Section Recap

You now have hash table proficiency:

$1.$ Hash sets and maps: $O(1)$ average lookup, insert, delete.

$2.$ Frequency counting: count occurrences of each element in $O(n)$.

$3.$ Complement lookup (two-sum): find pairs by checking if the complement exists.

$4.$ Custom keys: group equivalent items using canonical forms.

$5.$ Prefix sum + hash: count subarrays with exact sum in $O(n)$.

$6.$ 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 $O(n^2)$ problems become $O(n)$. In the next section, I'll show you heaps for efficient min/max tracking.