PAT_A1126#Eulerian Path
Source:
Description:
In graph theory, an Eulerian path is a path in a graph which visits every edge exactly once. Similarly, an Eulerian circuit is an Eulerian path which starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Konigsberg problem in 1736. It has been proven that connected graphs with all vertices of even degree have an Eulerian circuit, and such graphs are called Eulerian. If there are exactly two vertices of odd degree, all Eulerian paths start at one of them and end at the other. A graph that has an Eulerian path but not an Eulerian circuit is called semi-Eulerian. (Cited from https://en.wikipedia.org/wiki/Eulerian_path)
Given an undirected graph, you are supposed to tell if it is Eulerian, semi-Eulerian, or non-Eulerian.
Input Specification:
Each input file contains one test case. Each case starts with a line containing 2 numbers N (≤ 500), and M, which are the total number of vertices, and the number of edges, respectively. Then M lines follow, each describes an edge by giving the two ends of the edge (the vertices are numbered from 1 to N).
Output Specification:
For each test case, first print in a line the degrees of the vertices in ascending order of their indices. Then in the next line print your conclusion about the graph -- either
Eulerian
,Semi-Eulerian
, orNon-Eulerian
. Note that all the numbers in the first line must be separated by exactly 1 space, and there must be no extra space at the beginning or the end of the line.
Sample Input 1:
7 12
5 7
1 2
1 3
2 3
2 4
3 4
5 2
7 6
6 3
4 5
6 4
5 6
Sample Output 1:
2 4 4 4 4 4 2
Eulerian
Sample Input 2:
6 10
1 2
1 3
2 3
2 4
3 4
5 2
6 3
4 5
6 4
5 6
Sample Output 2:
2 4 4 4 3 3
Semi-Eulerian
Sample Input 3:
5 8
1 2
2 5
5 4
4 1
1 3
3 2
3 4
5 3
Sample Output 3:
3 3 4 3 3
Non-Eulerian
Keys:
Attention:
- 判断图的连通性与顶点度的奇偶性即可
Code:
/*
Data: 2019-06-01 19:33:52
Problem: PAT_A1126#Eulerian Path
AC: 56:58 题目大意:
欧拉路径可以访问图中所有的边且各边仅访问一次,欧拉回路是起点和终点相同的欧拉路径;
已知各顶点均含有偶数条边的图可构成欧拉回路,该图称作欧拉图;
若只有两个顶点含有奇数条边的图可构成欧拉路径,并且这两个结点作为欧拉路径的起点和终点;
含有欧拉路径但不含欧拉回路的图,称作半欧拉图
现在给定一个图,判断其是否为欧拉图
输入:
第一行给出,顶点数N<=500,边数M
接下来M行给出各边
输出:
第一行给出,各顶点边数
第二行给出,非欧拉图,半欧拉图,欧拉图 基本思路:
先判断含有奇数边顶点的数目,
再判断图的连通性,
若含有无奇数边顶点,且连通图,则为欧拉图
若含有两条奇数边顶点,且图连通,则为半欧啦图
否则,为非欧拉图
*/ #include<cstdio>
#include<algorithm>
using namespace std;
const int M=,INF=1e9;
int grap[M][M],vis[M],in[M],n,sum=; void DFS(int v)
{
vis[v]=;
sum++;
for(int u=; u<=n; u++)
if(vis[u]== && grap[u][v]!=INF)
DFS(u);
} int main()
{
#ifdef ONLINE_JUDGE
#else
freopen("Test.txt", "r", stdin);
#endif fill(in,in+M,);
fill(vis,vis+M,);
fill(grap[],grap[]+M*M,INF);
int m,v1,v2,cnt=;
scanf("%d%d", &n,&m);
for(int i=; i<m; i++)
{
scanf("%d%d", &v1,&v2);
grap[v1][v2]=;
grap[v2][v1]=;
in[v1]++;
in[v2]++;
}
for(int i=; i<=n; i++){
printf("%d%c", in[i], i==n?'\n':' ');
if(in[i]%==) cnt++;
}
DFS();
if(cnt== && sum==n)
printf("Semi-Eulerian\n");
else if(cnt== && sum==n)
printf("Eulerian\n");
else printf("Non-Eulerian\n"); return ;
}
PAT_A1126#Eulerian Path的更多相关文章
- Graph | Eulerian path
In graph theory, a Eulerian trail (or Eulerian path) is a trail in a graph which visits every edge e ...
- PAT1126:Eulerian Path
1126. Eulerian Path (25) 时间限制 300 ms 内存限制 65536 kB 代码长度限制 16000 B 判题程序 Standard 作者 CHEN, Yue In grap ...
- A1126. Eulerian Path
In graph theory, an Eulerian path is a path in a graph which visits every edge exactly once. Similar ...
- PAT A1126 Eulerian Path (25 分)——连通图,入度
In graph theory, an Eulerian path is a path in a graph which visits every edge exactly once. Similar ...
- 1126 Eulerian Path (25 分)
1126 Eulerian Path (25 分) In graph theory, an Eulerian path is a path in a graph which visits every ...
- PAT甲级 1126. Eulerian Path (25)
1126. Eulerian Path (25) 时间限制 300 ms 内存限制 65536 kB 代码长度限制 16000 B 判题程序 Standard 作者 CHEN, Yue In grap ...
- PAT 甲级 1126 Eulerian Path
https://pintia.cn/problem-sets/994805342720868352/problems/994805349851185152 In graph theory, an Eu ...
- PAT 1126 Eulerian Path[欧拉路][比较]
1126 Eulerian Path (25 分) In graph theory, an Eulerian path is a path in a graph which visits every ...
- PAT甲级——1126 Eulerian Path
我是先在CSDN上发布的这篇文章:https://blog.csdn.net/weixin_44385565/article/details/89155050 1126 Eulerian Path ( ...
随机推荐
- Spring MVC 一次简单的 CRUD
基本环境搭建 1.数据库 和 实体类 的名字相同,实体类 属性名即 数据库 字段名. 2.创建 实体类 对应 dao 类,持久层框架 mybatis 正处于学习中,这里就用原始的 jdbc 操作了. ...
- Java中处理线程同步
引自:http://blog.csdn.net/aaa1117a8w5s6d/article/details/8295527和http://m.blog.csdn.net/blog/undoner/1 ...
- HDU 5226
公式啊,公式啊....TAT 杭电题解.....高中生...... 对于卢卡斯定理,由于p较大,所以不可能按一般的来算,n,m较小,循处理出n!的逆元对p的,然后可以按照卢卡斯定理,降低,对后面的就可 ...
- webservices系列(五)——javaweb整合Axis2及多service配置
1.新建一个项目动态web项目webservice_test3. 2.打开<Tomcat安装目录>webapps/axis2/WEB-INF.将lib.conf.modules三个目录复制 ...
- 利用jQuery设计横/纵向菜单
在网页中,菜单扮演着"指路者"的角色.怎样设计一个人性化的菜单呢.以下小编带着大家一起做. 效果图: watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi ...
- Criteria——Hibernate的面向对象查询
提到Hibernate的查询.我们往往会想到HQL,他使我们的SQL语句面向对象话. 事实上细看,差点儿相同就是把SQL语句中的表和字段用所相应的实体和属性给取代了.事实上.Hibernate中还有还 ...
- luogu3469 [POI2008]BLO_Blockade
题目大意 给一个无向连通图,求对于每一个点,去掉该点后图中连通结点有序对的减少量. 思路 当时想这道题时,我想到:枚举每一个点,在删去它后连通的几个部分中Dfs得到各个部分的点的个数从而得到解,但是我 ...
- DirectFB学习之移植到nuc972平台 标签: DirectFBlinux图形加速驱动【转】
本文转载自:http://blog.csdn.net/jxgz_leo/article/details/70137304 [nuc972开发板购买地址,感谢支持](https://shop102749 ...
- Android中Calendar类的用法总结
Calendar是Android开发中需要获取时间时必不可少的一个工具类,通过这个类可以获得的时间信息还是很丰富的,下面做一个总结,以后使用的时候就不用总是去翻书或者查资料了. 在获取时间之前要先获得 ...
- PCB MS SQL 排序应用(row_number rank dense_rank NTILE PARTITION)
一.排序前,准备数据 --表变量 ),流程数 int) insert into @table union all union all union all union all --查看一下 select ...