1142 Maximal Clique (25分)
A clique is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. A maximal clique is a clique that cannot be extended by including one more adjacent vertex. (Quoted from https://en.wikipedia.org/wiki/Clique_(graph_theory))
Now it is your job to judge if a given subset of vertices can form a maximal clique.
Input Specification:
Each input file contains one test case. For each case, the first line gives two positive integers Nv (≤ 200), the number of vertices in the graph, and Ne, the number of undirected edges. Then Ne lines follow, each gives a pair of vertices of an edge. The vertices are numbered from 1 to Nv.
After the graph, there is another positive integer M (≤ 100). Then M lines of query follow, each first gives a positive number K (≤ Nv), then followed by a sequence of K distinct vertices. All the numbers in a line are separated by a space.
Output Specification:
For each of the M queries, print in a line Yes
if the given subset of vertices can form a maximal clique; or if it is a clique but not a maximal clique, print Not Maximal
; or if it is not a clique at all, print Not a Clique
.
Sample Input:
8 10
5 6
7 8
6 4
3 6
4 5
2 3
8 2
2 7
5 3
3 4
6
4 5 4 3 6
3 2 8 7
2 2 3
1 1
3 4 3 6
3 3 2 1
Sample Output:
Yes
Yes
Yes
Yes
Not Maximal
Not a Clique
最大点集,已知点集的定义:每两个点之间都必定有一条边。如果有其他点与这个集合的每个点都有公用边,则不是最大点集
#include <iostream> using namespace std; int N, M, K, G[300][300] = {0}, a, b, sz, *arr; int main() { scanf("%d%d", &N, &M); while(M--) { scanf("%d%d", &a, &b); G[a][b] = G[b][a] = 1; } scanf("%d", &K); while(K--) { int m[300] = {0}; bool notClique = false, notMaximal = false; scanf("%d", &sz); arr = new int(sz); for(int i = 0; i < sz; i++) { scanf("%d", &arr[i]); m[arr[i]] = 1; } for(int i = 0; i < sz - 1; i++) for(int j = i + 1; j < sz; j++) if(G[arr[i]][arr[j]] == 0) notClique = true; if(notClique) printf("Not a Clique\n"); else { // check maximal for(int i = 1; i <= N; i++) { if(m[i] == 0) { int judge = 0; for(int j = 0; j < sz; j++) if(i != arr[j] && G[i][arr[j]] == 1) judge++; if(judge == sz) { notMaximal = true; break; } } } if(notMaximal) printf("Not Maximal\n"); else printf("Yes\n"); } } return 0; }