Codeforces Beta Round #11 D. A Simple Task(状压DP)

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.

Examples
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.

分析：求简单环个数，n很小，但是爆搜是不行的。。因为结果是阶乘级别的，考虑状压dp,f[i][s][t]表示当前链中点的集合为i,起点为s终点为t的所有方案数,因为s,t必定属于i,而且一个简单环有多重表示方法，所以我们考虑精简状态，f[i][t]表示起点s 为 i 中编号最小点，终点为t的所有链方案数,最后如果edg(s,t)存在就将f[i][t]记入答案，因为环上每点有两个相邻点，所以最后答案要除以二。

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