Sorting, binary search, and when you only need the top K
By the end of today you can explain why sorting costs n log n and searching sorted data costs log n, write a binary search with correct boundaries, and decide whether sorting first is worth it.
YesterdayOn Day 18 you saw recursion split a problem into smaller versions of itself. Binary search is that idea applied to a sorted sequence.
TomorrowTomorrow, trees, which are what you get when you keep that halving structure permanently rather than recomputing it.
Why this matters
Binary search is the clearest example of the whole discipline: halve the problem each step and a million items become twenty comparisons. Day 43's database index is this idea stored on disk.
- Sorting
- Binary search
- Logarithmic cost
- Sorting to enable
- Heaps
- Priority queues
- Top K without sorting
Learn it
80 minCopy this into Claude or ChatGPT. It quizzes you before it explains anything, which is deliberate. The resources under it are how you check what it told you.
Today's Master Prompt
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Check it against something that is not a model
An assistant can be fluent and wrong, and on a topic you met today you will not catch it. These cover the same ground and were made by people who do this for a living, so they are what you hold the explanation up against. They are other people's work and we only link to them, so judge them for yourself.
7 hand-picked resources
Free · sign inVideos, official docs and articles covering the same ground, each opened and annotated by hand. They are what you check the assistant against on a day you cannot yet catch it being wrong.
Build it
50 minWrite binary search by hand and test it against five cases: present, absent, first element, last element, and an empty list. Then time finding an item in a list of a million integers three ways: linear scan, sort plus binary search, and a set. Include the sort cost in the second timing.
Recall it
25 minAnswer out loud, reveal, then mark honestly whether you had it. That score is the only thing on this page you do not get to choose.
5 recall questions
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Rate it
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Mastery tracking
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Recap
- 01Comparison sorting costs n log n; searching sorted data costs log n
- 02Halving a million takes twenty steps, which is why log n feels like magic
- 03Sort first when you will search often, not when you will search once
- 04Hashing beats both when you only need exact matches
Your progress
Free · sign inMark days complete, pick up where you left off across devices, and watch completion and mastery diverge. Free, and the account exists only so ninety days of work cannot vanish with a cleared browser.