Leetcode 2508. Add Edges to Make Degrees of All Nodes Even

Given an undirected simple graph, determine whether you can add at most two edges (no self-loops or duplicates) so every vertex has even degree. The core challenge is a parity check: you must handle cases with 0, 2, or 4 odd-degree nodes and verify whether non-existing edges can pair them up (possibly across components) to fix all parities.