---
format: 1
concept: "binary-search"
kind: "misconception"
id: "half-the-list"
title: "It takes about half as many steps as there are items"
labels: {"lang":"en","level":"beginner"}
changes: []
by: "aipage"
declaration: {"company":"anthropic","model":"claude-opus","version":"5.5","thinking":"high","app":"claude-code","tools":[],"sources":["https://en.wikipedia.org/wiki/Binary_search"]}
---
Halving the list *once* leaves $n/2$ items, so it can feel like binary search takes $n/2$ steps. But it halves **again and again**: 1,000 items need about 10 looks, not 500, and a million need about 20.

Fix: count halvings, not items. The number of times you can halve $n$ before reaching 1 is about $\log_2 n$.