PAT A1154 Vertex Coloring (25point(s))

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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.

题意:

给出一个图,判断所有边的两点的颜色是否都不相同。

解答

可以使用邻接表存储边也可以用结构替存储边,遍历所有边,如果两点的颜色相同,就标记false,并终止循环,最后输出结果。

#include<iostream>
#include<vector>
#include<set>
using namespace std;

int main()
{
	int vNum, eNum, v1, v2;
	cin >> vNum >> eNum;
	vector<vector<int>> adj; 
	adj.resize(vNum);
	for (int i = 0; i < eNum; i++) {
		cin >> v1 >> v2;
		adj[v1].push_back(v2);
	}
	int testNum;
	cin >> testNum;
	for (int i = 0; i < testNum; i++) {
		bool flag = true;
		vector<int> coloring(vNum);
		set<int> colors;
		for (int j = 0; j < vNum; j++) {
			cin >> coloring[j];
			colors.insert(coloring[j]);
		}
		for (int k = 0; k < vNum; k++) {
			for (int t = 0; t < adj[k].size(); t++) {
				if (coloring[adj[k][t]] == coloring[k]) {
					flag = false;
					break;
				}
			}
		}
		if (flag) printf("%lu-coloring\n", colors.size());
		else printf("No\n");
	}
	return 0;
}