平衡二叉树

#include<stdio.h>#include <stdlib.h>#define LH (1)#define EH (0)#define RH (-1)typedef struct BSTNode {int key;int bf;struct BSTNode * lchild, * rchild;} BSTNode, * BSTree;// 右旋处理void R_Rotate(BSTree &p) {// 对*p为根的二叉排序树做右旋处理，即旋转之后p指向新的树根节点，即旋转处理之前左孩子树的根节点。BSTree lc = p->lchild;p->lchild = lc->rchild;lc->rchild = p;p = lc;} // R_Rotate// 左旋处理void L_Rotate(BSTree &p) {// 对*p为根的二叉树做左旋处理BSTree rc = p->rchild;p->rchild = rc->lchild;rc->lchild = p;p = rc;} // L_Rotateint Compare(int key1, int key2) {if(key1 > key2)return LH;else if(key1 == key2) return EH;return RH;}void LeftBalance(BSTree &T){// 对指针T所指节点的二叉树左左旋平衡处理，算法结束指针T指向"新"的节点BSTree lc = T->lchild;switch(lc->bf) {case LH:T->bf = lc->bf = EH;R_Rotate(T);break;case RH:BSTree rd = lc->rchild;switch(rd->bf) {case LH:T->bf = RH; lc->bf = EH;break;case EH:T->bf = lc->bf = EH;break;// 该标签不会调用case RH:T->bf = EH; lc->bf = LH;break;break;}rd->bf = EH;L_Rotate(T->lchild);R_Rotate(T);break;} // switch(lc->bf)} // LeftBalancevoid RightBalance(BSTree &T) {BSTree rc = T->rchild;BSTree rd = rc->lchild;switch(rc->bf){case LH:switch(rd->bf){case LH: T->bf = EH; rc->bf = RH;break;case EH: T->bf = rc->bf = EH;break;// 该标签不会调用case RH: T->bf = LH; rc->bf = EH;break;}rd->bf = EH;R_Rotate(T->rchild);L_Rotate(T);break;case RH:T->bf = rc->bf = EH;L_Rotate(T);break;}}bool Insert(BSTree &T, int key, bool &taller) {// 插入节点为1，否则返回0，若因插入而使二叉树失去平衡，则做平衡旋转，taller反应T是否长高// child表示旋转之后子树的根节点if( !T ) {T = (BSTree) malloc(sizeof(BSTNode));T->key = key;T->rchild = T->lchild = NULL;T->bf = EH;//标识插入节点为等高taller = true;//插入之后高度增加} // if(!T))else {if(EH == Compare(T->key, key)) {taller = true;return false;} if(LH == Compare(T->key, key)){if(!Insert(T->lchild, key, taller)) return 0;// 未插入返回if(true == taller) {switch(T->bf) {// 在该处做左旋处理case LH: LeftBalance(T); taller = false; break;case  EH:T->bf = LH; taller = true; break;case RH:T->bf = EH; taller = false;break;} // switch(T->bf)} // if(true == taller)} else {if(!Insert(T->rchild, key, taller)) return 0;// 未插入数据if(true == taller) {switch(T->bf) {case LH: T->bf = EH; taller = false;break;case EH: T->bf = RH; taller = true;break;// 右旋处理case RH: RightBalance(T), taller = false;break;}}} // else} // else (!T)} // Insertvoid Print(BSTree &T) {if(T) {printf("%d ", T->key);Print(T->lchild);Print(T->rchild);}}void main() {BSTree T = NULL;bool taller = false;Insert(T, 13, taller);Insert(T, 24, taller);Insert(T, 37, taller);Insert(T, 90, taller);Insert(T, 53, taller);Insert(T, 60, taller);Insert(T, 40, taller);Insert(T, 50, taller);Print(T);system("pause");}