AVL树

数据结构与算法分析——c语言描述 第四章树 AVL树

以往都是照抄书上的头文件，自己实现。但是这次avl树insert不会写，竟然抄了这个函数七八成的代码，思路被牵着走，删掉代码重新自己写。看思路，自己写代码，切记切记。其实还是很简单的，画个图什么都懂了。采用懒惰删除，查找函数分两个

然后有一个出了一个bug，死活找不到原因，最后看函数调用情况才找出来，树的高度要记得更新。

所以啊，代码一看就懂，所以自己独立写出来是很有必要的。

avlTree.h

typedef int ElementType;

#ifndef _AvlTree_H
#define _AvlTree_H

struct AvlNode;
typedef struct AvlNode *Position;
typedef struct AvlNode *AvlTree;

AvlTree createAvlTree();
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);
#endif

avlTree.c

#include"avlTree.h"
#include<stdlib.h>
#include"fatal.h"

struct AvlNode {
	ElementType element;
	AvlTree left;
	AvlTree right;
	int isDeleted;
	int height;
};

static int height(Position p) {
	if (p == NULL)
		return -1;
	else {
		return p->height;
	}
}

static int Max(int lhs, int rhs) {
	return lhs > rhs ? lhs : rhs;
}

static Position singleRotateWithLeft(Position k2) {
	Position k1 = k2->left;
	Position y = k1->right;
	k2->left = y;
	k1->right = k2;
	k2->height = Max(height(k2->left), height(k2->right)) + 1;
	k1->height = Max(height(k1->left), height(k1->right)) + 1;
	return k1;
}


static Position singleRotateWithRight(Position k1) {
	Position k2 = k1->right;
	Position y = k2->left;
	k1->right = y;
	k2->left = k1;
	k1->height = Max(height(k1->left), height(k1->right)) + 1;
	k2->height = Max(height(k2->left), height(k2->right)) + 1;
	return k2;
}


static Position doubleRotateWithLeft(Position k3) {
	Position k1 = k3->left;
	k3->left = singleRotateWithRight(k1);
	return singleRotateWithLeft(k3);
}



static Position doubleRotateWithRight(Position k1) {
	Position k3 = k1->right;
	k1->right = singleRotateWithLeft(k3);
	return singleRotateWithRight(k1);
}



AvlTree createAvlTree() {
	return NULL;
}

AvlTree MakeEmpty(AvlTree T) {
	if (T != NULL) {
		MakeEmpty(T->left);
		MakeEmpty(T->right);
		free(T);
	}
	return NULL;
}

static Position findIgnoreDel(ElementType X, AvlTree t) {
	if (t == NULL)
		return NULL;
	else {
		if (X <retrieve(t))
			return findIgnoreDel(X, t->left);
		else if (X>retrieve(t))
			return findIgnoreDel(X, t->right);
		else
			return t;
	}
}

Position find(ElementType X, AvlTree t) {
	Position p = findIgnoreDel(X, t);
	if (p&&p->isDeleted == 0)
		return p;
	else
		return NULL;
}

Position findMin(AvlTree t) {

	if (t) {
		Position p = findMin(t->left);
		if (p)
			return p;
		else if (t->isDeleted == 0)
			return t;
		else
			return NULL;
	}
	return NULL;
}

Position findMax(AvlTree t) {
	if (t) {

		Position p = findMax(t->right);
		if (p)
			return p;
		else if (t->isDeleted == 0)
			return t;
		else
			return NULL;
	}
	return NULL;
}

AvlTree insert(ElementType X, AvlTree t) {
	if (t == NULL) {
		t = malloc(sizeof(struct AvlNode));
		if (t == NULL)
			Error("out of memory");
		t->element = X;
		t->left = NULL;
		t->right = NULL;
		t->height = 0;
		t->isDeleted = 0;
	}
	else if (X < retrieve(t)) {
		t->left = insert(X, t->left);
		if (height(t->left) - height(t->right) == 2) {
			if (X < retrieve(t->left)) {
				t = singleRotateWithLeft(t);
			}
			else
				t = doubleRotateWithLeft(t);
		}
	}
	else if ( X >retrieve(t)) {
		t->right = insert(X, t->right);
		if (height(t->right) - height(t->left) == 2) {
			if (X > retrieve(t->right))
				t = singleRotateWithRight(t);
			else
				t = doubleRotateWithRight(t);
		}
	}
	else {
		t->isDeleted = 0;
	}
	t->height = Max(height(t->left), height(t->right)) + 1;
	return t;
}

AvlTree Delete(ElementType X, AvlTree t) {
	Position p = findIgnoreDel(X, t);
	p->isDeleted = 1;
	return p;
}

ElementType retrieve(Position p) {
	return p->element;
}

main.c

#include"avlTree.h"
#include<stdio.h>
#include<stdlib.h>
struct AvlNode {
	ElementType element;
	AvlTree left;
	AvlTree right;
	int isDeleted;
	int height;
};
int main() {
	AvlTree t = createAvlTree();

	
	for (int i = 1; i < 1234567; i++) {
		t= insert(rand(), t);
	}
		
	printf("%d",t->height);
}