When Hashmaps Solve Hard Problems

Use hashmaps in hard problems when:

$1.$ You need to count occurrences or track frequencies in a sliding window

$2.$ You're looking for pairs or subarrays with a specific sum or property

$3.$ You need coordinate compression or value-to-index mapping

$4.$ You're implementing a cache with specific eviction rules

The pattern: define what lookup you need, then design keys and values to support that lookup in $O(1)$.