Graphs & Trees

Graph and tree problems are where Citadel's coding round tests whether you pick the right traversal before you start typing, not just whether you can code one. The problems in this family are rarely about an exotic algorithm. They are breadth-first search, depth-first search, and a topological peel, dressed in a setting that looks like the trading domain the firm lives in. The dressing is familiar: a chain of currency conversions, a graph of derived signals that must be computed in dependency order, a shortest sequence of one-step transformations. The grading is strict in a specific way. A correct answer produced with the wrong traversal can still be a reject.

That strictness is the thing to internalize. On a shortest-path question, the interviewer is watching for you to say "this is shortest path, so breadth-first" before any code exists. A depth-first solution that happens to pass the visible case tells them you did not see the structure. On a weighted-path question, the graded miss is usually an edge case the setting hides, like a currency converting to itself. On a dependency-order question, the tell is whether your termination check detects a cycle rather than silently returning a short answer. Three traversals carry almost all of it, so the rest of this lesson is about choosing the right one on sight and handling the edge the problem buries.