Solved–Adjacency matrix and adjacency list—Homework -Solution

Description

Show the steps of deriving your answers. Points will be deducted for answers without adequate steps discussed. Submit your homework via Blackboard as one PDF or Word document.

1. (25) [Asymptotic upper bound] Show that n^1000000 = O(1.000001ⁿ) based on the formal definition of big-O (see below). It suffices to present the values of c and n0 and explain how you obtained them. A complete proof (i.e., that it holds for all n n0) is not required.

Definition. We say T(n) = O(f(n)) if there exist constants c > 0 and n0 0 such that T(n) c f(n) holds for all n n0.

2. (25) [Adjacency matrix and adjacency list] Show an adjacency matrix representation and an adjacency list representation of the directed graph shown below. A node is not adjacent to itself unless there is a self-loop. In addition, show the pseudocode of algorithm Find_all_edges that outputs all edges in the graph, and show its big-O run-time complexity – make sure to show the steps of deriving the run-time complexity; no point will be given to an answer without the steps.