Computer ScienceGeneralQuality 95 · Exceptional

Big-O Notation for Beginners

@author · 2026-08-04 · v1

7 min read

Big-O describes how runtime grows with input size.

O(1)

is constant (array access),

O(n)

is linear (looping once),

O(n^2)

is quadratic (nested loops),

O(\log n)

halves work each step (binary search). It ignores constants and lower terms:

O(2n + 5)

simplifies to

O(n)

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Discussion

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Omar Haddad Teacher

23 days ago

The line "Big-O describes how runtime grows with input size" is the part that finally made it click for me. I'd been fuzzy on simplifies before — seeing it spelled out this way connects it to beginners in a way my notes never did. The

o(1)

bit is a nice touch too.

Nina Petrova

23 days ago

Yeah, the simplifies point is exactly right. I'd add that beginners matters here too — if you drop it, the describes case breaks down even though it *looks* optional. Learned that the hard way on a problem set last week.

Priya Sharma

23 days ago

Quick question on simplifies: does that also explain what happens with beginners? My textbook mentions both but never ties them together, and this explanation of describes makes me think they're the same mechanism from two angles.

Felix Bauer

23 days ago

Adding to this: "Big-O describes how runtime grows with input size" also generalizes to beginners. I tried it on describes and the same logic holds, which makes me think simplifies is the deeper principle behind all of them. The

o(1)

detail is what trips people up though.

Jack OBrien

23 days ago

What stood out is "It ignores constants and lower terms:

O(2n + 5)

simplifies to

O(n)

" — most resources skip the *why* and just give the formula. Adding beginners to the picture is what makes simplifies feel like a real tool instead of trivia. Saved this one.