2015 HUAS Summer Training#2 D

最新推荐文章于 2023-07-23 16:49:50 发布

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最新推荐文章于 2023-07-23 16:49:50 发布

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文章标签：数据结构与算法

原文链接：http://www.cnblogs.com/huaxiangdehenji/p/4674657.html

本文介绍了一种根据二叉树的先序遍历和中序遍历字符串来重建二叉树的方法，并通过递归方式构建二叉树，最后输出后序遍历结果。

题目：

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).

题目大意：给你树的先序遍历和中序遍历，要你输出后序遍历。

解题思路：给个结构体有树的根左子树和右子数。用递归把树构建起来。在输出。

代码：

 1 #include<iostream>
 2 #include<cstring>
 3 using namespace std;
 4 const int maxn=30;
 5 struct  shu
 6 {
 7     char a;
 8     shu* l;
 9     shu* r;
10 }b[maxn];
11 shu* goujianshu(shu* d,char* q,char* w,int n)
12 {
13     int i;
14     if(n==0)
15         return NULL;
16     for(i=0;i<n;i++)
17     {
18         if(q[0]==w[i])
19         {
20             d->a=q[0];
21             d->l=goujianshu(d+1,q+1,w,i);
22             d->r=goujianshu(d+1+i,q+i+1,w+i+1,n-i-1);
23         }
24     }
25     return d;
26 }
27 void houxu(shu* d)
28 {
29     if(d==NULL)
30         return;
31     houxu(d->l);
32     houxu(d->r);
33     cout<<char(d->a);
34 }
35 int main()
36 {
37     char e[maxn],t[maxn];
38     while(cin>>e>>t)
39     {
40         goujianshu(b,e,t,strlen(e));
41         houxu(b);
42         cout<<endl;
43     }
44     return 0;
45 }