graphs

The canonical grid question, and the template for every flood-fill, shortest-path, and region-labeling variant FDE loops throw at you. BFS vs DFS vs union-find: here's which to write and which to merely mention.

Kahn's algorithm gets you level one. The round is won at level three, where 'run up to K tasks at once' breaks naive topo sort, and the indegree bookkeeping you chose at L1 either saves you or sinks you.

The practical build that's secretly a graph problem: formulas are a dependency DAG, evaluation is DFS with memoization, and the three-color cycle trick decides whether A1=B1, B1=A1 crashes you or earns the offer.

Palantir's signature coding genre isn't an algorithm; it's working from unfamiliar documentation: a graph API, a custom serialization spec, a mini query language. The behaviors graders score, plus the BFS-over-an-opaque-client worked example.

A grid where some cells start infected, and each step every infected cell infects its orthogonal neighbors. How many steps until everything is infected, or -1 if some cell is unreachable? This is rotting oranges in disguise, and the multi-source BFS framing is what they want to hear.

It looks like the grid BFS everyone has written a hundred times, and the usual visited set is exactly what makes it wrong. The fix is one line and it is the whole point of the question.