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
#include<iostream>
#include<vector>
#include<unordered_set>
using namespace std;
int main(){
int nv, ne;
cin >> nv >> ne;
int graph[201][201] = {0};
for(int i = 0; i < ne; i++){
int temp_a, temp_b;
scanf("%d %d", &temp_a, &temp_b);
graph[temp_a][temp_b] = graph[temp_b][temp_a] = 1;
}
int m;
cin >> m;
for(int i = 0; i < m; i++){
int k;
scanf("%d", &k);
vector<int> vec(k);
int flag[201] = {0};
bool is_clique = true;
for(int j = 0; j < k; j++){
int temp;
scanf("%d", &vec[j]);
flag[vec[j]] = 1;
}
for(int j = 0; j < k; j++){
for(int z = j + 1; z < k; z++){
if(graph[vec[j]][vec[z]] == 0){
is_clique = false;
printf("Not a Clique\n");
break;
}
}
if(!is_clique){
break;
}
}
if(is_clique){
bool max_clique = true;
bool kkk = false;
for(int j = 1; j <= nv; j++){
if(flag[j] == 0){
int count = 0;
for(int w = 0; w < k; w++){
if(graph[j][vec[w]] == 0){
max_clique = false;
}else{
count++;
}
if(count == k){
kkk = true;
}
}
}
}
if(!kkk){
printf("Yes\n");
}else
{
printf("Not Maximal\n");
}
}
}
return 0;
}
