#include<iostream>
#include<stdio.h>
#include<stdlib.h>using namespace std;typedef int Status;constexpr auto LH = +1;
constexpr auto EH = 0;
constexpr auto RH = -1;//定义平衡二叉树的节点结构(在二叉排序树中加入一个bf来存储平衡因子)
typedef struct BiTNode
{int data;int bf;struct BiTNode* lchild, * rchild;
}BiTNode, * BiTree;void R_Rotate(BiTree* p);
void L_Rotate(BiTree* p);
void LeftBalance(BiTree *T);
void RightBalance(BiTree* T);
void InOrderTraverse(BiTree *T);
Status InsertAVL(BiTree *T,int e,Status *taller);//进行二叉平衡树时的右旋操作
void R_Rotate(BiTree *p)
{BiTree L;L = (*p)->lchild;(*p)->lchild = L->rchild;L->rchild = *p;*p = L;
}//进行二叉平衡树时的左旋操作
void L_Rotate(BiTree *p)
{BiTree R;R = (*p)->rchild;(*p)->rchild = R->lchild;R->lchild = (*p);*p = R;
}//构建二叉平衡树时左边太“重”，进行左平衡处理函数
void LeftBalance(BiTree* T)
{BiTree L, Lr;L = (*T)->lchild;switch (L->bf){/*检查T的左子树的平衡度，并做相应的处理*/case LH:/*新节点插入在了T的左孩子的左子树上，只要做单左旋处理*/(*T)->bf = L->bf = EH;R_Rotate(T);break;case RH:/*新节点插入在了T的左孩子的右子树上，要做双旋处理，通过判断T的左孩子的右子树的根节点的bf来决定进行双旋处理后各自的bf值*/Lr = L->rchild;switch (Lr->bf){case LH:(*T)->bf = RH;L->bf = EH;break;case EH:(*T)->bf = L->bf = EH;break;case RH:(*T)->bf = EH;L->bf = LH;break;}Lr->bf = EH;L_Rotate(&(*T)->lchild);R_Rotate(T);}
}//构建二叉平衡树时右边太“重”，进行右平衡处理函数
void RightBalance(BiTree* T)
{BiTree R, Rl;R = (*T)->rchild;switch (R->bf){/*检查T的右子树的平衡度，并做相应的处理*/case RH:/*新节点插入在了T的右孩子的右子树上，只要做单左旋处理*/(*T)->bf = R->bf = EH;L_Rotate(T);break;case LH:/*新节点插入在了T的右孩子的左子树上，要做双旋处理，通过判断T的右孩子的左子树的根节点的bf来决定进行双旋处理后各自的bf值*/Rl = R->lchild;switch (Rl->bf){case LH:(*T)->bf = EH;R->bf = RH;break;case EH:(*T)->bf = R->bf = EH;break;case RH:(*T)->bf = LH;R->bf = EH;break;}Rl->bf = EH;R_Rotate(&(*T)->rchild);L_Rotate(T);}
}//构建二叉平衡树函数
Status InsertAVL(BiTree* T, int e, Status* taller)
{if (!*T){*T = (BiTree)malloc(sizeof(BiTNode));(*T)->data = e;(*T)->bf = EH;(*T)->lchild = (*T)->rchild = NULL;*taller = true;}else{if (e==(*T)->data){*taller = false;return false;}if (e<(*T)->data){int result = InsertAVL(&(*T)->lchild,e,taller);if (!result){return false;}if (*taller){switch ((*T)->bf){case LH:LeftBalance(T);*taller = false;break;case EH:(*T)->bf = LH;*taller = true;break;case RH:(*T)->bf = EH;*taller = false;break;}}}else{int result = InsertAVL(&(*T)->rchild, e, taller);if (!result){return false;}if (*taller){switch ((*T)->bf){case LH:(*T)->bf = EH;*taller = false;break;case EH:(*T)->bf = RH;*taller = true;break;case RH:RightBalance(T);*taller = false;break;}}}}return true;
}//二叉树中序遍历递归算法
void InOrderTraverse(BiTree* T)
{if (*T==NULL){return;}InOrderTraverse(&(*T)->lchild);cout << (*T)->data << " ";InOrderTraverse(&(*T)->rchild);
}int main()
{int i;int a[10] = {3,2,1,4,5,6,7,10,9,8};BiTree T = NULL;Status Numtaller;for ( i = 0; i < 10; i++){InsertAVL(&T,a[i],&Numtaller);}//中序遍历输出结果InOrderTraverse(&T);
}