1154 Vertex Coloring

A proper vertex coloring is a labeling of the graph's vertices with colors such that no two vertices sharing the same edge have the same color. A coloring using at most k colors is called a (proper) k-coloring.

Now you are supposed to tell if a given coloring is a proper k-coloring.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers N and M (both no more than 104), being the total numbers of vertices and edges, respectively. Then M lines follow, each describes an edge by giving the indices (from 0 to N−1) of the two ends of the edge.

After the graph, a positive integer K (≤ 100) is given, which is the number of colorings you are supposed to check. Then K lines follow, each contains N colors which are represented by non-negative integers in the range of int. The i-th color is the color of the i-th vertex.

Output Specification:

For each coloring, print in a line k-coloring if it is a proper k-coloring for some positive k, or No if not.

Sample Input:

10 11
8 7
6 8
4 5
8 4
8 1
1 2
1 4
9 8
9 1
1 0
2 4
4
0 1 0 1 4 1 0 1 3 0
0 1 0 1 4 1 0 1 0 0
8 1 0 1 4 1 0 5 3 0
1 2 3 4 5 6 7 8 8 9

Sample Output:

4-coloring
No
6-coloring
No

#include 
#include 
#include 
using namespace std;
int n, m, k, u, v;
int c[10010];
vectorg[10010];

int main() {
	cin >> n >> m;
	for (int i = 0; i < m; i++) {
		cin >> u >> v;
		g[u].push_back(v);
		g[v].push_back(u);
	}
	cin >> k;
	while (k--) {
		sets;
		bool flag = 0;
		for (int i = 0; i < n; i++) {
			cin >> c[i];
			s.insert(c[i]);
		}
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < g[i].size(); j++) {
				if (flag) {
					break;
				}
				if (c[i] == c[g[i][j]]) {
					flag = 1;
					break;
				}
			}
		}
		if (flag) {
			cout << "No" << endl;
		} else {
			cout << s.size() << "-coloring" << endl;
		}
	}
	return 0;
}