[PAT] 1142 Maximal Clique(25 分)
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
题意:
clique是一个无向图的点的子集,clique里每两个不同的点都是相连的。最大clique是不能扩展更多相连点的clique。
判断给定的点的子集是否为一个最大的clique。
思路:
将输入存在一个二维数组(矩阵)内,对于每一个查询,先判断是否为clique(每两个点对应的二维数组为1),再判断是否为max clique(遍历给定点之外的点是否和给定的点都有连线)。
题解:
#include<cstdlib> #include<cstdio> #include<vector> using namespace std; ][]; int main() { int nv, ne, m; scanf("%d %d", &nv, &ne); ; i < ne; i++) { int a, b; scanf("%d %d", &a, &b); vertex[a][b] = vertex[b][a] = ; } scanf("%d", &m); ; i < m; i++) { int k; scanf("%d", &k); vector<); vector<int> verts; ; j < k; j++) { int t; scanf("%d", &t); verts.push_back(t); v[t] = true; } //判断是否为clique //只要给定查询中的每两个点对应矩阵上的值为0,说明它不是clique bool isClique = true; ; j < verts.size(); j++) { ; r < verts.size(); r++) { ) { printf("Not a Clique\n"); isClique = false; break; } } if (!isClique) break; } if (!isClique) continue; //如果是clique, //并且还存在给定之外的点与给定的所有点对应矩阵的值为1 //说明其不是max clique bool notMaximal = false; ; j <= nv; j++) { if (v[j] == true) continue; bool isMaxClique = false; ; r < verts.size(); r++) { ) { isMaxClique = true; break; } } if (!isMaxClique) { printf("Not Maximal\n"); notMaximal = true; break; } } if (!notMaximal) printf("Yes\n"); } ; }
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