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搜索（DFS）

2024-07-03 07:30:24   231人阅读

Sum It Up
Time Limit: 1000MS   Memory Limit: 10000K
Total Submissions: 5684   Accepted: 2894

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 x 1 , . . . , x n . 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 x 1 , . . . , x n 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 distinct; the same sum cannot 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
?
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#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
 
using namespace std;
 
const int maxn=10+5;
int a[maxn],cur[maxn];
int ok,sum,n;
 
inline void DFS(int index,int cursum,int cnt)
{
    if(cursum==0)
    {
        ok=0;
        printf("%d",cur[0]);
        for(int i=1;i<cnt;i++)
        {
            printf("+%d",cur[i]);
        }
        printf("\n");
        return ;
    }
    else
    {
        for(int i=index;i<n;i++)
        {
            if(i==index||a[i]!=a[i-1])      //注意去重，如果当前这个数是这一层的第一个，一定要，如果不是第一个，并且和前一个相同，就不用考虑
            {　　　　　　　　　　　　　　　　　　//因为如果与前面一个相同，就相当于当前这个串是前面的一个子串
                cur[cnt]=a[i];
                DFS(i+1,cursum-a[i],cnt+1);
            }
        }
    }
    return ;
}
 
int main()
{
    while(scanf("%d%d",&sum,&n)!=EOF&&n!=0)
    {
        memset(cur,0,sizeof(cur));
        memset(a,0,sizeof(a));
 
        for(int i=0;i<n;i++)
        scanf("%d",&a[i]);
 
        ok=1;
        printf("Sums of %d:\n",sum);
        DFS(0,sum,0);
 
        if(ok)
        printf("NONE\n");
    }
    return 0;
}

 


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