Stage 1 of 8 · 6 lessons · ~3 weeks

Complexity and Big-O

Learn to say what a piece of code costs in time and memory before you run it. Every later stage is about trading one cost for another, so this is the vocabulary for all of it.

Start: What Big-O means and the common growth rates

Lessons· one lesson for each topic, in this order

Start with· follow one of these

CoursePaid
Grokking Algorithm Complexity and Big-O
Design Gurus · Beginner · Subscription
Short course on exactly this stage, including the amortised and space cases people miss
CourseFree
MIT 6.006 Introduction to Algorithms
MIT OpenCourseWare · Intermediate
Free: lecture 1 and recitation 1 on asymptotic notation and the model of computation

Keep handy

Big-O Cheat Sheet
One page of operation costs to check your own analysis against

Also worth your time

Demystifying Big-O Notation: The Ultimate Guide to Understanding Algorithm Complexity (opens in a new tab)Read
Time and space complexity worked through five common algorithms

Before moving on: Take 10 of your own past solutions, write the time and space complexity of each, then time them on inputs of 1,000, 10,000 and 100,000 items and check the growth matches your analysis.

Tauseef's advice

Learn to count the loops in your own code instead of memorising a table, and always ask what happens to the call stack in recursion. If syntax in your language still slows you down, do the Programming foundations roadmap first, because DSA on shaky syntax is twice as slow.