Computer ScienceGeneralQuality 82 · Exceptional

How Binary Search Works

@author · 2026-08-18 · v1

7 min read

Binary search finds a value in a sorted list by repeatedly halving the search space. Compare the target to the middle element: if smaller, search the left half; if larger, the right. This gives

O(\log n)

time instead of

O(n)

for linear search — finding an item in a million entries takes about 20 steps.

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Lena Volkov

23 days ago

The line "Binary search finds a value in a sorted list by repeatedly halving the search space" is the part that finally made it click for me. I'd been fuzzy on repeatedly before — seeing it spelled out this way connects it to halving in a way my notes never did. The

o(\log n)

bit is a nice touch too.

Sanjay Gupta

23 days ago

Yeah, the repeatedly point is exactly right. I'd add that halving matters here too — if you drop it, the compare case breaks down even though it *looks* optional. Learned that the hard way on a problem set last week.

Theo Andersson

23 days ago

Quick question on repeatedly: does that also explain what happens with halving? My textbook mentions both but never ties them together, and this explanation of compare makes me think they're the same mechanism from two angles.

Elena Rossi

23 days ago

Adding to this: "Binary search finds a value in a sorted list by repeatedly halving the search space" also generalizes to halving. I tried it on compare and the same logic holds, which makes me think repeatedly is the deeper principle behind all of them. The

o(\log n)

detail is what trips people up though.

Amara Okafor

23 days ago

What stood out is "Compare the target to the middle element: if smaller, search the left half; if larger, the right" — most resources skip the *why* and just give the formula. Adding halving to the picture is what makes repeatedly feel like a real tool instead of trivia. Saved this one.