indeed2017-4-22笔试题C-Network Configuration

C - NetworkConfiguration
Time limit : 2sec / Memory limit : 256MB
Score : 100 points
Problem Statement
    There are N servers on thenetwork in your office. Each server can only communicate with the other N − 1 servers.
    You are given M forbidden pairs (a ,b)(1 ≤ i ≤ M) of servers. Each of them means that direct communication betweenserver a and b is forbidden.
    You will configure the network underthese constraints. More specifically, for every pair of two different servers,you will determine whether they will directly communicate each other. Twoconfigurations of network is considered different if there exist two servers thatdirectly communicate in one of the two configuration, and do not directly communicatein the other.
    Under these conditions, you need toconfigure the network so that every servers can communicate with all otherservers. How many different such configurations there are?
Constraints
2 ≤ N ≤ 6
0 ≤ M ≤ N(N − 1) ⁄2
1 ≤ a < b ≤ N
(a ,b ) ≠ (a ,b )(1 ≤ i < j ≤ M)
Input
Input is given from Standard Input in the following format:

Output
Print how many different configurations are possible.

Sample Input 1
4 2
1 2
3 4
Sample Output 1
5
The following five configurations are possible:
There is direct communication between server 1 and 3, between 1 and 4 and
between 2 and 3.
There is direct communication between server 1 and 3, between 1 and 4 and
between 2 and 4.
There is direct communication between server 1 and 3, between 2 and 3 and
between 2 and 4.
There is direct communication between server 1 and 4, between 2 and 3 and
between 2 and 4.
There is direct communication between server 1 and 3, between 1 and 4, between 2

and 3 and between 2 and 4.

Sample Input 2
5 0
Sample Output 2
728

Sample Input 3
6 2
1 2
3 4
Sample Output 3
5758

AC代码（Python）：组合+并查集，求解连通子图的个数

#coding=utf-8result = 0def problem3():    (N, M) = (int(x) for x in raw_input().split())    #先构造出所有的边    #edges = []    from itertools import combinations    edges = list(combinations(range(1,N+1), 2))    for _ in range(M):#M行2列        curPair = tuple(int(x) for x in raw_input().split())        if curPair in edges:            edges.remove(curPair)    #最多有N*(N-1)/2-M条边，最少有N-1条边    for eNums in range(N*(N-1)/2-M, N-1-1, -1):        tmp = list(combinations(edges, eNums))#选出eNums条边        for i in range(len(tmp)):            judge(tmp[i], N, eNums)    global result    print result    def judge(tmp1, N, M):       map = [0]*100    def find(i):        if map[i]==i:                       return i        else:            return find(map[i])            for i in range(N):        map[i]=i          for i in range(M):        (a, b) = tmp1[i]        map[find(a-1)]=map[find(b-1)]    cnt = 0    for i in range(N):        if map[i]==i:            cnt += 1    global result    if cnt==1:        result += 1 problem3()