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.

## 解答

#include<iostream>
#include<vector>
#include<set>
using namespace std;

int main()
{
int vNum, eNum, v1, v2;
cin >> vNum >> eNum;
for (int i = 0; i < eNum; i++) {
cin >> v1 >> v2;
}
int testNum;
cin >> testNum;
for (int i = 0; i < testNum; i++) {
bool flag = true;
vector<int> coloring(vNum);
set<int> colors;
for (int j = 0; j < vNum; j++) {
cin >> coloring[j];
colors.insert(coloring[j]);
}
for (int k = 0; k < vNum; k++) {
for (int t = 0; t < adj[k].size(); t++) {
if (coloring[adj[k][t]] == coloring[k]) {
flag = false;
break;
}
}
}
if (flag) printf("%lu-coloring\n", colors.size());
else printf("No\n");
}
return 0;
}