LeetCode 721 Accounts Merge - The Graph

Do not think of Accounts as nodes. Think of Emails as nodes!

$1.$ Assign every unique email an ID ($0, 1, 2, \ldots$).

$2.$ For each account, union all its emails together.

$3.$ Group emails by their leader.

$4.$ For each group, sort emails and prepend the account name.

This reframing makes the problem clean. The account name is metadata; the emails define connectivity. Time: $O(n \cdot \alpha(n))$ where $n$ is the total number of emails across all accounts.