Hash tables: a formula decides where each key lives

Seven buckets receive keys according to key mod 7, with collisions stacked as chains beneath each bucket. A lookup for the key 23 jumps directly to bucket 2, illustrating how hashing narrows the search space instantly. The animation highlights why insert and lookup operations run in average O(1) time, making it useful for students learning data structures, hash function design, and collision resolution strategies in computer science courses.

16:9 · every frame verified for overlaps, spacing and edges before rendering

The prompt that made it

Keys are placed in seven buckets by key mod 7, collisions are chained below the bucket, and a lookup of 23 goes straight to bucket 2; average O(1) insert and lookup.

Make your own version

Make the next one in this series

• Show what happens when the load factor grows too high and chains get long
• Compare chaining versus open addressing for resolving the same set of collisions
• Animate how a poor hash function creates uneven bucket distribution and slower lookups

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