1154 Vertex Coloring (25 point(s))

1154 Vertex Coloring (25 point(s))

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 10​4​​), 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

简单图论。

判断给定的涂色方案是否满足任何一条边的两个结点不同。如果满足，需要得到有多少个颜色。

使用vector<pair<int,int> > v来存储边，使用数组coloring[]来存储涂色方案。然后遍历每条边进行判断。颜色采用set去重实现。

#include<iostream>
#include<algorithm>
#include<set>
#include<vector>
using namespace std;
const int MAX = 1e4+7;
int N,M,q,a,b;
int coloring[MAX];
vector<pair<int,int> >v;
int main(void){
	cin>>N>>M;
	while(M--){
		cin>>a>>b;
		v.push_back(pair<int,int>(a,b));
	}
	cin>>q;
	set<int> s;
	while(q--){
		s.clear();
		for(int i=0;i<N;i++){
			 cin>>coloring[i];
			 s.insert(coloring[i]);
		}
		bool isOk = true;
		for(int i=0;i<v.size();i++){
			if(coloring[v[i].first]==coloring[v[i].second]){
				isOk =false;break;
			}
		}
		if(isOk) cout<<s.size()<<"-coloring"<<endl;
		else cout<<"No"<<endl;
	}
	return 0;
}