Suppose you are given a binary tree with n nodes, such that each node has exactly either zero or two children. The maximum height of the tree will beQuestion 49Select one:(n+1)/2cross outn/2-1cross outn/2+1cross out(n-1)/2
Question
Suppose you are given a binary tree with n nodes, such that each node has exactly either zero or two children. The maximum height of the tree will beQuestion 49Select one:(n+1)/2cross outn/2-1cross outn/2+1cross out(n-1)/2
Solution
The maximum height of a binary tree with n nodes, where each node has either zero or two children, will be (n-1)/2. This is because in a full binary tree (a binary tree in which every node has either 0 or 2 children), the number of nodes is maximum for a given height. The number of nodes n in a full binary tree of height h is given by the formula n = 2^(h+1) - 1. Solving this formula for h gives h = log2(n+1) - 1. In the worst case, when n is just less than a power of 2, the height of the tree is approximately log2(n) which is (n-1)/2 for large n.
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