Big O Notation Comparator — Interactive Classroom

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Select complexities to compare

Input size (n) 5

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Growth Chart

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Operations at n = 5

Complexity	Operations	If 1μs each	Verdict

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Real Algorithm Examples

Algorithm	What it's like	Complexity
Array access	Opening a book to page 42 — you go straight there	O(1) — instant
Binary Search	Guessing a number — "higher or lower?" halves the options each time	O(log n) — very fast
Linear Search	Looking for your name in an unsorted list — check every single one	O(n) — depends on size
Merge Sort	Split in half, sort each half, merge back together	O(n log n) — fast
Bubble Sort	Sorting cards by swapping neighbours — very slow on big lists	O(n²) — slow
Fibonacci (naive)	Recalculates the same thing over and over — doubles the work each step	O(2ⁿ) — impossibly slow

💡 Helpful hint — what does "log" mean?
log n is the number of times you can halve n before you reach 1.
For example: log₂(8) = 3, because 8 → 4 → 2 → 1 (halved 3 times).
log₂(1000) ≈ 10 — so even with 1,000 items, you only need about 10 steps!
That's why O(log n) is so fast — and why binary search beats linear search on large lists.

📈 Big O Notation

Select complexities to compare

Growth Chart

Operations at n = 5

Real Algorithm Examples