题目链接: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 \(10​^4\)), 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 1:

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

给定一个图,以及每个顶点的颜色,问是否所有边连接的两个顶点颜色不同。

思路

枚举每一条边即可。

代码

#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e4 + 10; pair<int, int> edges[maxn];
int colors[maxn]; int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, m;
cin >> n >> m;
for(int i = 0; i < m; ++i) {
int x, y;
cin >> x >> y;
edges[i] = {x, y};
}
int k;
cin >> k;
while(k--) {
map<int, int> mp;
for(int i = 0; i < n; ++i) {
cin >> colors[i];
mp[colors[i]]++;
}
int flag = 1;
for(int i = 0; i < m; ++i) {
int x = edges[i].first, y = edges[i].second;
if(colors[x] == colors[y]) {
flag = 0;
break;
}
}
if(flag) {
cout << mp.size() << "-coloring" << endl;
} else {
cout << "No" << endl;
}
}
return 0;
}

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