99 Elm Problems/Problem 60

60.a) Construct a height-­balanced binary trees with a given number of nodes.

Consider a height­-balanced binary tree of height H. What is the maximum number of nodes it can contain? Clearly, MaxN = 2**H ­ 1. However, what is the minimum number MinN? This question is more difficult.

60.b) Find the minimum number of nodes in a height-­balanced binary tree of height H.

60.c) Find the maximum height H a height­-balanced binary tree with N nodes can have. Find out how many height-­balanced trees exist for N = 15.

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Example in Elm:

Result:

Solutions