The following numbers are inserted into an empty binary search tree in the…

2004

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)?

  1. A.

    2

  2. B.

    3

  3. C.

    4

  4. D.

    6

Attempted by 409 students.

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Correct answer: B

Solution: Build the binary search tree by inserting the numbers in order, then find the maximum distance from root to any leaf.

  1. Insert 10 as the root.

  2. Insert 1: goes to the left of 10.

  3. Insert 3: less than 10 so left; greater than 1 so right child of 1.

  4. Insert 5: goes to the right of 3.

  5. Insert 15: right child of 10.

  6. Insert 12: left child of 15.

  7. Insert 16: right child of 15.

Paths from root (10) to leaves and their distances:

  • 10 → 1 → 3 → 5 (distance 3)

  • 10 → 15 → 12 (distance 2)

  • 10 → 15 → 16 (distance 2)

The maximum distance from the root to any leaf is 3.

Therefore the height of the binary search tree is 3

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