The Self-Taught Developer's Guide to Big O Notation

O(1) // instant O(log n) // the librarian O(n) // the line O(n log n) // the sweet spot O(n²) // the handshake problem O(2ⁿ) // the avalanche O(n!) // don't. O(1) // instant O(log n) // the librarian O(n) // the line O(n log n) // the sweet spot O(n²) // the handshake problem O(2ⁿ) // the avalanche O(n!) // don't.

// what's inside

Four things. That's the whole book. On purpose.

01 / containers

The Containers

Arrays, objects, maps, sets — what they're actually doing under the hood, and when each one saves you.

02 / speeds

The Speeds

O(1) to O(n!), each with a nickname you'll actually remember when it matters.

03 / recipes

The Recipes

Searching, sorting, hashing, memoization, and more — the patterns behind every fast program.

04 / fixes

The Fixes

Five changes that solve 90% of slow code. Find your bottleneck, apply, ship.

// a taste — the speeds

Nicknames you'll actually remember

notation	nickname	the vibe
O(1)	Instant	Same speed at 10 items or 10 million.
O(log n)	The Librarian	Cuts the problem in half every step.
O(n)	The Line	Twice the data, twice the wait. Fair enough.
O(n log n)	The Sweet Spot	As good as sorting honestly gets.
O(n²)	The Handshake Problem	Everyone greets everyone. Fine at a dinner party, fatal at a stadium.
O(2ⁿ)	The Avalanche	One more item, double the work.
O(n!)	Don't.	The universe ends before your function returns.

"Big O is a map of where cliffs are. You still have to look where you're walking."
— from the book

// the author

Why this book exists

I'm Robert M. Cavezza — Bobby. I learned to code by shipping things, which means I also learned what happens when the things you ship meet real users. This is the book I wish someone had handed me then: no proofs, no whiteboard hazing, just a clear mental model of why code gets slow and what to do about it — small enough to read in two sittings and keep in your back pocket.

Stay in the loop

Occasional emails about the book and what I'm writing next. No spam.