You now have hash table proficiency:
Hash sets and maps: average lookup, insert, delete.
Frequency counting: count occurrences of each element in .
Complement lookup (two-sum): find pairs by checking if the complement exists.
Custom keys: group equivalent items using canonical forms.
Prefix sum + hash: count subarrays with exact sum in .
Creative iteration: longest consecutive sequence shows that clever ordering avoids redundant work. Hash tables are your default when you need fast lookups. learn these patterns and many problems become . In the next section, I'll show you heaps for efficient min/max tracking.