判断是否是平衡二叉树

本文有两种方法判断一棵树是否为AVL树


#include <iostream>
#include<math.h>   //abs
#include<queue>
#include <string>
using namespace std;

typedef struct TreeNode
{
    string data;
    struct TreeNode* lchild;
    struct TreeNode* rchild;
}TreeNode;

void levelTraver(TreeNode* T)  //层次遍历
{
    if (!T)
        return;

    queue<TreeNode*> Q;

    TreeNode* cur = T;

    Q.push(cur);
    while (!Q.empty())
    {
        cout << Q.front()->data << " ";
        cur = Q.front();
        Q.pop();
        if (cur->lchild)
            Q.push(cur->lchild);
        if (cur->rchild)
            Q.push(cur->rchild);
    }
}

TreeNode* NodebyString(string s)  //根据s的值
{
    if (s == "#") //若str[i]的值为#，则不创建节点
        return NULL;
    else  //否则，创建节点并返回
    {
        TreeNode* node = new TreeNode;
        node->data = s;

        return node;
    }
}

TreeNode* levelDeSerialize(string str[])  //层序反序列化
{
    int index1 = 0;

    TreeNode* T = NodebyString(str[index1++]);

    queue<TreeNode*> Q;
    if (T != NULL)
        Q.push(T);

    TreeNode* cur;

    while (!Q.empty())
    {
        cur = Q.front();
        Q.pop();

        cur->lchild = NodebyString(str[index1++]);
        cur->rchild = NodebyString(str[index1++]);
        if (cur->lchild)
            Q.push(cur->lchild);
        if (cur->rchild)
            Q.push(cur->rchild);
    }
    return T;
}

int height(TreeNode* T)  //求树的高度
{
    if (!T)
        return 0;

    //后序遍历求树的高度
    int LH = height(T->lchild);
    int RH = height(T->rchild);

    return (LH > RH) ? (1 + LH) : (1 + RH);
}

//方法一：
bool isAVLTree1(TreeNode* T)  //是否为平衡二叉树
{
    if (!T)  //求以T为根的二叉树是否为AVL树
        return true;

    int LH = height(T->lchild); //求左子树的高度
    int RH = height(T->rchild); //求右子树的高度

    if (abs(LH - RH) > 1)
        return false;

    //再判断T的左子树和右子树是否为AVL树
    return isAVLTree1(T->lchild) && isAVLTree1(T->rchild);  
}

//方法二：
//二叉树的层序遍历，顺便记录每一个节点的高度depth、平衡性
bool isAVLTree2(TreeNode* T,int &depth)  //传入的必须是引用
{
    if (!T)
    {
        depth = 0;
        return true;
    }

    int LH = 0;
    int RH = 0;
    if (isAVLTree2(T->lchild, LH) && isAVLTree2(T->rchild, RH))
    {
        if (abs(LH - RH) <= 1)
        {
            depth = 1 + (LH > RH ? LH : RH);
            return true;
        }
    }
    return false;
}


int main()
{
    string str[] = { "1", "2", "3", "#", "4", "5", "#", "6", "#", "#", "#", "#","#" };

    TreeNode* T = levelDeSerialize(str); //反序列化

    cout << "层序遍历" << endl;
    levelTraver(T);
    cout << "\n高度 = ";
    int H = height(T);
    cout << H << endl;

    int depth = 0;

    bool isAVL = isAVLTree2(T, depth);
    cout <<"是否为平衡二叉树"<<isAVL << endl;

    return 0;
}