7-1 graph coloring (25 minutes)

Graph coloring problem is a well-known NP-complete problem. Given an undirected graph G = ( V , E ), by asking whether K colors as vertices assigned a color of each of a V, so that no two adjacent vertices with the same color?

But this problem is not to solve the problem of coloring you, but given a color assignment, you determine whether this is a solution graph coloring problem.

Input formats:

Input is given in the first row three integers V ( 0 < V ≤ . 5 0 0), E ( ≥ 0) and K ( 0 < K ≤ V), respectively, is no, the number of edge points toward the top graph, and the color number. Vertex and colors from 1 to No. V. Then E lines of a given number of sides of the two end points. After the information is given in FIG gives a positive integer N ( ≤ 2 0), is the number of color assignment scheme to be examined. Then N rows, each row is sequentially given V vertex colors (the i-th digit represents the i-th vertex color), separated by spaces between digits. Title ensure that a given undirected graph is a legitimate (i.e., the absence of self-weight and edge loop).

Output formats:

For each color allocation, graph coloring problem is if a solution is output Yes, otherwise the output No, each sentence per line.

Sample input:

6 8 3
2 1
1 3
4 6
2 5
2 4
5 4
5 6
3 6
4
1 2 3 3 1 2
4 5 6 6 4 5
1 2 3 4 5 6
2 3 4 2 3 4

Sample output:

Yes
Yes
No
No

#include<iostream>
#include<string>
#include<vector>
#include<set>
using namespace std;
vector<vector<int>>G(501);
int color[501] = { 0 };
bool check(int V)
{
    for (int i = 1; i <= V; i++)
        for (int j = 0; j < G[i].size(); j++)
            if (color[i] == color[G[i][j]])
                return false;
    return true;
}
int main()
{
    int V, E, K, N;
    cin >> V >> E >> K;
    for (int i = 0; i < E; i++)
    {
        int start, end;
        cin >> start >> end;
        G[start].push_back(end);
        G[end].push_back(start);
    }
    cin >> N;
    for (int i = 0; i < N; i++)
    {
        set<int>color_kind;
        for (int j = 1; j <=V; j++)
        {
            cin >> color[j];
            color_kind.insert(color[j]);
        }
        if (check(V) && color_kind.size() == K)
            cout << "Yes" << endl;
        else
            cout << "No" << endl;
    }
    return 0;
}