Algorithms & Big-O

What it is

Big-O is shorthand for how the cost of an algorithm grows as its input grows. You ignore constants and hardware and ask a simpler question: if I double the input, does the work double, quadruple, or barely move? The alphabet of answers — constant, logarithmic, linear, linearithmic, quadratic, exponential — is small enough to carry in your head and precise enough to tell you which of two designs will survive real data.

Why it matters

Algorithms are where a small, correct-looking program turns into an outage. A nested loop over two lists is four lines and costs the product of their sizes; at a hundred rows nobody notices, at a hundred thousand the request times out. Big-O is also how engineers argue about a design without benchmarking it: it names the reason one approach will not scale. And the standard algorithms — sorting, searching, traversing — are solved problems, so recognising them saves you from inventing a slower version of something that already exists.

In this track

1. How cost grows (Big-O) (01-cs-fundamentals/14-algorithms-big-o/01-how-cost-grows-big-o) — reading growth rates and choosing the notation that describes an algorithm honestly.
2. Sorting, searching and traversal (01-cs-fundamentals/14-algorithms-big-o/02-sorting-searching-and-traversal) — the standard procedures, and the cost each one carries.

Prerequisites

• Data Structures (01-cs-fundamentals/02-data-structures)

Go deeper

• Pseudocode (01-cs-fundamentals/07-pseudocode) — writing an algorithm in plain language before judging how it grows.
• Operating Systems (01-cs-fundamentals/15-operating-systems) — what the memory access pattern behind an algorithm costs on real hardware.
• Database Internals (01-cs-fundamentals/04-database-internals) — where sorting and searching happen for you, and why the notation still applies.