二叉树平衡因子应用举例

#include "stdafx.h"
#include <fstream>
#include <iostream>
using namespace std;

typedef struct _Node
{
    int data;
    struct _Node *left;
    struct _Node *right;
    int bf;              //平衡因子
    _Node()
    {
        data = 0;
        left = NULL;
        right = NULL;
        bf = 0;
    }
}Node, *_PNode;

//创建二叉树利用先序创建
/*
                                             1
                                          /     \
                                         2       3
                                        / \      / 
                                       4   5    6
                                      / \   \  / \
                                     7   8  9  10 11
                                    /     \
                                   12      13
*/
void CreateBitree(_PNode &pNode, fstream &fin)
{
    int dat;
    fin>>dat;
    if(dat==0)
    {
        pNode = NULL;
    }
    else 
    {
        pNode = new Node();
        pNode->data=dat;      
        CreateBitree(pNode->left, fin);      
        CreateBitree(pNode->right, fin);
    }
}


//**************************************求各结点的平衡因子**************************************begin

//递归求二叉树的深度
int Depth(_PNode pNode)
{
    if (NULL != pNode)
    {
        int hl = Depth(pNode->left);
        int hr = Depth(pNode->right);
        return hl > hr ? hl + 1: hr + 1;
    }
    return 0;
}

//递归求二叉树每个结点的平衡因子
void Balance(_PNode pNode)
{
    if (NULL != pNode)
    {
        Balance(pNode->left);
        Balance(pNode->right);
    
        int hl = Depth(pNode->left);
        int hr = Depth(pNode->right);
        pNode->bf = hl - hr;
    }
}

//前序递归遍历
void PreTravelTree(_PNode pRoot)       
{
    if(pRoot)
    {
        cout<<pRoot->data<<"("<<pRoot->bf<<")"<<" ";
        PreTravelTree(pRoot->left);    
        PreTravelTree(pRoot->right);
    }
}

//中序递归遍历
void MidTravelTree(_PNode pRoot)        
{
    if(pRoot)
    {
        MidTravelTree(pRoot->left);  
        cout<<pRoot->data<<"("<<pRoot->bf<<")"<<" ";
        MidTravelTree(pRoot->right);
    }
}

//**************************************求各结点的平衡因子**************************************end

int _tmain(int argc, _TCHAR* argv[])
{
    _PNode pRoot = NULL;
    fstream fin("tree.txt");
    CreateBitree(pRoot, fin);
    Balance(pRoot);
    cout<<"前序：";
    PreTravelTree(pRoot);
    cout<<endl<<"后序：";
    MidTravelTree(pRoot);
    cout<<endl;
    return 0;
}

运行界面如下：

建造二叉树用到的tree.txt文件如下：

1 2 4 7 12 0 0 0 8 0 13 0 0 5 0 9 0 0 3 6 10 0 0 11 0 0 0