PAT_A1154#Vertex Coloring

Posted 2021-11-29 blue-lin

Source:

PAT A 1154 Vertex Coloring (25 分)

Description:

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 1), 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

Keys:

• set（C++ STL）
• 散列（Hash）

Attenrion:

• 矩阵存储图，规模小于10^3
• 对于多组测试用例的输入，要注意统计值和哈希函数的初始化（出题老师太坏了，测试用例即使不初始化也是对的-,-）

Code:

 1 /*
 2 Data: 2019-05-10 20:56:31
 3 Problem: PAT_A1154#Vertex Coloring
 4 AC: 17:39
 5 */
 6 
 7 #include<cstdio>
 8 #include<set>
 9 using namespace std;
10 const int M=1e4+10;
11 struct node
12 {
13     int v1,v2;
14 }grap[M];
15 int c[M],n,m,k;
16 set<int> color;
17 
18 int IsColoring()
19 {
20     for(int i=0; i<m; i++)
21         if(c[grap[i].v1] == c[grap[i].v2])
22             return 0;
23     return 1;
24 }
25 
26 int main()
27 {
28 #ifdef    ONLINE_JUDGE
29 #else
30     freopen("Test.txt", "r", stdin);
31 #endif
32 
33     scanf("%d%d", &n,&m);
34     for(int i=0; i<m; i++)
35         scanf("%d%d", &grap[i].v1,&grap[i].v2);
36     scanf("%d", &k);
37     for(int i=0; i<k; i++)
38     {
39         color.clear();
40         for(int j=0; j<n; j++)
41         {
42             scanf("%d", &c[j]);
43             color.insert(c[j]);
44         }
45         if(IsColoring())
46             printf("%d-coloring\n", color.size());
47         else
48             printf("No\n");
49     }
50 
51     return 0;
52 }