Hdu-5765 Bonds(状压)

Problem Description

Given an undirected connected graph with N points and M edges. ?? wants to know the number of occurrence in all bonds of graph for every edge.The index of points starts from 0.
An edge cut E of a Graph G is a set of edges of G and the G would be disconnected after deleting all the edges of E.
A bond of a graph is an edge cut does not have any other edge cut as a proper subset.

 

Input

The first line of the input gives the number of test cases T; T test cases follow.
Each test case consists of two integers: N, M, followed by M lines, each line contains two integers u, v, implying an undirected edge between u and v.

limits
T <= 20
2 <= N <= 20
N-1 <= M <= N*(N-1)/2
Edges are distinct.
No edge connects to the point itself.
N is larger than 10 in no more than 5 cases.

 

Output

For each test case output “Case #x: y1 y2 … yN” (without quotes), where x is the test case number (starting from 1), and yi is the occurrence times in all bonds of i-th edge.

 

Sample Input

2 3 3 0 1 0 2 1 2 3 2 0 1 0 2

 

Sample Output

Case #1: 2 2 2 Case #2: 1 1

Hint

In first case, {(0,1),(0,2)} , {(0,1),(1,2)} , {(0,2),(1,2)} are bonds. In second case, {(0,1)},{(0,2)} is bond.

分析：点数很少，根据bonds的定义它一定是把原图分成两个联通块，那么我们枚举一下原图的连通子集个数除以二就是全图的bonds数量，然后对于每个询问，我们求一下不包含这条边两端的连通块数量再减去就行了。

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