Hdu1342 Lotto

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本文介绍了一种基于深度优先搜索(DFS)的算法，用于解决从给定的k个数中选择6个数进行Lotto游戏的问题。该算法通过递归的方式枚举所有可能的组合，并确保每组数按升序排列。

Lotto

Time Limit : 2000/1000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 16 Accepted Submission(s) : 8

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Problem Description

In a Lotto I have ever played, one has to select 6 numbers from the set {1,2,...,49}. A popular strategy to play Lotto - although it doesn't increase your chance of winning - is to select a subset S containing k (k>6) of these 49 numbers, and then play several games with choosing numbers only from S. For example, for k=8 and S = {1,2,3,5,8,13,21,34} there are 28 possible games: [1,2,3,5,8,13], [1,2,3,5,8,21], [1,2,3,5,8,34], [1,2,3,5,13,21], ... [3,5,8,13,21,34].

Your job is to write a program that reads in the number k and the set S and then prints all possible games choosing numbers only from S.

Input

The input file will contain one or more test cases. Each test case consists of one line containing several integers separated from each other by spaces. The first integer on the line will be the number k (6 < k < 13). Then k integers, specifying the set S, will follow in ascending order. Input will be terminated by a value of zero (0) for k.

Output

For each test case, print all possible games, each game on one line. The numbers of each game have to be sorted in ascending order and separated from each other by exactly one space. The games themselves have to be sorted lexicographically, that means sorted by the lowest number first, then by the second lowest and so on, as demonstrated in the sample output below. The test cases have to be separated from each other by exactly one blank line. Do not put a blank line after the last test case.

Sample Input

7 1 2 3 4 5 6 7
8 1 2 3 5 8 13 21 34
0

Sample Output

1 2 3 4 5 6
1 2 3 4 5 7
1 2 3 4 6 7
1 2 3 5 6 7
1 2 4 5 6 7
1 3 4 5 6 7
2 3 4 5 6 7

1 2 3 5 8 13
1 2 3 5 8 21
1 2 3 5 8 34
1 2 3 5 13 21
1 2 3 5 13 34
1 2 3 5 21 34
1 2 3 8 13 21
1 2 3 8 13 34
1 2 3 8 21 34
1 2 3 13 21 34
1 2 5 8 13 21
1 2 5 8 13 34
1 2 5 8 21 34
1 2 5 13 21 34
1 2 8 13 21 34
1 3 5 8 13 21
1 3 5 8 13 34
1 3 5 8 21 34
1 3 5 13 21 34
1 3 8 13 21 34
1 5 8 13 21 34
2 3 5 8 13 21
2 3 5 8 13 34
2 3 5 8 21 34
2 3 5 13 21 34
2 3 8 13 21 34
2 5 8 13 21 34
3 5 8 13 21 34

Source

University of Ulm Local Contest 1996

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题意：以升序的形式给定k个数，输出从中挑选6个数满足升序的所有情况。

思路：DFS，两个参数，第一个保存当前搜索的位置，第二个保存个数。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
#include<cmath>
using namespace std;
int n,flag;
int a[20],s[20];
int q;

void print()
{

    for(int i=0; i<5; i++)
        printf("%d ",s[i]);
    printf("%d\n",s[5]);
}

void dfs(int num,int cnt)
{
    if(cnt==6)
    {
        print();
        return;
    }

    for(int i=num; i<n; i++)
    {
        flag=0;
        for(int j=0; j<cnt; j++)
        {
            if(a[i]==s[j])
            {
                flag=1;
                break;
            }
        }
        if(!flag)
        {
            s[cnt]=a[i];
            dfs(i+1,cnt+1);
        }
    }
}


int main()
{
q=0;
    while(~scanf("%d",&n)&&n)
    {
        for(int i=0; i<n; i++)
        {
            scanf("%d",&a[i]);
        }
        sort(a,a+n);
        if(q++)
printf("\n");
        dfs(0,0);
    }
    return 0;
}