Halloween treats HDU 1808 鸽巢（抽屉）原理

Halloween treats

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1097    Accepted Submission(s): 435
Special Judge

Problem Description

Every year there is the same problem at Halloween: Each neighbour is only willing to give a certain total number of sweets on that day, no matter how many children call on him, so it may happen that a child will get nothing if it is too late. To avoid conflicts, the children have decided they will put all sweets together and then divide them evenly among themselves. From last year's experience of Halloween they know how many sweets they get from each neighbour. Since they care more about justice than about the number of sweets they get, they want to select a subset of the neighbours to visit, so that in sharing every child receives the same number of sweets. They will not be satisfied if they have any sweets left which cannot be divided.

Your job is to help the children and present a solution.

 

Input

The input contains several test cases. 
The first line of each test case contains two integers c and n (1 ≤ c ≤ n ≤ 100000), the number of children and the number of neighbours, respectively. The next line contains n space separated integers a₁ , ... , a_n (1 ≤ a_i ≤ 100000 ), where a_i represents the number of sweets the children get if they visit neighbour i.

The last test case is followed by two zeros.

 

Output

For each test case output one line with the indices of the neighbours the children should select (here, index i corresponds to neighbour i who gives a total number of a_i sweets). If there is no solution where each child gets at least one sweet, print "no sweets" instead. Note that if there are several solutions where each child gets at least one sweet, you may print any of them.

 

Sample Input

4 5
1 2 3 7 5
3 6
7 11 2 5 13 17
0 0

 

Sample Output

3 5
2 3 4

 

Source

HDOJ 2007 Summer Exercise（1）

 

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鸽巢原理的意思是一定存在一个连续的区间，满足题目要求（是n的倍数）

所以我们只需要求一段连续区间的和是否是n的倍数

#include <map>
#include <set>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <string>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <algorithm>
#define debug(a) cout << #a << " " << a << endl
using namespace std;
const int maxn = 1e5 + 10;
const int mod = 1e9 + 7;
typedef long long ll;
ll vis[maxn], a[maxn];
int main() {
    std::ios::sync_with_stdio(false);
    ll n, m;
    while( cin >> n >> m ) {
        if( !n && !m ) {
            break;
        }
        ll sum = 0, t;
        memset( vis, 0, sizeof(vis) );
        for( ll i = 1; i <= m; i ++ ) {
            cin >> a[i];
        }
        for( ll i = 1; i <= m; i ++ ) {
            sum += a[i];
            t = sum%n;
            if( t == 0 ) {
                for( ll j = 1; j < i; j ++ ) {
                    cout << j << " ";
                }
                cout << i << endl;
                break;
            } else if( vis[t] ) {  //如果余数在前面出现过，现在又出现了，则中间一定加了n的倍数
                for( ll j = vis[t]+1; j < i; j ++ ) {
                    cout << j << " ";
                }
                cout << i << endl;
                break;
            }
            vis[t] = i;
        }
    }
    return 0;
}