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
数据量非常小，暴力模拟即可。不用担心超时的问题主要是理解题意，Clique（派系）：当一个集合中任何两个不同顶点都是undirected（题目给定了）时，成该集合为一个Clique；如果不能通过增加一个或者更多的新节点使该派系扩大时，则成该派系为最大派系（Maximal Clique）
#include<iostream>
#include <bits/stdc++.h>
using namespace std
;
const int maxn
= 210;
int nv
, ne
, m
;
int g
[maxn
][maxn
];
bool
judge(int num
[], int k
)
{
int t
[maxn
] = {0};
for(int i
= 0; i
< k
; ++i
){
int v
= num
[i
];
for(int j
= 1; j
<= nv
; ++j
){
if(g
[v
][j
] == 1) t
[j
]++;
}
}
for(int i
= 1; i
<= nv
; ++i
){
if(t
[i
] == k
) return false
;
}
return true
;
}
int main()
{
scanf("%d%d",&nv
,&ne
);
for(int i
= 0; i
< ne
; ++i
){
int a
, b
;
scanf("%d%d",&a
,&b
);
g
[a
][b
] = g
[b
][a
] = 1;
}
scanf("%d",&m
);
int num
[210];
while(m
--){
int k
;
scanf("%d",&k
);
for(int i
= 0; i
< k
; ++i
){
scanf("%d",&num
[i
]);
}
bool clique
= true
, maximal
= true
;
for(int i
= 0; i
< k
; ++i
){
for(int j
= i
+ 1; j
< k
; ++j
){
if(g
[num
[i
]][num
[j
]] != 1){
clique
= false
;
break;
}
}
if(!clique
) break;
}
if(!clique
) printf("Not a Clique\n");
else {
if(judge(num
, k
)) printf("Yes\n");
else printf("Not Maximal\n");
}
}
return 0;
}
