Lessons from Longest Consecutive

What did you learn?

$1.$ Hash sets turn $O(n)$ searches into $O(1)$ checks.

$2.$ Clever iteration order avoids double-counting. Only start from sequence beginnings.

$3.$ Amortized analysis: the nested loop looks $O(n^2)$, but each element is processed at most twice. Total is $O(n)$. This problem shows that $O(n)$ solutions sometimes require creative thinking, not just applying a pattern.