dfs

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.

The third member of the grid trilogy, and the one that tests backtracking discipline: marking, unmarking, and the early-exit pruning that turns a timeout into a pass.

Almost everyone writes the version that only compares each node to its immediate children, and almost every interviewer has a counterexample ready. The fix is to carry a valid (low, high) range down the recursion, or to check that an inorder traversal is strictly increasing.

The longest path between any two nodes need not pass through the root, which is what trips people up. The clean answer is one DFS that returns each node's height while updating a global best as it goes. First, nail down whether diameter counts edges or nodes.

A path can start and end anywhere and bends through at most one node, values can be negative, and you want the maximum sum. The move is a DFS that returns the best downward gain (clamped at zero) while a global max tracks the best path that bridges through each node.