1154 Vertex Coloring

Statement

Metadata

作者: 陈越
单位: 浙江大学
代码长度限制: 16 KB
时间限制: 900 ms
内存限制: 64 MB

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 $K$ ( $\le$ 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

Last update: May 4, 2022