Trees & Heaps

Trees and heaps at Apple lean toward the clean classics rather than puzzle-box twists. The questions that recur have a tidy correct answer and a small number of edge cases. Those cases separate a working solution from one that crashes on a single node or a skewed chain. Three carry most of this slice: a Premium question, a Premium question of two nodes, and the streaming median. The first two are tree recursion. The third is the two-heap pattern, and it is the one that tests whether you can keep an invariant true across a long sequence of operations.

Two shapes cover all three. When a node needs a value from each of its subtrees, you are in a bottom-up recursion. Solve both children first, combine what they report, return one thing to the parent, and let the real answer accumulate in a variable off to the side. The streaming median runs on two heaps kept balanced against each other, which parks the middle of the data at the top of one heap or the other. Name the shape first. After that the work is bookkeeping, getting the base cases and the balance right.