Sum It Up(HDU-1258)

最新推荐文章于 2020-09-03 14:54:13 发布

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本文介绍了一个经典的组合问题——寻找列表中元素的所有可能组合，这些组合的和等于给定的目标值。通过递归深度优先搜索的方法，结合使用集合来避免重复结果，实现了问题的有效解决。

Problem Description

Given a specified total t and a list of n integers, find all distinct sums using numbers from the list that add up to t. For example, if t=4, n=6, and the list is [4,3,2,2,1,1], then there are four different sums that equal 4: 4,3+1,2+2, and 2+1+1.(A number can be used within a sum as many times as it appears in the list, and a single number counts as a sum.) Your job is to solve this problem in general.

Input

The input will contain one or more test cases, one per line. Each test case contains t, the total, followed by n, the number of integers in the list, followed by n integers x1,...,xn. If n=0 it signals the end of the input; otherwise, t will be a positive integer less than 1000, n will be an integer between 1 and 12(inclusive), and x1,...,xn will be positive integers less than 100. All numbers will be separated by exactly one space. The numbers in each list appear in nonincreasing order, and there may be repetitions.

Output

For each test case, first output a line containing 'Sums of', the total, and a colon. Then output each sum, one per line; if there are no sums, output the line 'NONE'. The numbers within each sum must appear in nonincreasing order. A number may be repeated in the sum as many times as it was repeated in the original list. The sums themselves must be sorted in decreasing order based on the numbers appearing in the sum. In other words, the sums must be sorted by their first number; sums with the same first number must be sorted by their second number; sums with the same first two numbers must be sorted by their third number; and so on. Within each test case, all sums must be distince; the same sum connot appear twice.

Sample Input

4 6 4 3 2 2 1 1
5 3 2 1 1
400 12 50 50 50 50 50 50 25 25 25 25 25 25
0 0

Sample Output

Sums of 4:
4
3+1
2+2
2+1+1
Sums of 5:
NONE
Sums of 400:
50+50+50+50+50+50+25+25+25+25
50+50+50+50+50+25+25+25+25+25+25

题目大意：输入一个sum，和n个数据，输出所有数据组合相加和为sum的组合，输出不重复；

思路：普通的dfs，用set判重；

代码如下：

#include<bits/stdc++.h>
using namespace std;
int sum,a[15],n,b[15],flag;
set<vector<int> >p;
void dfs(int s,int pos,int k)
{
    if(s==sum)
    {
        flag=0;
        vector<int>v;
        for(int i=0;i<k;i++)
            v.push_back(b[i]);
        if(p.find(v)==p.end())
        {
            for(int i=0;i<k-1;i++)
            cout<<b[i]<<'+';
            cout<<b[k-1]<<endl;
            p.insert(v);
        }
        return;
    }
    for(int i=pos+1;i<n;i++)
    {
        b[k]=a[i];
        dfs(s+a[i],i,k+1);
    }

}
int main()
{
    while(cin>>sum>>n&&sum&&n)
    {
        flag=1;
        for(int i=0;i<n;i++)
            cin>>a[i];
        cout<<"Sums of "<<sum<<':'<<endl;
        dfs(0,-1,0);
        if(flag)
            cout<<"NONE\n";
    }
    return 0;
}