【数据结构与算法】AVL树（3）——C++实现

函数

结点定义

typedef struct TreeNode
{
	int val;    //结点的值
	TreeNode* left;    
	TreeNode* right;    
	int balance;    //平衡因子		
	int height;	    //树高
    //构造函数
	TreeNode(int x):val(x), left(nullptr), right(nullptr), balance(0), height(0){}			
}*AVLTree;

树的高度

int getHeight(AVLTree t)//获取树的高度 
{
	return ( t==nullptr ? -1:t->height );
}

计算树高和平衡因子

void AVL_Cal(AVLTree root)//计算树高和平衡因子 
{
	int hl = getHeight(root->left);
	int hr = getHeight(root->right);

	root->height =  max(hl, hr) + 1;
	root->balance = hl - hr;	
}

LL旋转

void LL_rotation(AVLTree& A)//左-左旋转 
{
	AVLTree t  = A;						
	AVLTree B  = A->left;	
	AVLTree BR = B->right;	
	
	B->right = t;
	t->left = BR;
	A = B;		
	
	AVL_Cal(A->right);
	AVL_Cal(A); 
}

RR旋转

void RR_rotation(AVLTree& A)//右-右旋转 
{
	AVLTree t  = A;		 					
	AVLTree B  = A->right;	
	AVLTree BL = B->left;	
	
	B->left = t;	
	t->right = BL;	
	A = B;	

	AVL_Cal(A->left);
	AVL_Cal(A); 	
}

LR旋转

void LR_rotation(AVLTree& A)//左-右旋转 
{
	RR_rotation(A->left);	
	LL_rotation(A);		
} 

RL旋转

void RL_rotation(AVLTree& A)//右-左旋转 
{
	LL_rotation(A->right);		
	RR_rotation(A);		
} 

AVL树的插入与旋转调整

bool AVL_Insert(AVLTree& root, int& x)//插入并调整AVL树 
{
	if( !root )
	{
		root = new TreeNode(x);
		return true;
	}
	else if( x < root->val )
	{
		AVL_Insert(root->left, x);
		AVL_Cal(root);    
		if( root->balance > 1 )
		{
			if( x < root->left->val )
				LL_rotation(root);
			else
				LR_rotation(root);			
		}			
	}
	else if( x > root->val )
	{
		AVL_Insert(root->right, x);
		AVL_Cal(root);   
		if( root->balance < -1 )
		{
			if( x > root->right->val )
				RR_rotation(root);
			else
				RL_rotation(root);			
		}			
	}
	return true;
}

测试

测试代码

#include<bits/stdc++.h>

using namespace std;
 
typedef struct TreeNode
{
	int val;
	TreeNode* left;
	TreeNode* right;
	int balance;		
	int height;	
	TreeNode(int x):val(x), left(nullptr), right(nullptr), balance(0), height(0){}			
}*AVLTree;

int getHeight(AVLTree t)//获取树的高度 
{
	return ( t==nullptr ? -1:t->height );
}
 
void AVL_Cal(AVLTree root)//计算树高和平衡因子 
{
	int hl = getHeight(root->left);
	int hr = getHeight(root->right);

	root->height =  max(hl, hr) + 1;
	root->balance = hl - hr;	
}

void LL_rotation(AVLTree& A)//左-左旋转 
{
	AVLTree t  = A;						
	AVLTree B  = A->left;	
	AVLTree BR = B->right;	
	
	B->right = t;
	t->left = BR;
	A = B;		
	
	AVL_Cal(A->right);
	AVL_Cal(A); 
}

void RR_rotation(AVLTree& A)//右-右旋转 
{
	AVLTree t  = A;		 					
	AVLTree B  = A->right;	
	AVLTree BL = B->left;	
	
	B->left = t;	
	t->right = BL;	
	A = B;	

	AVL_Cal(A->left);
	AVL_Cal(A); 	
}

void LR_rotation(AVLTree& A)//左-右旋转 
{
	RR_rotation(A->left);	
	LL_rotation(A);		
} 

void RL_rotation(AVLTree& A)//右-左旋转 
{
	LL_rotation(A->right);		
	RR_rotation(A);		
} 

bool AVL_Insert(AVLTree& root, int& x)//插入并调整AVL树 
{
	if( !root )
	{
		root = new TreeNode(x);
		return true;
	}
	else if( x < root->val )
	{
		AVL_Insert(root->left, x);
		AVL_Cal(root);    
		if( root->balance > 1 )
		{
			if( x < root->left->val )
				LL_rotation(root);
			else
				LR_rotation(root);			
		}			
	}
	else if( x > root->val )
	{
		AVL_Insert(root->right, x);
		AVL_Cal(root);   
		if( root->balance < -1 )
		{
			if( x > root->right->val )
				RR_rotation(root);
			else
				RL_rotation(root);			
		}			
	}
	return true;
}

void visit(TreeNode* p)
{
	cout << p->val << " ";
}

void preOrder(AVLTree root)
{
	if( root )
	{
		visit(root);
		preOrder(root->left);
		preOrder(root->right);	
	}	
}
 
void inOrder(AVLTree root)
{
	if( root )
	{
		inOrder(root->left);
		visit(root);
		inOrder(root->right);	
	}
}
 
void postOrder(AVLTree root)
{
	if( root )
	{
		postOrder(root->left);
		postOrder(root->right);	
		visit(root);
	}	
}

int main( )
{
	AVLTree root = nullptr;
	int n, t;
	
	int value[] = {};
	cin>>n;	
	for(int i=0;i<n;i++)
	{
		cin>>t;
		AVL_Insert(root, t);
	}
	cout << "根结点：" << root->val;
	cout << "\n" << "先序遍历：";
	preOrder(root);
	cout << "\n" << "中序遍历：";	
	inOrder(root);
	cout << "\n" << "后序遍历：";	
	postOrder(root);
	
    return 0;
}

测试输入

  第一行输入插入结点的个数，第二行按顺序输入插入结点的值。

9
8 4 10 2 1 3 11 6 5

测试输出

  输出根结点和遍历的结果。

根结点：4
先序遍历：4 2 1 3 10 6 5 8 11 
中序遍历：1 2 3 4 5 6 8 10 11 
后序遍历：1 3 2 5 8 6 11 10 4 

动图演示

相关文章

AVL树（1）——简介
AVL树（2）——插入与旋转调整
AVL树（3）——C++实现