(PAT 1154) Vertex Coloring (图的广度优先遍历)

小灰灰 2022-03-22 14:22 108阅读 0赞

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 Klines 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:

k着色问题,任意相邻的两个顶点之间不能有相同的颜色

利用广度优先遍历图即可,一个顶点和它每个相邻顶点的颜色都不相同。出现相同的情况之间返回false

至于k怎么得到,利用一个set来存储颜色即可

#include <iostream>
    #include <algorithm>
    #include <queue>
    #include <vector>
    #include <set>
    #include <string.h>
    using namespace std;
    int colorhashMap[10010];
    class gGraph {
    public:
    	int n;
    	vector<int>* edges;
    	bool* visited;
    public:
    	gGraph(int _n) {
    		n = _n;
    		edges = new vector<int>[n];
    		visited = new bool[n];
    	}
    	void gInsert(int x, int y) {
    		edges[x].push_back(y);
    		edges[y].push_back(x);
    	}
    
    	bool BFS(int start_node) {
    		queue<int> bfs_queue;
    		visited[start_node] = true;
    		bfs_queue.push(start_node);
    		while (!bfs_queue.empty()) {
    			int tempNode = bfs_queue.front();
    			bfs_queue.pop();
    			for (int adj_node : edges[tempNode]) {
    				if (colorhashMap[tempNode] == colorhashMap[adj_node]) { return false; }
    				if (!visited[adj_node]) {
    					visited[adj_node] = true;
    					bfs_queue.push(adj_node);
    				}
    			}
    		}
    		return true;
    	}
    };
    
    int main() {
    	int N, M;
    	scanf("%d %d", &N, &M);
    	gGraph colorMap(N);
    	for (int i = 0; i < M; ++i) {
    		int nx, ny;
    		scanf("%d %d", &nx, &ny);
    		colorMap.gInsert(nx, ny);
    	}
    	int K;
    	scanf("%d", &K);
    	for (int i = 0; i < K; ++i) {
    		set<int> colorSet;
    		for (int j = 0; j < N; ++j) {
    			int ncolor;
    			scanf("%d", &ncolor);
    			colorhashMap[j] = ncolor;
    			colorSet.insert(ncolor);
    		}
    		memset(colorMap.visited, 0, N);
    		bool res = colorMap.BFS(0);
    		if (res) {
    			printf("%d-coloring\n", colorSet.size());
    		}
    		else {
    			printf("No\n");
    		}
    	}
    
    	system("PAUSE");
    	return 0;
    }