O(log n)
—Logarithmic Time
DreamInput doubles → only 1 more step. Incredibly efficient.
Mental model
Searching a phone book: open to the middle page, decide which half has your name, ignore the other half. Repeat. Each step eliminates 50% of what's left — so a million entries takes only ~20 steps.
Interactive Visualisation
📖 Searching a phone book: open to the middle page. Is your name before or after? Ignore the wrong half. Open to the middle of what's left. Repeat. Each step cuts the problem in half — so a million names takes only ~20 steps.
Array size:Target: 0 · max 4 steps
Steps needed (max) as n grows
83
164
325
646
1287
1k10
1M20
How it scales
n = 8
3 steps
n = 64
6 steps
n = 1,024
10 steps
n = 1,048,576
20 steps