1154 Vertex Coloring 甲级 xp_xht123

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 104), 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

解题思路：给定的序列，任意两个相连的点不能涂相同的颜色， 满足条件的序列中有几个不同颜色的点就是几色问题。

#include
#include
#include
#include
 
using namespace std;
 
const int N = 1e4 + 10;
 
int n , m;
vector< vector<int> >v(N);
int a[N];
 
bool check()
{
    for(int i = 0;i < n;i ++)
    {
        for(int j = 0;j < v[i].size();j ++)
        {
            if(a[i] == a[v[i][j]]) return false;
        }
    }
    return true;
}
 
int main()
{
    cin >> n >> m;
    for(int i = 0;i < m;i ++)
    {
        int x , b;
        cin >> x >> b;
        v[x].push_back(b);
        v[b].push_back(x);
    }
    
    int k;
    cin >> k;
    while(k --)
    {
        unordered_map<int , int>mp;
        for(int i = 0;i < n;i ++) 
        {
            cin >> a[i];
            mp[a[i]] ++;
        }
        
        int cnt = mp.size();//可能方案数
        
        bool flag = check();
        if(flag) printf("%d-coloring\n" , cnt);
        else puts("No");
    }
    return 0;
}