18年冬季第三题 PAT甲级 1154 Vertex Coloring (25分) 两种思路

柔情只为你懂 2023-07-13 10:45 80阅读 0赞

题目来源：[https://pintia.cn/problem-sets/994805342720868352/problems/1071785301894295552][https_pintia.cn_problem-sets_994805342720868352_problems_1071785301894295552]

备考汇总贴：[2020年3月PAT甲级满分必备刷题技巧][2020_3_PAT]

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

# 题目大意（本栏、思路一及其代码源自[liuchuo][]，我改得更通顺和好懂） #

给出一个图（即给出所有边），然后给出多种图着色的查询，问是否满足 k个颜色的图着色（i.e. 涂上k个颜色后，所有的边的两个点的颜色不相同），如果满足还要指明k是多少。

# 题目分析 #

思路一：把所有边存起来，把所有点的颜色存起来（存的过程中放入set统计颜色个数），枚举所有边，检查是否每条边的两点个颜色是否相同；若全不相同，则输出颜色个数k，否则输出No

思路二：用邻接表的方式存图（双重vector），访问每个顶点的邻接顶点，如果存在颜色相同就输出No；如果全部都不同，就输出颜色个数k，否则输出No

# 满分代码 #

## 思路一 ##

#include <iostream>
    #include <vector>
    #include <set>
    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[10009] = {0};
            bool flag = true;
            set<int> se;
            for (int i = 0; i < n; i++) {
                scanf("%d", &a[i]);
                se.insert(a[i]);
            }
            for (int i = 0; i < m; i++) {
                if (a[v[i].t1] == a[v[i].t2]) {
                    flag = false;
                    break;
                }
            }
            if (flag) 
                printf("%d-coloring\n", se.size());
            else 
                printf("No\n");
        }
        return 0;
    }

## 思路二 ##

#include<iostream>
    #include<vector>
    #include<set>
    using namespace std;
    int main(){
        int n,m,k,a,b;
        scanf("%d %d",&n,&m);
        vector<vector<int>> v(n);
        for(int i=0;i<m;i++){
            scanf("%d %d",&a,&b);
            v[a].push_back(b);
            v[b].push_back(a);
        }
        scanf("%d",&k);
        for(int i=0;i<k;i++){
            vector<int> t(n);
            set<int> kc;
            for(int j=0;j<n;j++){
                scanf("%d",&t[j]);
                kc.insert(t[j]);
            }
            bool flag=true;
            for(int j=0;j<n;j++){
                for(auto it:v[j]){
                    if(t[it]==t[j]){
                        flag=false;
                        break;
                    }
                }
            }
            if(flag)printf("%d-coloring\n",kc.size());
            else printf("No\n");
        }
        return 0;
    }

备考汇总贴：[2020年3月PAT甲级满分必备刷题技巧][2020_3_PAT]

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[https_pintia.cn_problem-sets_994805342720868352_problems_1071785301894295552]: https://pintia.cn/problem-sets/994805342720868352/problems/1071785301894295552
[2020_3_PAT]: https://blog.csdn.net/allisonshing/article/details/104213959
[liuchuo]: https://blog.csdn.net/liuchuo/article/details/84973030