100
+20
+10 30
+100
+
+Root is: 20
+10 20 30 50 100
+20
+10 50
+
+Root is: 50
+10 20 30 50 70 100
+50
+20 100
+10 30 70
+
+Root is: 50
+10 20 30 50 70 80 100
+50
+20 80
+
+Root is: 50
+10 20 30 50 60 70 80 100
+50
+20 80
+10 30 70 100
+60
+
+To erase:
+Root is: 50
+10 20 30 50 70 80 100
+50
+20 80
+10 30 70 100
+
+Root is: 50
+10 20 30 50 70 80
+50
+20 80
+*/

BinaryTree/BalanceTree/AVLTree/treenode.h

@@ -0,0 +1,38 @@
+//
+// Created by PC on 25-8-17.
+//
+
+#ifndef TREENODE_H
+#define TREENODE_H
+template<class T>
+class TreeNode {
+public:
+    T element;
+    TreeNode<T>* left;
+    TreeNode<T>* right;
+    int height;
+
+    TreeNode(): left(nullptr), right(nullptr), height(0) {}
+    explicit TreeNode(T e): element(e), left(nullptr), right(nullptr), height(1) {}
+    TreeNode(T e, TreeNode<T>* l, TreeNode<T>* r): element(e), left(l), right(r), height(1) {}
+};
+
+#endif //TREENODE_H
+/*
+        30
+      /   \
+     25    35
+    / \
+   20  32
+  /
+ 5
+
+ 旋转之后应该是：
+        1
+      /   \
+     r     4
+    / \
+   3   2
+/
+5
+*/