ITEC 360: Exam 2 topics - Spring 2020

DRAFT

• Updates :
  1. No updates at this time.

1. Coverage
1. Material since previous exam: Chapters 5 (Div/Con), 6 (Trans/Con), 8 (DP), Appendix B (Recurrences)
• Performance: Definition of Big Oh
• Recurrence Equations and their solution
2. Lecture and notes, supplemented by relevant sections of the text
3. Homework


2. Chapter 5: Divide and Conquer
• Mergesort:
• Basic algorithm
• Space requirements
• Performance: Best, worst, expected
• Quicksort
• Algorithms for quicksort and partition
• Space requirements
• Performance: Best, worst, expected
• Improvements
• Binary Search Trees
• Recursive algorithms to process
• How to add elements and search
• Performance: best, worst, expected - and why
• Importance of balance
• Largest and smallest elements
• Closest Pair: 1D and 2D cases, recursive algorithm, points in strip
• Convex Hull: definition




3. Chapter 8: Dynamic Programming
• 3 approaches: recursion, memoized recursion, bottom up DP
• Definition and role of memoized recursion
• Relation between memoized recursion and DP
• Relation between recurrence relation, recursive function, and DP solution
• Initial conditions
• Subproblems: Definition and role
• Collapsing two dimensional array into 1D
• Finding solution from table
• Order
• What cells mean
• Definitions of and approaches to common problems: coin selection, robot coins, paths, knapsack (not on exam: bars with and without repetition and dust, optimal bst)
• Reconstructing solution: Basic approach, examples


4. Appendix B: Solving Recurrence Equations (RE)
• Define Recurrence Equation and explain their relevance to algorithm analysis.
• Express the performance of a recursive algorithm using a recurrence relation.
• Derive a recurrence equation for a recursive algorithm.
• Use forward and backward substitution to guess/find a solution to a recurrence equation.
• Use the Master Method (aka Master Theorem) from the text or notes to determine the solution to a RE.
• Use a characteristic equation to solve a second degree linear homogeneous recurrence equation.
• Use a recurrence tree to express the solution of a recurrence relation and/or the performance of a recursive algorithm.
• Explain the relation between a recurrence tree and the master method.
• Use substitution to verify a solution to a recurrence.
• Use induction to prove the correctness of a solution to an RE. (???)


5. The following topics are NOT on the Spring 2020 exam:
• Horner's method: