Warm up 16 Loopy transit

Loopy transit

Time Limit: 10000ms, Special Time Limit:25000ms, Memory Limit:65536KB

Total submit users: 22, Accepted users: 20

Problem 12781 : No special judgement

Problem description

Luke likes to ride on public transit in different cities he visits, just for fun. He tries to find unique ways to travel in loops: leaving from one transit station, traveling along the transit connections to at least one other station, and returning to the station where he started. He is finding lots of loops, and he wants to know just how many there are in different transit systems. There may be so many he won’t ever have time to try them all, but he’ll find some atisfaction in knowing they are there. He’s particularly interested in counting simple loops. A simple loop is a sequence of unique transit stations t1, t2, . . . , tj , where there’s a way to connect directly from ti to ti+1 for 1 ≤ i < j and also from tj to t1. Of course, we can write down a simple loop starting with any of the stations in the loop, therefore we consider any cyclic shift of such a sequence to be the same simple loop. However, two simple loops which visit the same set of transit stations in a different order are considered distinct. Help Luke by writing a program to count how many unique simple loops there are in each transit system. The following figures illustrate the transit stations (numbered ovals) and one-way connections (arrows) of the sample input. 

Input

Input contains a description of one transit system. The description begins with a line containing an integer 3 ≤ m ≤ 9 indicating the number of transit stations in the system. Stations are numbered 0 to m − 1. The next line contains an integer 1 ≤ n ≤ m(m−1) indicating the number of connections that follow, one connection per line. Each connection is a pair of integers s t (0 ≤ s < m, 0 ≤ t < m, s = t), indicating that there is a one-way connection from station s to station t.

Output

Print the number of unique simple loops in the transit system.

Sample Input

Sample Input 1
5
5
0 1
1 2
2 3
3 4
4 2

Sample Input 2
8
10
0 1
1 2
2 3
3 4
4 5
5 0
2 6
6 0
3 7
7 0

Sample Input 3
4
8
0 1
1 2
2 3
3 0
1 0
2 1
3 2
0 3

Sample Output

Sample Output 1
1

Sample Output 2
3

Sample Output 3
6

Problem Source

NAQC 2012

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#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <map>
#include <queue>
#include <vector>
#include <string>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
#define maxn 15
#define ll long long
#define mod 1000000007
#define INF 0x7fffffff
#define eps 1e-8
int n, m, x;
int g[maxn][maxn];
int vis[maxn];
double s;
double dfs(int x, int m, int k, int p){
    if (k == m){ if (g[p][x])return 1.0; else return 0.0; }
    for (int i = 0; i < n; i++){
        if (vis[i]||!g[p][i])continue;
        if (i == x)continue;
        vis[i] = 1;
        s+=dfs(x,m,k+1,i)/(m);
        vis[i] = 0;
    }
    return 0.0;
}
    int main(){
        /*int t;
        scanf("%d", &t);
        while (t--){
        scanf("%I64d", &n);

        }*/
        while (~scanf("%d", &n)){
            scanf("%d", &m);
            memset(vis, 0, sizeof vis);
            memset(g, 0, sizeof g);
            for (int i = 0; i < m; i++){
                int u, v;
                scanf("%d%d", &u, &v);
                g[u][v] = 1;
            }
            double ans = 0;
            for (int i = 0; i < n; i++)
                for (int j = 1; j <= n; j++){
                    s = 0;
                    dfs(i,j,1,i);
                    ans += s;
                    memset(vis, 0, sizeof vis);
                }
            printf("%d\n",(int)(ans+0.5));
        }
        return 0;
    }