Arrays & hashing

If you need “have I seen this value?”, choose a Set. If you need “what value belongs to this key?”, choose a Map. If a key is a compound value, define a stable primitive key or use nested maps rather than expecting two objects to compare by shape.

Frequency maps discard order and retain multiplicity. They are useful for duplicates, anagrams, and “how many times?” questions. Be clear about what counts as equal in the input domain.

Trade space for time. A hash map turns "search the rest of the array" (O(n)) into a lookup (O(1) on average). A nested loop becomes a single pass: O(n) time, O(n) space.

Reach for it whenever a problem asks you to find a pair, a partner or a previous occurrence.

Sorting characters is easy to reason about and costs O(k log k) per item. A frequency signature can reduce key construction to O(k) for a small fixed alphabet, but it needs an unambiguous encoding and an explicit alphabet constraint.

Buckets give a simple linear scan over the bounded frequency range, at the cost of O(n) bucket slots. A size-k heap is attractive for small k, with O(u log k) selection and less selection memory. Sorting all distinct values is another option when u log u time is acceptable and simpler code matters.