Big-O Complexities

All Around Us

🟢 O(1) — Constant Time

Doing something in the same time, no matter how big the input is.

🧃 Example:
You grab a juice box from the fridge.
Doesn’t matter if the fridge has 2 or 200 drinks — you know exactly where it is.

📌 Key Idea: One step. Always.

🔵 O(n) — Linear Time

The more you have, the longer it takes.

🧦 Example:
You search for your favorite socks in a messy pile.
More socks = More searching.

📌 Key Idea: You check one by one.

🔶 O(n²) — Quadratic Time

You compare every pair.

🎒 Example:
You’re making sure every toy in your bag gets along with every other toy.
You ask: “Teddy, do you like Dino?” — for every possible pair.

📌 Key Idea: For each item, you check all others.

🔷 O(n³) — Cubic Time

Triple nested work.

🧁 Example:
You’re baking a 3-layer cake and trying every combination of frosting, sponge, and…