## Problem #

Source: [PAT 1154]

### Description #

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
```

## Solution #

- 题意 给你一张图，再给你一串颜色，你判断该串颜色是否能保证每个边的两个顶点颜色不一样
- 构件图，然后判断判断

## Code #

```
#include <iostream>
#include <vector>
#include <set>
#define maxsize 10001
using namespace std;
int n, m, colors[maxsize];
set<int> color_num;
vector<int> matrx[maxsize];
void check()
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < matrx[i].size(); j++)
{
if (colors[i] == colors[matrx[i][j]])
{
cout << "No" << endl;
return;
}
}
}
cout << color_num.size() << "-coloring" << endl;
}
int main()
{
int a, b;
cin >> n >> m;
for (int i = 0; i < m; i++)
{
cin >> a >> b;
matrx[a].push_back(b);
matrx[b].push_back(a);
}
cin >> a;
for (int i = 0; i < a; i++)
{
color_num.clear();
for (int j = 0; j < n; j++)
{
cin >> colors[j];
color_num.insert(colors[j]);
}
check();
}
return 0;
}
```