CS 2223 Skills

If I had ever learnt, I should have been a great proficient.

Lady Catherine de Bourgh
Pride and Prejudice

1 Skills

I have identified a number of skills you will learn in this course. You will learn about these skills in lectures and readings. You will demonstrate your knowledge of these skills on the homeworks and in lecture. You will be assessed on these skills in the homeworks and the exams.

1.1 Mathematical

• Recurrence Relation

• Counting operations
  
  Page 185 of the text contains a number of formulae that will prove useful during our analysis.

  There are others that will be useful.

  Sum of Squares, including odd and even.

  All: 12 + 22 + 32 + ... + n2 = n*(n+1)*(2n+1)/6
  Even: 22 + 42 + 62 + ... + n2 = 2n*(n+1)*(2n+1)/3
  Odd: 12 + 32 + 52 + ... + n2 = n*(2n+1)*(2n-1)/3
  

• Master Theorem

• Karatsuba

• Asymptotic Complexity

• O, Omega, Theta notations

• Proof by Induction

1.2 Data Structures

• Stack

• Queue

• Bag

• Linked List

• Heap

• Binary Tree

• Balanced Binary Trees

1.3 Overall Strategies

• Divide and Conquer

• Greedy Strategy

1.4 Array-based Aggregates

• Hashing (open addressing)

• Sorting (QuickSort, MergeSort, InsertionSort)

• Heaps

• Heapify in O(n) time [Math explanation as to why not O(n log n)]

• Growing array size (*2) and shrinking (/2 when /4 of size)

• Binary Array Search (search, insertion)

• Dynamic Programming

1.5 Linear Linked List Aggregates and (one-way) Iterators

• Hashing (bins/buckets)

• MergeSort of LinkedList

1.6 Binary Trees

• Binary Trees

• Traversal – pre, post, in

• Traversal maintaining state

• Balancing via AVL (also point to Red Black)

• B-Tree extension

1.7 Graphs

• Breadth-first search

• Depth-first search

• Single-source, Shortest Path

• All-pairs Shortest Path

1.8 Version : 2020/03/04

(c) 2021, George T. Heineman