1154 Vertex Coloring （25 分）

最新推荐文章于 2021-11-27 09:32:51 发布

原创最新推荐文章于 2021-11-27 09:32:51 发布 · 179 阅读

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本文探讨了图论中的k-着色问题，详细解释了如何判断一个图是否可以进行k-着色，并提供了具体的算法实现。通过检查每条边的两个顶点颜色是否相同，来验证给定的颜色分配是否有效。

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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 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

题意是问是否每条边的两个顶点都是不同颜色的顶点，如果是输出颜色种类，不是输出NO

可以用结构体数组来存储相连的边，根据输入的顶点的颜色来进行判断对应的点

#include<bits/stdc++.h>
using namespace std;
struct node
{
int t1,t2;
};
int main()
{
int n,m,k;
cin>>n>>m;
vector<node>v(m);
for(int i=0;i<m;i++)
{
scanf("%d %d", &v[i].t1, &v[i].t2);
}
cin>>k;
while(k--)
{
int a[10005]={0},flag=1;
set<int>ans;
for(int i=0;i<n;i++)
{
scanf("%d", &a[i]);
ans.insert(a[i]);
}
for(int i=0;i<m;i++)
{
if(a[v[i].t1]==a[v[i].t2])
{
flag=0;
break;
}
}
if(flag)
printf("%d-coloring\n", ans.size());
else
printf("No\n");
}
return 0;
}

记着一定要return 0