求简单无向图中环的个数

Question

D. A Simple Task

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Given a simple graph, output the number of simple cycles in it. A simple cycle is a cycle with no repeated vertices or edges.

Input

The first line of input contains two integers n and m (1 ≤ n ≤ 19, 0 ≤ m) – respectively the number of vertices and edges of the graph. Each of the subsequent m lines contains two integers a and b, (1 ≤ a, b ≤ n, a ≠ b) indicating that vertices a and b are connected by an undirected edge. There is no more than one edge connecting any pair of vertices.

Output

Output the number of cycles in the given graph.

Sample test(s)

input

4 6
1 2
1 3
1 4
2 3
2 4
3 4

output

7

Note

The example graph is a clique and contains four cycles of length 3 and three cycles of length 4.

求简单无向图中环的个数？简单无向图即 无自环，无重边的无向图。

 这个是NP问题； codeforces 上有一题用的是状态压缩写的。

 dp[s][i] s集合里最小的点到其他点的路径数；

dp[s][i] += dp[s^(1<

ans加上可以构成环的路径数．怎么才能构成环呢？　如a－>b->.....->c ,如果知道ac是可达的，只要加上a,经过ab...到达c的路径数就可以了。注意a是这个集合里最小的数。而且同一个环会被记录两次，因为2条路径才是一个环。

codeforces 11D  http://www.codeforces.com/contest/11/problem/D

code ：

#include 
#include 
#include 
#include 
using namespace std;

typedef __int64 ll;
#define maxn 20
ll dp[1<> n >> m ) {
        memset(g, 0, sizeof g);
        int state = (1<>1) << endl;
    }
};

转载地址：

http://www.cnblogs.com/TengXunGuanFangBlog/archive/2013/04/19/loop_problem.html