1154 Vertex Coloring （25 分)

分手后的思念是犯贱 2022-03-02 15:59 257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 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

给定一个图的结点数n和边数m，给出k个查询，问图相邻结点的颜色不能相同。

把m条边存下来，在k个查询中跑一遍，如果有一条边的两个结点是一样，则No。

否则输出给出的查询中有几种颜色。

#include<stdio.h>
    #include<string.h>
    #include<math.h>
    #include<iostream>
    #include<string>
    #include<sstream>
    #include<algorithm>
    #include<map>
    #include<set>
    #include<queue>
    #include<stack>
    #include<vector>
    using namespace std;
    #define inf 0x3f3f3f3f
    #define LL long long
    int op[10005],x[10005],y[10005];
    int main()
    {
    	int n,m,k,i,j,f;
    	scanf("%d%d",&n,&m);
    	for(i=0;i<m;i++)
    	{
    		scanf("%d%d",&x[i],&y[i]);
    	}
    	scanf("%d",&k);
    	while(k--)
    	{
    		map<int,int> s;
    		f=0;
    		for(i=0;i<n;i++)
    		{
    			scanf("%d",&op[i]);
    			s[op[i]]++;
    		}		
    		for(i=0;i<m;i++)
    		{
    			if(op[x[i]]==op[y[i]])
    			{
    				f=1;
    				break;
    			}
    		}
    		if(f==0)
    		{
    			printf("%d-coloring\n",s.size());
    		}
    		else
    		printf("No\n");
    	}
    }