PAT甲级——A1141 PATRankingofInstitution【25】
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
Solution:
Yes
Yes
Yes
Not Maximal
Not a Clique
题意是,在给出的连通图中,判断查询的点是不是两两相连?如果是,那就是Clique,然后在判断这些查询点是是不是最大的集,即没有其他的点与查询的点是两两相连的
若存在,则不是最大集
#include <iostream>
#include <vector>
using namespace std;
int main()
{
int n, m, k;
cin >> n >> m;
vector<vector<int>>v(n + , vector<int>(n + , ));
while (m--)
{
int a, b;
cin >> a >> b;
v[a][b] = v[b][a] = ;
}
cin >> k;
while (k--)
{
cin >> m;
vector<int>temp(m);
vector<bool>otherNum(n + , true);
for (int i = ; i < m; ++i)
{
cin >> temp[i];
otherNum[temp[i]] = false;
}
bool flag = true, isMax = true;
for (int i = ; i < m && flag; ++i)//判断查询的点是不是两两相连
for (int j = i + ; j < m; ++j)
if (v[temp[i]][temp[j]] == )
flag = false;
if (flag == false)
cout << "Not a Clique" << endl;
else
{
for (int i = ; i <= n && isMax; ++i)//判断查询之外的点与查询中的点是不是两两相连
{
if (otherNum[i] == false)continue;//在查询中的点不用判断
int nums = ;
for (int j = ; j < m; ++j)
if (v[i][temp[j]] == )
++nums;
if (nums == m)
isMax = false;
}
if (isMax)
cout << "Yes" << endl;
else
cout << "Not Maximal" << endl;
}
}
return ;
}
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