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 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

浅析

Q：问图中是否每条边的两个顶点颜色不同

Code

#include 
#include 
#include 
using namespace std;

struct Node{
    int u, v;
    Node(int _u,int _v):u(_u),v(_v){}
};
vector v;
int main(){
    int n, m;
    cin >> n >> m;
    for (int i = 0; i < m;i++){
        int u, ve;
        cin >> u >> ve;
        v.push_back(Node(u, ve));
    }
    int k;
    cin>>k;
    for (int i = 0; i < k;i++){
        int a[10009]={0};
        set<int> s;
        for (int j = 0; j < n;j++){
            cin >> a[j];
            s.insert(a[j]);
        }
        bool flag = true;
        for (int j = 0; j < m;j++)
            if(a[v[j].u]==a[v[j].v]){
                flag = false;
                break;
            }
        if(flag)
            printf("%d-coloring\n", s.size());
        else
            printf("No\n");
    }
    return 0;
}