A1154 Vertex Coloring (25 point(s))

同一边两顶点颜色不同

1. 原文

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

2. 解析

3. AC代码

#include<vector>
#include<cstdio>
#include<set>
using namespace std;
vector<int> v[10010];
int color[10010]={};
set<int> s;
int main()
{
	int n,m;
	scanf("%d%d",&n,&m);
	int a,b;
	for (int i = 0; i < m; ++i)
	{
		scanf("%d%d",&a,&b);
		v[a].push_back(b);
		v[b].push_back(a);
	}
	int k;
	scanf("%d",&k);
	while(k--){
		int flag=0;
		for (int i = 0; i < n; ++i)
		{
			scanf("%d",&color[i]);
			s.insert(color[i]);
		}
		for (int i = 0; i < n; ++i)
		{
			for (int j = 0; j < v[i].size(); ++j)
			{
				if (color[i]==color[v[i][j]])
				{
					flag=1;
					break;
				}
			}
			if (flag==1)
			{
				break;
			}
		}
		if (flag==1)
		{
			printf("No\n");
		}else{
			printf("%lu-coloring\n",s.size());
		}
		s.clear();
	}
	return 0;
}