Implementation
You are required to implement correctly and efficiently the Breadth-First Search (BFS) graph algorithm (Section 22.2 from the book[1]). For graph representation, you should use adjacency lists.
You are also required to pretty-print the resulting tree/forest of trees (use Assignment 8 to achieve this) – only for the demo.
Since, for a graph, both |V| and |E| may vary, and the running time of BFS depends on both (how?), we will make each analysis in turn:
1. Set |V| = 100 and vary |E| between 1000 and 5000, using a 100 increment. Generate the input graphs randomly – make sure you don’t generate the same edge twice for the same graph. Run the BFS algorithm for each <|V|, |E|> pair value and count the number of operations performed; generate the corresponding chart (i.e. the variation of the number of operations with |E|).
2. Set |E| = 9000 and vary |V| between 100 and 200, using an increment equal to 10. Repeat the procedure above to generate the chart which gives the variation of the number of operations with |V|.
3. Interpret your charts.
