ITEC 360: Exam 1 topics - Spring 2020

1. 2020 Mar 29 08:05:25 PM: Clarified about chapter 1 graphs and dfs/bfs.
2. 2020 Mar 29 08:05:25 PM: Removed draft

1. Coverage
1. Appendix A (Math), Chapters 2 (Asymptotic analysis), 3 (Brute Force), 4 (Decrease and Conquer)
2. Lecture and notes, supplemented by relevant sections of the text
3. Homeworks


2. Chapter 1: Introduction
• Graphs: Only enough to do DFS and BFS of directed and undirected graphs
• Differentiate between a directed and undirected graph.
• Define, give the space efficiency of, and use the adjacency list and adjacency matrix data structures for graph representation.
• Define these terms for graphs: node, vertex, edge, acyclic, cycle, tree.
• Well, you do have to know enough about graphs to do DFS and BFS.


3. Appendix A: Math
• Give an informal definition of a logarithm
• Distinguish among log, lg, and ln.
• Recognize and describe relations among exponentials and logarithms.
• State and apply properties of logarithms


• Give closed forms for common summations
• Recognize, and use floor and ceiling notation.


• Write inductive proofs


4. Chapter 2: Asymptotic analysis
• Define and be able to determine among Best, Worst, Expected, performance of an algorithm.
• Know the Best, Worst, Expected, performance of a number of common algorithms (eg sorts, search, factorial, nested loops)
• Give the formal definitions of Big O, Ω, Θ.
• Give alternate formal definitions of Big O, Ω, Θ using limits.
• Describe the relationship among: O, Ω, Θ
• Describe the meaning of little o.
• Prove that f(n) is O(g(n)), and similarly for Ω, and Θ.
• Explain and appropriately use notation such as f(n) = O(g(n)) and f(n) ∈ O(g(n)).
• State and apply properties of order.
• Recognize relative order of various common functions
• Describe the importance of order in determining the size problem that can feasibly be solved by an algorithm.
• Recognize when we can ignore lower order terms and explain why.
• Analyze the order of non-recursive algorithms
• Analyze the order of recursive algorithms (see also Appendix B)


5. Chapter 3: Brute Force and Exhaustive Search
• Explain what brute force and exhaustive search algorithms are.
• Explain the pros and cons of brute force and exhaustive search as approaches to solving a problem.
• Describe a solution for or solve a simple instance of the following problems:
• String matching
• Closest pair
• Convex Hull
• Traveling Salesman
• Knapsack
• Assignment
• Define and perform, using a stack, a depth-first search of a graph.
• Define and perform, using a queue, a breadth-first search of a graph.


6. Chapter 4: Decrease and Conquer
• List and describe the steps of the Decrease and Conquer approach.
• List and describe different approaches to the Decrease and Conquer approach.
• Describe and perform the following algorithms and explain how each illustrates the decrease and conquer approach:
• Topological sort (DFS and source elimination)
• Binary Search
• Median and selection problems (quick select)
• Binary search tree operations
• Nim games

NOT ON EXAM

1. Chapter 1: Introduction
• Graphs: You do need to know enough to do DFS and BFS of directed and undirected graphs


• Other than knowing DFS and BFS, the following will not be on the exam:
• Differentiate between a directed and undirected graph.
• Define, give the space efficiency of, and use the adjacency list and adjacency matrix data structures for graph representation.
• Define these terms for graphs: node, vertex, edge, acyclic, cycle, tree.