Description
Description A strongly connected component (SCC) of a directed graph G = (V, E) is defined
as a maximal set of vertices C ⊆ V such that for every pair of vertices u and v in C, the two
vertices are reachable from each other. In this lab assignment, you are asked to decompose a
given directed graph G = (V, E) into a collection of SCCs.
Input The input will have the following format. The first integer refers to the number of
vertices, |V |. The second integer is the number of edges, |E|. Vertices are indexed by 0, 1, …,
|V | − 1. Then, two numbers u v appearing in each line means an edge (u, v). See the example
given below.
Output Output the SCC ID of every vertex. A SCC’s ID is defined as the smallest index of
any vertex in the SCC. In other words, you have to output, for each vertex v, the ID of the unique
SCC the vertex v belongs to. You must output the ID for each vertex, considering vertices in
the order of 0, 1, …, |V | − 1.
Examples of input and output
Input
8
13
0 1
1 2
1 4
1 5
2 3
2 6
3 2
3 7
4 0
4 5
5 6
6 5
6 7
Output for problem 2
0
0
2
2
0
5
5
7
What this answer implies is that the graph is decomposed into four SCCs, {0, 1, 4}, {2, 3}, {5, 6}, {7}.
Note that all vertices in the same SCC have the same label, which is equal to the smallest index
of all vertices in the same component. For example, vertices 0,1 and 4 are all labeled with 0.
See the lab guidelines for submission/grading, etc., which can be found in Files/Labs.
