PAT (Advanced Level) Practise 1126 Eulerian Path (25)
2017-03-04 19:21
417 查看
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 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", or "Non-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 3Non-Eulerian
判断一张图是否有欧拉回路,欧拉路径.先用并查集判断连通性,之后判断每个点的度数即可。
#include<map>
#include<set>
#include<ctime>
#include<cmath>
#include<queue>
#include<string>
#include<vector>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<functional>
using namespace std;
#define ms(x,y) memset(x,y,sizeof(x))
#define rep(i,j,k) for(int i=j;i<=k;i++)
#define per(i,j,k) for(int i=j;i>=k;i--)
#define loop(i,j,k) for (int i=j;i!=-1;i=k[i])
#define inone(x) scanf("%d",&x)
#define intwo(x,y) scanf("%d%d",&x,&y)
#define inthr(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define infou(x,y,z,p) scanf("%d%d%d%d",&x,&y,&z,&p)
#define lson x<<1,l,mid
#define rson x<<1|1,mid+1,r
#define mp(i,j) make_pair(i,j)
#define ft first
#define sd second
typedef long long LL;
typedef pair<int, int> pii;
const int low(int x) { return x&-x; }
const int INF = 0x7FFFFFFF;
const int mod = 1e9 + 7;
const int N = 3e5 + 10;
const double eps = 1e-10;
int n, m, x, y, cnt
, fa
, tot, odd;
int get(int x) { return x == fa[x] ? x : fa[x] = get(fa[x]); }
int main()
{
intwo(n, m);
rep(i, 1, n) fa[i] = i, cnt[i] = 0;
tot = n - 1; odd = 0;
rep(i, 1, m)
{
intwo(x, y);
cnt[x]++; cnt[y]++;
int fx = get(x), fy = get(y);
if (fx == fy) continue;
fa[fx] = fy; tot--;
}
rep(i, 1, n)
{
if (cnt[i] & 1) odd++;
printf("%d%s", cnt[i], i == n ? "\n" : " ");
}
if (!tot && (!odd || odd == 2))
puts(odd ? "Semi-Eulerian" : "Eulerian");
else puts("Non-Eulerian");
return 0;
}
相关文章推荐
- PAT (Advanced Level) Practise 1126 Eulerian Path (25)
- PAT (Advanced Level) 1126. Eulerian Path (25)
- 【PAT】【Advanced Level】1126. Eulerian Path (25)
- PAT (Advanced Level) 1126. Eulerian Path (25) 解题报告
- 1040. Longest Symmetric String (25)【最长回文子串-马拉车(manacher算法)——PAT (Advanced Level) Practise
- 1048. Find Coins (25)【排序】——PAT (Advanced Level) Practise
- PAT (Advanced Level) Practise 1012. The Best Rank (25)
- PAT (Advanced Level) Practise 1113 Integer Set Partition (25)
- 1075. PAT Judge (25)【排序】——PAT (Advanced Level) Practise
- PAT (Advanced Level) Practise 1024. Palindromic Number (25)
- PAT (Advanced Level) Practise 1012 The Best Rank (25)
- PAT (Advanced Level) Practise 1070 Mooncake (25)
- PAT (Advanced Level) Practise 1033 To Fill or Not to Fill (25)
- PAT (Advanced Level) Practise 1037 Magic Coupon (25)
- 1086. Tree Traversals Again (25)【二叉树】——PAT (Advanced Level) Practise
- PAT (Advanced Level) Practise 1086 Tree Traversals Again (25)
- PAT (Advanced Level) Practise 1101 Quick Sort (25)
- PAT (Advanced Level) Practise 1102. Invert a Binary Tree (25) 二叉树的层序和中序遍历
- PAT (Advanced Level) Practise - 1093. Count PAT's (25)
- PAT (Advanced Level) Practise 1006. Sign In and Sign Out (25)