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
C++:
/*
@Date : 2018-08-03 22:11:04
@Author : 酸饺子 ([email protected])
@Link : https://github.com/SourDumplings
@Version : $Id$
*/
/*
https://pintia.cn/problem-sets/994805342720868352/problems/994805343979159552
*/
#include <iostream>
#include <cstdio>
#include <set>
using namespace std;
const int MAXN = 203;
bool G[MAXN][MAXN];
int main(int argc, char const *argv[])
{
for (int i = 0; i < MAXN; ++i)
{
for (int j = 0; j < MAXN; ++j)
{
G[i][j] = false;
}
}
int Nv, Ne;
scanf("%d %d", &Nv, &Ne);
for (int i = 0; i < Ne; ++i)
{
int v, w;
scanf("%d %d", &v, &w);
G[v][w] = G[w][v] = true;
}
int W;
scanf("%d", &W);
for (int i = 0; i < W; ++i)
{
int K;
scanf("%d", &K);
set<int> c;
bool isC = true;
for (int j = 0; j < K; ++j)
{
int m;
scanf("%d", &m);
if (j && isC)
{
for (auto &cMember : c)
{
if (!G[cMember][m])
{
isC = false;
break;
}
}
}
c.insert(m);
}
if (isC)
{
bool isM = true;
for (int j = 1; j <= Nv; ++j)
{
if (c.find(j) == c.end())
{
bool flag = false;
for (auto &cMember : c)
{
if (!G[cMember][j])
{
flag = true;
break;
}
}
if (!flag)
{
isM = false;
break;
}
}
}
if (isM)
{
printf("Yes\n");
}
else
printf("Not Maximal\n");
}
else
printf("Not a Clique\n");
}
return 0;
}