The depth (height) of a complete binary tree with n nodes is given by which formula?
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The depth (height) of a complete binary tree with $n$ nodes is given by which formula?
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Answer: A. floor(log2(n))
In a complete binary tree with n nodes, the maximum level index (height/depth) is given by floor(log2(n)).
Step-by-step Derivation:
Step 1: A complete binary tree of depth d has between 2^d and 2^(d+1) - 1 nodes.
Step 2: Taking base-2 logarithm: d <= log2(n) < d + 1.
Step 3: Therefore, the depth d = floor(log2(n)).