Explain hash maps intuitively: key, hash, bucket, collision — without language APIs.

Hash map mechanics

A hash map stores key → value. The key's hash code picks a bucket index; if two keys land in the same bucket, that's a collision—resolved by chaining (list in bucket) or open addressing (probe next slot).

hash(key) % buckets → bucket i → (key,value) chain

• Average O(1) get/put if load factor stays reasonable and hash spreads keys.
• Bad hash / many collisions degrade toward O(n)—attackers can craft keys (hash DoS).
• Equals contract: equal keys must have equal hash codes.