【分治】POJ-2255 Tree Recovery

Tree Recovery

Time Limit: 1000MS		Memory Limit: 65536K

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

The input 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

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

————————————————————ゆっくりとの分割線————————————————————

思路：有了中序，还差一个就可以唯一确定一棵树。
这样就可以采取分治的思想：
左            根            右
左   根   右|左   根   右
    。。。       。。。
代码如下：

/*
ID: j.sure.1
PROG:
LANG: C++
*/
/****************************************/
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <ctime>
#include <cmath>
#include <stack>
#include <queue>
#include <vector>
#include <map>
#include <set>
#include <string>
#include <climits>
#include <iostream>
#define LL long long
using namespace std;
const int INF = 0x3f3f3f3f;
/****************************************/
int n;
//s1:根左右 s2:左根右
void build(int cur, char *s1, char *s2)
{
if(cur <= 0) return ;
int p = 0;
while(s2[p] != s1[0]) p++;
build(p, s1+1, s2);//s2中p左边都是左儿子，p右边都是右儿子
build(cur-p-1, s1+p+1, s2+p+1);
putchar(s1[0]);
}

int main()
{
#ifdef J_Sure
//	freopen("000.in", "r", stdin);
//	freopen(".out", "w", stdout);
#endif
char s1[30], s2[30];
while(~scanf("%s%s", s1, s2)) {
n = strlen(s1);
build(n, s1, s2);
puts("");
}
return 0;
}