Big-O Visualized

Big-O notation answers one question: as the input gets bigger, how fast does the work grow? It ignores constants and hardware and focuses on the shape of the growth — which is what decides whether your code still works at a million items.

What you’ll learn

• what O(1), O(log n), O(n), and O(n²) mean in practice
• how dramatically they diverge as n grows
• how to spot each one in real code

The common complexities

Big-O	Name	Grows	Example
O(1)	constant	not at all	dict/set lookup, list[i]
O(log n)	logarithmic	very slowly	binary search
O(n)	linear	steadily	scanning a list, x in list
O(n²)	quadratic	explosively	nested loops, bubble sort

Watch them diverge

Same axes, four growth rates. At small n they look similar — but O(n²) shoots off the chart almost immediately while O(1) and O(log n) barely move:

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O(1) stays flat, O(log n) crawls, O(n) rises steadily, and O(n squared) explodes off the chart.

The lesson: an O(n²) algorithm that’s fine for 100 items can be hopeless at 100,000. When your data can grow, the Big-O is what matters — not how fast the code feels on a small test.

Try it: Big-O Exercises

Exercise 1 – Constant time O(1)

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Exercise 2 – Linear time O(n)

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Exercise 3 – Quadratic time O(n²)

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