Cyclic Components（并查集）

最新推荐文章于 2022-12-03 20:24:44 发布

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最新推荐文章于 2022-12-03 20:24:44 发布 · 856 阅读

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给定一个无向图，任务是找到构成环的连通分量的数量。图由顶点和边组成，边是双向的，不允许自环。连通分量是存在路径连接的所有顶点的集合。一个连通分量是环当且仅当其顶点可以重新排列，使得每个顶点与下一个顶点通过边相连，并且所有边都是不同的。题目提供了一个包含66个连通分量，其中2个是环的例子。解决方案涉及计算每个顶点的度，只有度为2的顶点才可能属于环。通过并查集来检查是否有环，若父节点相同，则环的数量加一。

链接：http://codeforces.com/contest/977/problem/E

E. Cyclic Components

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given an undirected graph consisting of $n$ vertices and $m$ edges. Your task is to find the number of connected components which are cycles.

Here are some definitions of graph theory.

An undirected graph consists of two sets: set of nodes (called vertices) and set of edges. Each edge connects a pair of vertices. All edges are bidirectional (i.e. if a vertex $a$ is connected with a vertex $b$ , a vertex $b$ is also connected with a vertex $a$ ). An edge can't connect vertex with itself, there is at most one edge between a pair of vertices.