GATE | GATE-CS-2017 (Set 1) | Question 17

Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:

Note: The height of a tree with a single node is 0.
(A) 4 and 15 respectively
(B) 3 and 14 respectively
(C) 4 and 14 respectively
(D) 3 and 15 respectively


Answer: (B)

Explanation:

  • The minimum height of a binary search tree will be when tree is full complete tree:

    g20172_18

    Now, let h be the height of the binary tree, then, 2^{0}+2^{1}+2^{2}+2^{3}+…+2^{h}=2^{h+1}-1 <= n
    So, Min height of a binary search tree = log2(n+1) – 1 = log2(15+1) – 1 = 4 – 1 = 3

  • The maximum height of a binary search tree will be when the tree is fully skewed: (like below)

    g20172_19

    Max height of the binary search tree = n-1 = 15 – 1 = 14, where the tree is Skewed tree

Therefore, option B 

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