Question

Which of the following is incorrect with respect to binary trees?

(a) Let T be a binary tree. For every k ≥ 0, there are no more than 2k nodes in level k

(b) Let T be a binary tree with λ levels. Then T has no more than 2^λ – 1 nodes

(c) Let T be a binary tree with N nodes. Then the number of levels is at least ceil(log (N + 1))

(d) Let T be a binary tree with N nodes. Then the number of levels is at least floor(log (N + 1))

I want to ask this question from Binary Tree Properties in chapter Binary Trees of Data Structures & Algorithms I

The question was asked in semester exam.

Answer 1

The correct option is (d) Let T be a binary tree with N nodes. Then the number of levels is at least floor(log (N + 1))

To explain: In a binary tree, there are atmost 2k nodes in level k and 2^k-1 total number of nodes. Number of levels is at least ceil(log(N+1)).