Baseline Binary Trees · Traversals O(1) · O(1)
A tournament organizer is drafting a single-elimination bracket on a whiteboard. The first round is a single title-holder at the top, and every subsequent round can field at most twice as many contenders as the round before it, because each slot in a round spawns at most two slots in the next. The organizer wants a one-line formula so the venue can be sized for any round number without redrawing the whole board.
Input: A single integer n — the 1-indexed level of the binary tree.
Output: Return one integer: the maximum number of nodes that can exist on level n.
1 <= n <= 30The answer always fits in a 32-bit signed integer for the given rangeInput: {"n":1}
Output: 1
Level 1 holds only the root, so the cap is 1.
Input: {"n":3}
Output: 4
Doubling each round: level 2 holds 2, level 3 holds 2^(3-1) = 4.