聲明： 博客內所有英文題目來自 https://pintia.cn/ 中 PAT(Advanced Level) Practice, 博客內容只用於學術目的，僅爲PAT入門提供一個參考，不用於任何商業行爲。 轉載請註明出處。
1154 Vertex Coloring (25分)
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
思路：圖的塗色問題， 可以試試遞歸搜索 加判斷周圍結點是否共色。
Code：
#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <stack>
#include <set>
#define abs(x) (x>0?x:-x)
#define edge 0x7fffffff
using namespace std;
vector<int> graph[10005];
int vertex[10004];
bool check(int len){
for(int i=0;i<len;++i){
int length = graph[i].size();
for(int j=0;j<length;++j){
int tmp = graph[i][j];
if(vertex[i]==vertex[tmp]) return 0;
}
}
return 1;
}
int main(){
int n,m;
scanf("%d %d",&n,&m);
int e1,e2;
for(int i=0;i<m;++i){
scanf("%d %d",&e1,&e2);
graph[e1].push_back(e2);
graph[e2].push_back(e1);
}
int k;
scanf("%d",&k);
for(int i=0;i<k;++i){
set<int> ss;
for(int j=0;j<n;++j){
scanf("%d",&vertex[j]);
ss.insert(vertex[j]);
}
int k_color = ss.size();
bool res = check(n);
if(res){
printf("%d-coloring\n",k_color);
}
else{
printf("No\n");
}
}
return 0;
}