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