PAT甲级2018冬7-3 1154 Vertex Coloring (25分)

灰太狼 2023-02-25 10:08 3阅读 0赞

[算法笔记总目录][Link 1]  
[关键英语单词解释][Link 2]  
[1154 Vertex Coloring (25分)][1154 Vertex Coloring _25]  
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:**

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

邻接表建图，然后dfs，相邻元素颜色不一致。

#include<bits/stdc++.h>
    using namespace std;
    int n,k,flag=true,d1,d2,g;
    int main(){ 
    	scanf("%d %d",&n,&k);
    	vector<int> Adj[n];
    	for(int i=0;i<k;i++){ 
    		scanf("%d %d",&d1,&d2);
    		Adj[d1].push_back(d2);
    	} 
    	scanf("%d",&g);
    	for(int i=0;i<g;i++){ 
    	    vector<int> v(n);
    		set<int> s;
    		flag=true;
    		for(int j=0;j<n;j++){ 
    			scanf("%d",&v[j]);
    			s.insert(v[j]);	
    		}
    		for(int j=0;j<n;j++){ 
    			if(!flag)break;
    		    for(int p=0;p<Adj[j].size();p++){ 
    		    	if(v[j] == v[ Adj[j][p]]){ 
    		 		  flag=false;
    		 		  break;
    			    }
    		   }	 
    		}
    		if(flag)printf("%d-coloring\n",s.size());
    		else printf("No\n");
    	}
    	return 0;
    }

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIxNDgwNjA3_size_16_color_FFFFFF_t_70]

[Link 1]: https://blog.csdn.net/qq_21480607/article/details/106660085
[Link 2]: https://blog.csdn.net/qq_21480607/article/details/106987591
[1154 Vertex Coloring _25]: https://pintia.cn/problem-sets/994805342720868352/problems/1071785301894295552
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIxNDgwNjA3_size_16_color_FFFFFF_t_70]: /images/20230209/4cf96845e5cd413ca30ed75709919148.png