AVL树

本节内容介绍AVL树，具体看下面：

 

 

 

具体看如下代码：

AVLTree.h

#pragma once

struct AVLNode;
typedef struct AVLNode* Position;
typedef struct AVLNode* AVLTree;


typedef int ElementType;

AVLTree MakeEmpty(AVLTree T);
Position Find(ElementType X,AVLTree T);
Position FindMin(AVLTree T);
Position FindMax(AVLTree T);
AVLTree Insert(ElementType X,AVLTree T);
AVLTree Delete(ElementType X,AVLTree T);
ElementType Retrieve(Position P);

AVLTree SingleRotateLeft(AVLTree T);
AVLTree SingleRotateRight(AVLTree T);
AVLTree DoubleRotateLeft(AVLTree T);
AVLTree DoubleRotateRight(AVLTree T);

void PrintTree(AVLTree T,int depth);
void PrintTree(AVLTree T);
void PrintDepth(ElementType A,int dpth);


struct  AVLNode
{
	ElementType Element;
	AVLTree Lchild;
	AVLTree Rchild;
	int Hight;
};

AVLTree.cpp

#include
#include 
#include "AVLTree.h"

using namespace std;

#define Max(a,b)  ((a)>(b)?(a):(b))


//返回树节点的高度，如果为NULL返回-1
int Height(AVLTree T)
{
	if (T == NULL)
	{
		return -1;
	}
	return T->Hight;
}


AVLTree MakeEmpty(AVLTree T)
{
	if (T != NULL)
	{
		MakeEmpty(T->Lchild);
		MakeEmpty(T->Rchild);
		free(T);
	}
	return NULL;
}


//递归查找
Position Find(ElementType X, AVLTree T)
{
	if (T == NULL)
	{
		return NULL;
	}

	if (X < T->Element)
	{
		return Find(X,T->Lchild);
	}
	else if (X > T->Element)
	{
		return Find(X,T->Rchild);
	}
	else
	{
		return T;
	}
}


//非递归查找
Position FindMin(AVLTree T)
{
	if (T != NULL)
	{
		while (T->Lchild!=NULL)
		{
			T = T->Lchild;
		}
		return T;
	}
	return NULL;
}


//非递归查找
Position FindMax(AVLTree T)
{
	if (T != NULL)
	{
		while (T->Rchild != NULL)
		{
			T = T->Rchild;
		}
		return T;
	}
	return NULL;
}



//递归插入
AVLTree Insert(ElementType X, AVLTree T)
{
	if (T == NULL)
	{
		T = (AVLTree)malloc(sizeof(AVLNode));
		if (T == NULL)
		{
			exit(1);
		}
		T->Element = X;
		T->Lchild = T->Rchild = NULL;
		T->Hight = 0;
	}

	if (X < T->Element)
	{
		T->Lchild = Insert(X,T->Lchild);
		//左边插入之后检查是否满足平衡条件，如果不平衡需要进行旋转
		if ((Height(T->Lchild)) - (Hight(T->Rchild)) == 2)
		{
			if (X < T->Lchild->Element)
			{
				T = SingleRotateLeft(T);
			}
			else
			{
				T = DoubleRotateLeft(T);
			}
		}
	}
	if (X > T->Element)
	{
		T->Rchild = Insert(X,T->Rchild);
		//右边插入之后检查是否满足平衡条件，如果不平衡需要进行旋转
		if (((Height(T->Rchild)) - Height(T->Lchild)) == 2)
		{
			if (X > T->Rchild->Element)
			{
				T = SingleRotateRight(T);
			}
			else
			{
				T = DoubleRotateRight(T);
			}
		}
	}

	//插入完成更新该节点高度
	T->Hight = Max(Height(T->Lchild), Height(T->Rchild)) + 1;
	return T;
}


//左边树枝旋转
AVLTree SingleRotateLeft(AVLTree T)
{
	AVLTree k1;

	k1 = T->Lchild;
	T->Lchild = k1->Rchild;
	k1->Rchild = T;

	T->Hight = Max(Height(T->Lchild),Height(T->Rchild))+1;
	k1->Hight = Max(Height(k1->Lchild),Height(k1->Rchild))+1;

	return k1;
}

//右边树旋转
AVLTree SingleRotateRight(AVLTree T)
{
	AVLTree k1;

	k1 = T->Rchild;
	T->Rchild = k1->Lchild;
	k1->Lchild = T;

	T->Hight = Max(Height(T->Lchild),Height(T->Rchild))+1;
	k1->Hight = Max(Height(k1->Lchild),Height(k1->Rchild))+1;

	return k1;
}

//左边树枝双旋转
AVLTree DoubleRotateLeft(AVLTree k3)
{
	k3->Lchild = SingleRotateRight(k3->Lchild);
	return SingleRotateLeft(k3);
}

//右边树枝双旋转
AVLTree DoubleRotateRight(AVLTree k4)
{
	k4->Rchild = SingleRotateLeft(k4->Rchild);
	return SingleRotateRight(k4);
}


//递归删除
AVLTree Delete(ElementType X, AVLTree T)
{
	if (T == NULL)
	{
		fprintf(stderr,"%d not exists\n",X);
	}
	else
	{
		if (XElement)
		{
			T->Lchild = Delete(X,T->Lchild);
			//删除之后需要更新该节点高度
			T->Hight = Max(Height(T->Lchild),Height(T->Rchild))+1;
			//删除之后检查是否满足平衡条件，不满足需要旋转
			if ((Height(T->Rchild) - Height(T->Lchild)) == 2)
			{
				if (Height(T->Rchild->Rchild) >= Height(T->Rchild->Lchild))
				{
					T = SingleRotateRight(T);
				}
				else
				{
					T = DoubleRotateRight(T);
				}
			}
		}
		else if (X > T->Element)
		{
			T->Rchild = Delete(X,T->Rchild);
			//删除之后需要更新节点T的高度
			T->Hight = Max(Height(T->Lchild),Height(T->Rchild))+1;
			//如果不是平衡二叉树，那么就需要通过旋转来进行调整
			if (Height(T->Lchild)-Height(T->Rchild)==2)
			{
				if (Height(T->Lchild->Lchild) >= Height(T->Lchild->Rchild))
				{
					T = SingleRotateLeft(T);
				}
				else
				{
					T = DoubleRotateLeft(T);
				}
			}
		}
		else
		{
			//找到的树节点如果有两个孩子的话就用它右子树的最小值代替该点，再删除右子树上的最大值
			if (T->Lchild && T->Rchild)
			{
				T->Element = FindMin(T->Rchild)->Element;
				T->Rchild = Delete(T->Element,T->Rchild);

				T->Hight = Max(Height(T->Lchild),Height(T->Rchild))+1;

				if (Height(T->Lchild) - Height(T->Rchild) == 2)
				{
					if (Height(T->Lchild->Lchild) >= Height(T->Lchild->Rchild))
					{
						T = SingleRotateLeft(T);
					}
					else
					{
						T = DoubleRotateLeft(T);
					}
				}

			}
			else
			{
				AVLTree temp = T;
				if (T->Lchild == NULL)
				{
					T = T->Rchild;
				}
				else
				{
					T = T->Lchild;
				}
				free(temp);
			}
		}
	}

	return T;
}



void PrintDepth(ElementType A,int depth)
{
	while (depth!=0)
	{
		printf(" ");
		depth--;
	}
	printf("%d\n",A);
}


//中序遍历
void PrintTree(AVLTree T, int depth)
{
	if (T == NULL)
	{
		perror("wrong tree");
		exit(1);
	}

	if (T->Lchild != NULL)
	{
		PrintTree(T->Lchild,depth+1);
	}
	PrintDepth(T->Element,depth);
	if (T->Rchild != NULL)
	{
		PrintTree(T->Rchild,depth+1);
	}
}



void PrintTree(AVLTree T)
{
	if (T == NULL)
	{
		perror("wrong tree");
		exit(1);
	}
	if (T->Lchild != NULL)
		PrintTree(T->Lchild);

	printf("%d\n", T->Element);
	if (T->Rchild != NULL)
		PrintTree(T->Rchild);
}