Discussion
What is the maximum number of nodes at level 'L' in a binary tree ?
Answer: A
The maximum number of nodes at level L is \(2^{L}\), counting the root as level 0.
Each node has at most two children, so each level can hold at most twice as many nodes as the one above: 1 at level 0, 2 at level 1, 4 at level 2, and \(2^{L}\) at level L.
Some books number the root as level 1, and with that convention the same count is written \(2^{L-1}\). The key follows the root-at-level-0 convention. \(2^{L} - 1\) is a different quantity, the total number of nodes in a full tree of L levels, and \(L^{2}\) grows far too slowly.
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