2017年上海金马五校程序设计竞赛：Problem C : Count the Number

Problem C : Count the Number

From: DHUOJ, 2017060303

Submit (Out of Contest)

Time Limit: 3 s

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Description

Given n numbers, your task is to insert '+' or '-' in front of each number to construct expressions. Note that the position of numbers can be also changed.

You can calculate a result for each expression. Please count the number of distinct results and output it.

 

Input

There are several cases.
For each test case, the first line contains an integer n (1 ≤ n ≤ 20), and the second line contains n integers a₁,a₂, ... ,a_n(-1,000,000,000 ≤ a_i ≤ 1,000,000,000).

 

Output

For each test case, output one line with the number of distinct results.

 

Sample Input

21 231 3 5

 

Sample Output

48

题目意思：

给出一个数n，n的规模不超过20（问题规模比较小），接下来一行给出N个数字，然后我们可以在任何一个数字前面放置+或-号。然后计算出一个值。

问由这组数经过不同的加减组合能得到多少种不同的答案。

解题思路：

这个也是简单题，题目时间给了3秒，问题规模不超过20也不大，直接暴力，dfs + map(用来映射某个答案出没出现过)

#include<iostream>#include<stdio.h>#include<string.h>#include<algorithm>#include<map>using namespace std;long long a[25];map<long long,int>m;long long ans;int n;void dfs(int sum,int i){    if(i == n+1)    {       if(m[sum]==0) ///没有出现过       {           m[sum] = 1;           ans++;       }       return;    }    dfs(sum+a[i],i+1);    dfs(sum-a[i],i+1);}int main(){    while(~scanf("%d",&n))    {        for(int i = 1; i <= n; i++)            scanf("%d",&a[i]);        m.clear();        ans = 0;        dfs(0,1);        printf("%d\n",ans);    }    return 0;}