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The following numbers are inserted into an empty binary search tree in the given order: 10, 1, 3, 5, 15, 12, 16. What is the height of the binary search tree (the height is the maximum distance of a leaf node from the root)? (GATE CS 2004)
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    6
Correct answer is option 'B'. Can you explain this answer?
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Binary Search Tree:

A binary search tree is a binary tree where the left subtree of a node contains only nodes with keys lesser than the node’s key and the right subtree of a node contains only nodes with keys greater than the node’s key.

Height of Binary Search Tree:

The height of a binary search tree is the maximum distance of a leaf node from the root.

Solution:

The given numbers are 10, 1, 3, 5, 15, 12, 16.

Inserting these numbers in an empty binary search tree will result in the following tree:

10
/ \
1 15
\ / \
3 12 16
\
5

The maximum distance of a leaf node from the root is 3, which is the height of the binary search tree.

Therefore, the correct answer is option 'B' (3).
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The following numbers are inserted into an empty binary search tree in the given order: 10, 1, 3, 5, 15, 12, 16. What is the height of the binary search tree (the height is the maximum distance of a leaf node from the root)? (GATE CS 2004)a)2b)3c)4d)6Correct answer is option 'B'. Can you explain this answer?
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