BEGINNER · 10 MIN · FREE LESSON
Hash functions
Explore hash functions through a visual, step-by-step model.
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BEGINNER · 10 MIN · FREE LESSON
Explore hash functions through a visual, step-by-step model.
Loading interactive lesson…
Enter {"text":"hello","modulus":7}. This polynomial ASCII hash is not cryptographic.
A hash compresses a key into a bounded bucket index.
Every character contributes once to a bounded rolling accumulator. Bucket reduction creates collisions and does not provide security.
Measured reads + comparisons, seed 42. Plotted sample sizes respect each lesson’s explicit input limits.
Keyboard: Space play/pause · ←/→ step · R restart · 1–5 speed. Reduced motion disables transitions.
A coat-check ticket chooses a rack, but two coats can still share a rack.
Compress a key, then check equality. Follow changing buckets, bits or owner links using step forward and back.
Predict the next bucket, matching key, membership conclusion or successor owner. Use a collision-heavy preset and explain what changes.
O(L) time and O(1) auxiliary space. A good table hash spreads ordinary keys; it does not prevent a determined attacker. This polynomial example is deliberately noncryptographic.
The reference implementations show the core operation in four languages. Bloom-filter snippets accept a hash-position function so insertion and queries share exactly the same hash family. Ring snippets show the successor lookup used for both initial assignment and reassignment.
Use table hashing to choose a candidate bucket before comparing full keys.
Hash equality does not prove key equality.
Check the invariant, cost model and boundary conditions below.
MAKE IT STICK
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