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
思路:模拟题,判断给出的点集是否满足团的条件。
程序:
#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
int arr[201][201];
int n,m;
void func(vector<int> v)
{
bool isClique = true;
for(int i = 0; i < v.size(); i++)
{
for(int j = i+1; j < v.size(); j++)
{
if(arr[v[i]][v[j]] != 1)
{
isClique = false;
printf("Not a Clique\n");
return;
}
}
}
bool isMaximal = true;
if(isClique)
{
for(int i = 1; i <= n; i++)
{
bool isExist = false;
for(int k = 0; k < v.size(); k++)
{
if(v[k] == i)
{
isExist = true;
break;
}
}
if(!isExist)
{
bool isAllConnected = true;
for(int j = 0; j < v.size(); j++)
{
if(arr[i][v[j]] != 1)
{
isAllConnected = false;
}
}
if(isAllConnected)
{
isMaximal = false;
printf("Not Maximal\n");
return;
}
}
}
}
if(isMaximal)
printf("Yes\n");
}
int main()
{
scanf("%d%d",&n,&m);
for(int i = 0; i < m; i++)
{
int a,b;
scanf("%d%d",&a,&b);
arr[a][b] = arr[b][a] = 1;
}
int p;
scanf("%d",&p);
for(int i = 0; i < p; i++)
{
int k;
scanf("%d",&k);
vector<int> v;
for(int j = 0; j < k; j++)
{
int num;
scanf("%d",&num);
v.push_back(num);
}
func(v);
}
return 0;
}