uva-10344 - 23 out of 5

最新推荐文章于 2021-01-20 21:52:48 发布

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#回溯法

本文详细介绍了如何使用递归和排列组合的方法解决数学问题，即从五个给定的正整数中找出一个算术表达式，使其结果为23。通过枚举数的排列顺序和符号状态，实现对所有可能组合的搜索，从而判断是否存在符合条件的表达式。

Problem I

23 Out of 5

Input: standard input

Output: standard output

Time Limit: 1 second

Memory Limit: 32 MB

Your task is to write a program that can decide whether you can find an arithmetic expression consisting of five given numbers (1<=i<=5) that will yield the value 23.
For this problem we will only consider arithmetic expressions of the following from:

where : {1,2,3,4,5} -> {1,2,3,4,5} is a bijective function

and  {+,-,*} (1<=i<=4)

1 1 1 1 1

1 2 3 4 5

2 3 5 7 11

0 0 0 0 0

Sample Output

Impossible

Possible

Possible

先枚举5个数的排列顺序，再搜索4个符号的状态+-*。

#include <iostream>
#include <algorithm>

using namespace std;

int num[5];   
int pos[5];  //保存5个数的排列顺序

int search(int cur, int value)
{
    if(cur == 5){
        return value == 23 ? 1 : 0;
    }

    if(search(cur+1, value*num[pos[cur]])) return 1;
    if(search(cur+1, value+num[pos[cur]])) return 1;
    return search(cur+1, value-num[pos[cur]]);
}

int main()
{
    while(1){
        int ans, sum = 0;
        for(int i = 0; i < 5; i++){
            cin >> num[i];
            sum += num[i];
            pos[i] = i;
        }
        if(!sum) break; //全都为0跳出 循环

        do{
            ans = search(1, num[pos[0]]);
            if(ans) break;
        }while(next_permutation(pos, pos+5));

        if(ans) cout << "Possible\n";
        else cout << "Impossible\n";

    }
    return 0;
}