数据结构——二叉树的遍历

Description

Little Valentine liked playing with binary trees very much. Her favorite game was constructing randomly looking binary trees with capital letters in the nodes.

This is an example of one of her creations:

                                    D
                                   / 
                                  /   
                                 B     E
                                /      
                               /         
                              A     C     G
                                         /
                                        /
                                       F

To record her trees for future generations, she wrote down two strings for each tree: a preorder traversal (root, left subtree, right subtree) and an inorder traversal (left subtree, root, right subtree).

For the tree drawn above the preorder traversal is DBACEGF and the inorder traversal is ABCDEFG.

She thought that such a pair of strings would give enough information to reconstruct the tree later (but she never tried it).

Now, years later, looking again at the strings, she realized that reconstructing the trees was indeed possible, but only because she never had used the same letter twice in the same tree.

However, doing the reconstruction by hand, soon turned out to be tedious.

So now she asks you to write a program that does the job for her!

Input Specification 

The input file will contain one or more test cases. Each test case consists of one line containing two strings preord and inord, representing the preorder traversal and inorder traversal of a binary tree. Both strings consist of unique capital letters. (Thus they are not longer than 26 characters.)

Input is terminated by end of file.

Output Specification 

For each test case, recover Valentine's binary tree and print one line containing the tree's postorder traversal (left subtree, right subtree, root).

Sample Input 

DBACEGF ABCDEFG
BCAD CBAD

Sample Output 

ACBFGED
CDAB


解题思路：用递归调用的形式，来根据前序，中序求后序，前序遍历的第一个数即是树的根，再将找出根在中序遍历的位置，放在P中，依次调用先序和后序，然后再寻找中序
程序代码：

#include <iostream>
using namespace std;

void build(int n,char * s1,char * s2,char * s)
{
    if(n<=0)    return;
    int p=strchr(s2,s1[0])-s2;
    build(p,s1+1,s2,s);
    build(n-p-1,s1+p+1,s2+p+1,s+p);
    s[n-1]=s1[0];
}
int main()
{
    char s1[30],s2[30],s[30];
    while(cin>>s1>>s2)
    {
        int n=strlen(s1);
        build(n,s1,s2,s);
        s[n]='';
        cout<<s<<"
";
    }
    return 0;
}