W2232 Big-O Notation

Within these castle walls be forged Mavens of Computer Science ...

— Merlin, The Coder

Big-O

Prerequisites

• W1352 Bubble Sort
• W2202 Insertion Sort
• W2203 Selection Sort
• W2225 Merge Sort

Background

• Watch Introduction to Big O Notation and Time Complexity (CS Dojo)
• Watch Getting Sorted & Big O Notation (Computerphile)
• Read A beginner's guide to Big O notation (Rob Bell)
• Watch Why My Teenage Code Was Terrible: Sorting Algorithms and Big O Notation (Tom Scott)

Big-O Notation

Big-O Notation is used to describe the performance of an algorithm and establishes a worst-case run time. It calculates the number of operations performed and the memory required for an algorithm to conclude. Different formulas can be used to calculate the operations performed and memory requirements for each sorting algorithm. Big-O Notation is unable to tell you how long an algorithm will run because too many factors can influence the time an algorithm takes to run.

Common Formulas

O(log n) - Binary Search

O(n) - Linear Search

O(n * log n) - Quicksort

O(n²) - Bubble Sort/Insertion Sort/Selection Sort

Growth Rate	Name	Description
O(1)	Constant	Statement
O(log(n))	Logarithmic	Divide in half / Binary search
O(n)	Linear	Loop
O(n * log(n))	Linearithmic	Effective sorting algorithm
O(n^2)	Quadratic	Nested loop
O(n^3)	Cubic	Triple-nested loop
O(xn)	Example	Exhaustive search

Big-O Notation can also be calculated by hand. You can go through each line of code and determine if it will be "1", "log(n)", n, etc. You can then add up all the growth rates, and as one example, it can be expressed as O ( 1 + 3n) where the "1" represents one line of O(1), and the "3n" represents 3 lines of O(n).

	Coming Soon
	Timing execution in Linux

Exercises

Exercises

Write an essay (minimum 500 words) which:

• Defines Big-O
• Compares and contrasts Big-O for:
  • Bubble-Sort
  • Selection Sort
  • Insertion Sort
  • Merge Sort
• Based upon the above, which sort is most time-efficient for the average case?

Complete your essay in your Journal directory and push to GitHub.

References

Big-O Notation for Beginners (AdrianMejia)

Big-O Notation (Wikipedia)