必备算法之二叉树的相关操作

树的结构定义如下

typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
    ElementType Data;
    BinTree Left;
    BinTree Right;
};

1、求树的高度

int GetHeight( BinTree BT )
{
    int h=0;
    int hl,hr;
    if( !BT)
    {
        h = 0;
    }
    else
    {
        hl = GetHeight(BT->Left);  //左子树高度
        hr = GetHeight(BT->Right); //右子树高度
        if( hl>hr)
        {
            h = hl+1;
        }
        else
        {
            h = hr+1;
        }
    }

    return h;
}

2、树的先序遍历

void PreorderTraversal( BinTree BT )
{
    if( BT==NULL )
        return;

    printf(" %c",BT->Data);
    PreorderTraversal(BT->Left);
    PreorderTraversal(BT->Right);
}

3、树的中序遍历

void InorderTraversal( BinTree BT )
{
    if( BT==NULL )
        return;

    InorderTraversal(BT->Left);
    printf(" %c",BT->Data);
    InorderTraversal(BT->Right);
}

4、树的后序遍历

void PostorderTraversal( BinTree BT )
{
    if( BT==NULL )
        return;

    PostorderTraversal(BT->Left);
    PostorderTraversal(BT->Right);
    printf(" %c",BT->Data);
}

5、树的层次遍历

void LevelorderTraversal( BinTree BT )
{
    if(BT==NULL)
        return ;
        
    BinTree T[100];
    int i=0,j=0;
    T[j++]=BT;
    while(i<j)
    {
        BinTree s=T[i];
        printf(" %c",s->Data);
        if(s->Left)
            T[j++]=s->Left;
        if(s->Right)
            T[j++]=s->Right;
        i++;
    }
}

 6.树的还原——已知先序中序

#include<stdio.h>
#include<stdlib.h>
#include<string.h>

typedef struct TNode
{
    char data;
    struct TNode *lchild,*rchild;
} TNode,*Tree;

Tree CreatTree( char xian[],char zhong[],int n);
int GetHigh( Tree t);

char xian[55];   //先序序列
char zhong[55];  //中序序列
int n;

int main()
{
    scanf("%d",&n);
    scanf("%s",xian);
    scanf("%s",zhong);
    Tree tree = CreatTree( xian,zhong,n);
    printf("%d",GetHigh(tree));
    return 0;
}

Tree CreatTree( char xian[],char zhong[],int n)
{
    if( n==0 ) return NULL;
    int index = 0;
    Tree temp = (Tree) malloc(sizeof(struct TNode));

    while( index < n)
    {
        if( zhong[index]==xian[0]) break;
        index ++;
    }
    temp->data = xian[0];
    temp->lchild = CreatTree(xian+1,zhong,index);
    temp->rchild = CreatTree(xian+1+index,zhong+index+1,n-index-1);
    return temp;
}

   树的还原——已知中序后序

BinTree Creathou( char zhong[],char hou[],int n)
{
    if( n==0 ) return NULL;
    int index=0;
    BinTree temp;
    temp=( BinTree)malloc(sizeof(struct Node));
    while( index<n)
    {
        if( zhong[index]==hou[n-1])
            break;
        index++;
    }
    temp->data = hou[n-1];
    temp->left = Creathou( zhong,hou,index);
    temp->right = Creathou(zhong+index+1,hou+index,n-index-1);
    return temp;
}