Algorithms: 二叉平衡树(AVL)

二叉平衡树(AVL):

  这个数据结构我在三月份学数据结构结构的时候遇到过。但当时没调通。也就没写下来。前几天要用的时候给调好了！详细AVL是什么，我就不介绍了，维基百科都有。

 后面两月又要忙了。和同学组队去比赛，预计博客这边也不常写了。等这段时间过了再继续更新！

 这是我第一次画电路图（原理图）晒晒，事实上我对电子非常感兴趣的。看着网上人家做的电子作品。就想自己也做做。兴奋的想试试。呵呵，以后我做电子小作品了也把他放到博客，开源和大家一起分享。DIY的乐趣。

 

 

 

第一次正儿八经会电路图，别笑啊！

 

/*------------------------------------------------------------------------------------
 * Project: AVLTree.h
 * Name: zwp
 * Date: 2014/3
 *------------------------------------------------------------------------------------*/

#ifndef AVLTREE_H_
#define AVLTREE_H_

typedef int ElementType;

typedef struct AvlNode
{
	ElementType Element;
	AvlNode*	Left;
	AvlNode*    	Right;
	int			Height;

}*AvlTree;

/*
** 初始化
*/
AvlTree Initialize(void);

/*
** 遍历树
*/
void Traverse(AvlTree H);

/*
** 清空元素
*/
void MakeEmpty(AvlTree H);

/*
** 寻找元素
*/
AvlTree Find(ElementType X, AvlTree T);

/*
** 找最大
*/
AvlTree FindMax(AvlTree T);

/*
** 找最小
*/
AvlTree FindMin(AvlTree T);

/*
** 插入元素
*/
AvlTree Insert(ElementType X, AvlTree T);

/*
** 删除元素
*/
AvlTree Delete(ElementType X, AvlTree T);

#endif

 

/*-----------------------------------------------------------------------------
 * Project: AVLTree.cpp
 * Name: zwp
 * Date: 2014/3
 *------------------------------------------------------------------------------*/

#include "AVLTree.h"
#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>

/*
** 返回树的高度
*/
static int Height(AvlTree P)
{
	if(P == NULL)
		return -1;
	else
		return P->Height;
}

/*
** 返回最大值
*/
int Max(int num1, int num2)
{
	return ((num1 > num2) ?

num1 : num2);
}

/*
** 右旋转
*/
static AvlTree SingleRotateWithLeft(AvlTree K2)
{
	AvlTree K1;

	K1 = K2->Left;
	K2->Left = K1->Right;
	K1->Right = K2;

	K2->Height = Max(Height(K2->Left), Height(K2->Right)) + 1;

	K1->Height = Max(Height(K1->Left), K2->Height) + 1;

	return K1;

}

/*
** 左旋转
*/
static AvlTree SingleRotateWithRight(AvlTree K2)
{
	AvlTree K1;

	K1 = K2->Right;
	K2->Right = K1->Left;
	K1->Left = K2;

	K2->Height = Max(Height(K2->Left), Height(K2->Right)) + 1;
	K1->Height = Max(Height(K1->Right), K2->Height) + 1;

	return K1;
}

/*
** 右双旋转
*/
static AvlTree DoubleRotateWithLeft(AvlTree K3)
{
	/* Rotate between K1 and K2
	 * K2 Left Rotate
	 */
	K3->Left = SingleRotateWithRight(K3->Left);	

	/* Rotate between K3 and K2
	 * K2 Right Rotate
	 */
	return SingleRotateWithLeft(K3);

}

/*
** 左双旋转
*/
static AvlTree DoubleRotateWithRight(AvlTree K3)
{
	/* Rotate between K1 and K2
	 * K2 Right Rotate
	 */
	K3->Right = SingleRotateWithLeft(K3->Right);	

	/* Rotate between K3 and K2
	 * K2 Left Rotate
	 */
	return SingleRotateWithRight(K3);

}

AvlTree Insert(ElementType X, AvlTree T)
{
	if(T == NULL)
	{
		/* Create and return a one-node tree */
		T = (AvlTree)malloc(sizeof(struct AvlNode));
		if(T == NULL)
			printf("Out of space...\n");
		else
		{
			T->Element = X;
			T->Height  = 0;
			T->Left = T->Right = NULL;
		}

	}
	else if(X < T->Element)			/* 插入树的左子枝 */
	{
		T->Left = Insert(X, T->Left);
		/* 左子树的高度与右子树高度相差2 */
		if(Height(T->Left) - Height(T->Right) == 2)
		{
			if(X < T->Left->Element)
				T = SingleRotateWithLeft(T);		/* CASE : left-left sing rotate Right   */
			else
				T = DoubleRotateWithLeft(T);		/* CASE : left-right double rotate Right */
		}
	}
	else if(X > T->Element)			/* 插入树的右子枝 */
	{
		T->Right = Insert(X, T->Right);
		/* 右子树的高度与左子树高度相差2 */
		if(Height(T->Right) - Height(T->Left) == 2)
		{
			if(X > T->Right->Element)
				T = SingleRotateWithRight(T);		/* CASE: right-right sing rotate Left */
			else
				T = DoubleRotateWithRight(T);		/* CASE: right-left double rotate Left */
		}
	}

	/*
	 * else X is in the tree already
	 * +1 because root Node
	 */
	T->Height = Max(Height(T->Left), Height(T->Right)) + 1; 

	return T;
}

/*
** 初始化
*/
AvlTree Initialize(void)
{
	/* Create and return a one-node tree */
	AvlTree T = (AvlNode*)malloc(sizeof( struct AvlNode));
	T->Element = 0;
	T->Height = 0;
	T->Left = T->Right = NULL;

	return T;

}

/*
** 寻找元素
*/
AvlTree Find(ElementType X, AvlTree T)
{
	if(T == NULL)
		return NULL;
	if(X < T->Element)
		return Find(X, T->Left);
	else if(X > T->Element)
		return Find(X, T->Right);
	else
		return T;
}

/*
** 找最大
*/
AvlTree FindMax(AvlTree T)
{
	ElementType max = 0;
	AvlTree P = T;

	/* Find in AVLTree Right */
	while(P != NULL)
	{
		if(max < P->Element)
		{
			max = P->Element;
			P = P->Right;
		}
		else
			P = P->Right;
	}
	return P;
}

/*
** 找最小
*/
AvlTree FindMin(AvlTree T)
{
	ElementType min = 0;
	AvlTree P = T;

	while(P != NULL)
	{
		if(min > P->Element)
		{
			min = P->Element;
			P = P->Left;
		}
		else
			P = P->Left;

	}
	return P;
}

/*
** 删除元素
*/
AvlTree Delete(ElementType X, AvlTree T)
{
	AvlTree TmpCell;

	if(T == NULL)
		printf("Elememt not found....\n");
	else if(X < T->Element)
		T->Left = Delete(X, T->Left);		/* Go Left */
	else if(X > T->Element)
		T->Right = Delete(X, T->Right);		/* Go Right */
	else if(T->Left && T->Right)
	{
		/*
		** Two children
		** Replace with smallest in right subtree
		*/
		TmpCell = FindMin(T->Right);
		T->Element = TmpCell->Element;
		T->Height = TmpCell->Height;
		T->Right = Delete(T->Element, T->Right);
	}
	else
	{
		/*
		** One or zero children
		*/
		TmpCell = T;
		if(T->Left == NULL)
			T = T->Right;
		else if(T->Right == NULL)
			T = T->Left;
		free(TmpCell);
	}

	return T;
}

/*
** 清空元素
*/
void MakeEmpty(AvlTree H)
{
	if(H != NULL)
	{
		MakeEmpty(H->Left);
		MakeEmpty(H->Right);
		free(NULL);
	}
}

/*
** 遍历树
*/
void Traverse(AvlTree H)
{

	if(H != NULL)
	{
		Traverse(H->Left);
		printf("%d \n", H->Element);
		Traverse(H->Right);
	}

}

 

/*-----------------------------------------------------------------------------
 * Project: Main.cpp
 * Name: zwp
 * Date: 2014.3
 *------------------------------------------------------------------------------*/

#include "AVLTree.h"
#include <stdio.h>
#include <stdlib.h>

int main(int argc, char* argv[])
{

	AvlTree T =  Initialize();

	for(int index = 0; index < 10; ++ index)
		T = Insert(index, T);

	Traverse(T);

	//printf("%d \n", Find(3, T));

	system("pause");

}