AVLTree平衡二叉树---C++实现

最新推荐文章于 2020-04-22 18:29:52 发布

~AC~

最新推荐文章于 2020-04-22 18:29:52 发布

阅读量161

点赞数

CC 4.0 BY-SA版权

分类专栏：数据结构文章标签： AVL

本文链接：https://blog.youkuaiyun.com/qq_42673507/article/details/89142702

数据结构专栏收录该内容

50 篇文章

订阅专栏

本文详细介绍了AVL树的插入、删除及自平衡调整等核心操作，并提供了完整的C++代码实现，深入解析了AVL树如何维持其高度平衡特性。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

#include <iostream>
#include <algorithm>
#include <queue>
using namespace std;

/*
*AVL树
*/

typedef struct btree{
	int data;
	int height;
	struct btree* lchild;
	struct btree* rchild;
	btree() {
		data = height = 0;
		lchild = rchild = NULL;
	}
	btree(int num) {
		data = num;
		height = 0;
		lchild = rchild = NULL;
	}
}node;

void fixAVL(node* &root);
node* getMin(node* root);
int getHeight(node* root);
node* insertIntoAvl(node* &root, int num);
void deleteInAVLTree(node* &root, int num);

//获取以该节点为根节点树的高度
int getHeight(node* root) {
	return root == NULL ? -1 : root->height;
}

//AVL的插入操作
node* insertIntoAvl(node* &root, int num) {
	if (root == NULL) {
		root = new node(num);
	}
	else {
		if (root->data > num) {
			root->lchild = insertIntoAvl(root->lchild, num);
		}
		if (root->data < num) {
			root->rchild = insertIntoAvl(root->rchild, num);
		}
		//此时不平衡了
		if (fabs(getHeight(root->lchild) - getHeight(root->rchild)) == 2) {
			fixAVL(root);
		}
	}
	root->height = max(getHeight(root->lchild), getHeight(root->rchild)) + 1;
	return root;
}

//AVL删除
void deleteInAVLTree(node* &root, int num) {
	if (root) {
		if (root->data == num) {
			//叶子节点
			if (root->lchild == NULL && root->rchild == NULL) {
				delete root;
				root = NULL;
			}
			//左子树为空 右子树不为空
			else if (root->lchild == NULL && root->rchild != NULL) {
				node* t = root;
				root = root->rchild;
				delete t;
				t = NULL;
			}
			//左子树不为空 右子树为空
			else if (root->lchild != NULL && & root->rchild == NULL) {
				node* t = root;
				root = root->lchild;
				delete t;
				t = NULL;
			}
			//左右子树都不为空 则选择右子树最小值来填补被删除的结点
			else {
				node* rightMinNode = getMin(root->rchild);
				deleteInAVLTree(root, rightMinNode->data);
				root->data = rightMinNode->data;
			}
		}
		else if(root->data > num){
			deleteInAVLTree(root->lchild, num);
		}
		else {
			deleteInAVLTree(root->rchild, num);
		}
		if (root && fabs(getHeight(root->lchild) - getHeight(root->rchild)) == 2) {
			fixAVL(root);
			root->height = max(getHeight(root->lchild), getHeight(root->rchild)) + 1;
		}
	}
}
	
//返回全树的最小值所在结点
node* getMin(node* root) {
	if (root) {
		node* p = root;
		while (p->lchild) {
			p = p->lchild;
		}
		return p;
	}
	throw new exception("tree is empty!");
	return NULL;
}
//LL
void AVLTreeBalanceOfLL(node* &root) {
	if (root) {
		node* p = root->lchild;
		root->lchild = p->rchild;
		p->rchild = root;
		root->height = max(getHeight(root->lchild), getHeight(root->rchild)) + 1;
		p->height = max(getHeight(p->lchild), getHeight(p->rchild)) + 1;
		root = p;
	}
}

//LR
void AVLTreeBalanceOfLR(node* &root) {
	if (root) {
		node* p = root->lchild->rchild;
		node* q = root->lchild;
		root->lchild = p->rchild;
		q->rchild = p->lchild;
		p->lchild = q;
		p->rchild = root;
		root->height = max(getHeight(root->lchild), getHeight(root->rchild)) + 1;
		q->height = max(getHeight(q->lchild), getHeight(q->rchild)) + 1;
		p->height = max(getHeight(p->lchild), getHeight(p->rchild)) + 1;
		root = p;
	}
}

//RR
void AVLTreeBalanceOfRR(node* &root) {
	if (root) {
		node* p = root->rchild;
		root->rchild = p->lchild;
		p->lchild = root;
		root->height = max(getHeight(root->lchild), getHeight(root->rchild)) + 1;
		p->height = max(getHeight(p->lchild), getHeight(p->rchild)) + 1;
		root = p;
	}
}

//RL
void AVLTreeBalanceOfRL(node* &root) {
	if (root) {
		node* p = root->rchild->lchild;
		node* q = root->rchild;
		root->rchild = p->lchild;
		q->lchild = p->rchild;
		p->lchild = root;
		p->rchild = q;
		root->height = max(getHeight(root->lchild), getHeight(root->rchild)) + 1;
		q->height = max(getHeight(q->lchild), getHeight(q->rchild)) + 1;
		p->height = max(getHeight(p->lchild), getHeight(p->rchild)) + 1;
		root = p;
	}
}
//AVL的自平衡函数
void fixAVL(node* &root) {
	if (root) {
		//判断是LL 还是LR
		if (getHeight(root->lchild) - getHeight(root->rchild) == 2) {
			//LL
			if (getHeight(root->lchild->lchild) > getHeight(root->lchild->rchild)) {
				AVLTreeBalanceOfLL(root);
			}
			//LR
			else {
				AVLTreeBalanceOfLR(root);
			}
		}
		//判断是RR还是RL
		else {
			//RR
			if (getHeight(root->rchild->rchild) > getHeight(root->rchild->lchild)) {
				AVLTreeBalanceOfRR(root);
			}
			//RL
			else {
				AVLTreeBalanceOfRL(root);
			}
		}
	}
}

//中序遍历测试
void inorder(node* root) {
	if (root) {
		inorder(root->lchild);
		cout << root->data << "  ";
		inorder(root->rchild);
	}
}

int main()
{
	node* root = NULL;
	insertIntoAvl(root, 4);
	insertIntoAvl(root, 5);
	insertIntoAvl(root, 6);
	insertIntoAvl(root, 7);
	insertIntoAvl(root, 8);
	deleteInAVLTree(root, 6);
	inorder(root);
	return 0;
}