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 1), 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

题意：

给出相邻的两个顶点的编号，然后再给出每个方块的颜色，判断相邻的顶点的颜色是否相同，如果不同则计算不同颜色的种类。

思路：

先存下来相邻的顶点，然后将每个定点的颜色存入一个数组中，最后遍历存下的相邻的顶点，判断相邻的顶点颜色是否相同。用一个set存放颜色的种类。

Code：

#include<iostream>
#include<vector>
#include<set>
#include<map>

using namespace std;

int main() {
    int n, m, c;
    cin >> n >> m;
    vector<pair<int, int> > v;
    int v1, v2;
    for (int i = 0; i < m; ++i) {
        cin >> v1 >> v2;
        v.push_back({v1, v2});
    }
    set<int> s;
    vector<int> color;
    int k;
    cin >> k;
    for (int i = 0; i < k; ++i) {
        s.clear();
        color.clear();
        for (int j = 0; j < n; ++j) {
            cin >> c;
            color.push_back(c);
            s.insert(c);            
        }
        for (int j = 0; j < v.size(); ++j) {
            v1 = v[j].first;
            v2 = v[j].second;
            if (color[v1] == color[v2]) {
                cout << "No" << endl;
                break;
            }
            if (j == v.size()-1) {
                cout << s.size() << "-coloring" << endl;
            }
        }
    }
    return 0;
}