Big-O Notation, Intuitively

Why Big-O matters

Big-O describes how an algorithm's work grows as the input grows. It lets us compare approaches before we even run them.

• O(1) — constant: array index access
• O(n) — linear: a single loop
• O(n log n) — good sorts
• O(n²) — nested loops

A quick benchmark in JavaScript:

function sum(arr) {
  let total = 0;            // O(1)
  for (const n of arr) {    // O(n)
    total += n;
  }
  return total;
}

One loop over the input → linear, O(n).