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Lecture Notes: Order Notation

Preliminaries

Course Content

Tuesday Review

Thursday Review

Draw these functions:

Tuesday Review

Give four examples of functions which are O(n).

Motivation

Time and Memory

Definitions

Example Runtime Functions

Input Size

Comparing Functions

Asymptotic Equivalence

Growth Order

Big O

Big Omega

Big Theta

Summary

O(c) \subsetneq O(\log(n)) \subsetneq O(n) \subsetneq O(n^2) \subsetneq O(n^3) \subsetneq O(2^n) \Omega(2^n) \subsetneq \Omega(n^3) \subsetneq \Omega(n^2) \subsetneq \Omega(n) \subsetneq \Omega(\log(n)) \subsetneq \Omega(c) \Theta(n^2) = \Theta(2n^2) = \Theta(2n^2 + 2n + 2) \Theta(n) = \Theta(2n) = \Theta(2n + 2)

Little O and Little Omega

Theorems

Example Algorithms

Connection to Counting

Compute Budget

The textbook works through an example of compute budget on page 228. Skipped for time.