【PAT甲级 - C++题解】1154 Vertex Coloring

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📝原题地址：题目详情 - 1154 Vertex Coloring (pintia.cn)
🔑中文翻译：顶点着色
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1154 Vertex Coloring

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
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

Sample Output:

4-coloring
No
6-coloring
No
1
2
3
4

题意

一个合适的顶点着色是指用各种颜色标记图中各个顶点，使得每条边的两个端点的颜色都不相同。

如果一种合适的顶点着色方案使用了一共 k 种不同的颜色，则称其为合适的 k 着色（k-coloring)。

现在，你需要判断给定的着色方案是否是合适的 k 着色方案。

思路

1. 直接用一个结构体数组 e 来存储每一条边。
2. 输入每种染色方案后，遍历每一条边，判断是否每一条边都满足两个点的颜色都不相同，只要有一个边出现两点颜色相同，则都不是一个合法的着色方案。
3. 根据判断结果输出答案，我们可以用一个 set 容器来对颜色进行去重，set 容器会帮我们将相同的值去掉。

代码

#include
using namespace std;

const int N = 10010;

struct Edge {
    int a, b;
}e[N];

int n, m;
int color[N];

int main()
{
    cin >> n >> m;

    //输入每条边
    for (int i = 0; i < m; i++)    cin >> e[i].a >> e[i].b;

    //开始查询
    int k;
    cin >> k;
    while (k--)
    {
        //输入每种染色方案
        for (int i = 0; i < n; i++)  cin >> color[i];

        //判断每条边的两个点颜色是否都是不同
        bool success = true;
        for (int i = 0; i < m; i++)
            if (color[e[i].a] == color[e[i].b])
            {
                success = false;
                break;
            }

        if (success)
        {
            //可以用set来对颜色进行去重
            unordered_set<int> s;
            for (int i = 0; i < n; i++)  s.insert(color[i]);
            printf("%d-coloring\n", s.size());
        }
        else puts("No");
    }

    return 0;
}
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