usaco3.4.1 American Heritage

最新推荐文章于 2023-01-05 16:48:43 发布

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本文介绍了一种根据给定的二叉树前序遍历和中序遍历来求解后序遍历的方法。通过使用C++实现，构建了二叉树结构，并通过递归算法实现了从输入到输出的转换。

一原题

American Heritage

Farmer John takes the heritage of his cows very seriously. He is not, however, a truly fine bookkeeper. He keeps his cow genealogies as binary trees and, instead of writing them in graphic form, he records them in the more linear `tree in-order' and `tree pre-order' notations.

Your job is to create the `tree post-order' notation of a cow's heritage after being given the in-order and pre-order notations. Each cow name is encoded as a unique letter. (You may already know that you can frequently reconstruct a tree from any two of the ordered traversals.) Obviously, the trees will have no more than 26 nodes.

Here is a graphical representation of the tree used in the sample input and output:

The in-order traversal of this tree prints the left sub-tree, the root, and the right sub-tree.

The pre-order traversal of this tree prints the root, the left sub-tree, and the right sub-tree.

The post-order traversal of this tree print the left sub-tree, the right sub-tree, and the root.

PROGRAM NAME: heritage

INPUT FORMAT

Line 1:	The in-order representation of a tree.
Line 2:	The pre-order representation of that same tree.

SAMPLE INPUT (file heritage.in)

ABEDFCHG
CBADEFGH

OUTPUT FORMAT

A single line with the post-order representation of the tree.

SAMPLE OUTPUT (file heritage.out)

AEFDBHGC

二分析

给定二叉树的前序遍历和中序遍历，求后序遍历。

三代码

运行结果：

USER: Qi Shen [maxkibb3]
TASK: heritage
LANG: C++

Compiling...
Compile: OK

Executing...
   Test 1: TEST OK [0.000 secs, 4188 KB]
   Test 2: TEST OK [0.000 secs, 4188 KB]
   Test 3: TEST OK [0.000 secs, 4188 KB]
   Test 4: TEST OK [0.000 secs, 4188 KB]
   Test 5: TEST OK [0.000 secs, 4188 KB]
   Test 6: TEST OK [0.000 secs, 4188 KB]
   Test 7: TEST OK [0.000 secs, 4188 KB]
   Test 8: TEST OK [0.000 secs, 4188 KB]
   Test 9: TEST OK [0.000 secs, 4188 KB]

All tests OK.

YOUR PROGRAM ('heritage') WORKED FIRST TIME! That's fantastic -- and a rare thing. Please accept these special automated congratulations.

AC代码：

/*
ID:maxkibb3
LANG:C++
PROB:heritage
*/

#include<iostream>
#include<fstream>
using namespace std;

string in, pre, post;
ifstream fin;
ofstream fout;
int pre_idx;

struct Node {
    char val;
    Node *left, *right;
};

Node *build_tree(int l, int r) {
    if(l > r) return NULL;
    Node *root = new Node();
    pre_idx++;
    int in_idx = in.find(pre[pre_idx]);
    root->val = pre[pre_idx];
    if(l != r) {
        root->left = build_tree(l, in_idx - 1);
        root->right = build_tree(in_idx + 1, r);
    }
    return root;
}

void post_dfs(Node *node) {
    if(!node) return;
    post_dfs(node->left);
    post_dfs(node->right);
    fout << node->val;
}

int main() {
    fin.open("heritage.in");
    fout.open("heritage.out");

    fin >> in >> pre;

    pre_idx = -1;
    Node *root = build_tree(0, in.length() - 1);
    post_dfs(root);
    fout << endl;
    delete root;

    fin.close();
    fout.close();
}