GATE CS 2025 Set 2 Q.35: Binary Trees, Binary Search Trees and Balanced Trees

Suppose the values $10, -4, 15, 30, 20, 5, 60, 19$ are inserted in that order into an initially empty binary search tree. Let $T$ be the resulting binary search tree. The number of edges in the path from the node containing $19$ to the root node of $T$ is ___________. (Answer in integer)

Your answer

Official answer and solution

Official answer: 4
From: Official GATE 2025 answer key

Solution

Insert the keys sequentially into the BST and count the edges from the root 10 down to 19.

Inserting $10, -4, 15, 30, 20, 5, 60, 19$ into an initially empty BST:

10 becomes the root (depth $0$ ).
-4 goes to the left of 10; 5 goes to the right of -4.
15 goes to the right of 10 (depth $1$ ).
30 goes to the right of 15 (depth $2$ ).
20 goes to the left of 30 (depth $3$ ); 60 goes to the right of 30.
19 goes to the left of 20 (depth $4$ ).

The unique path from 19 to the root 10 is $19 \rightarrow 20 \rightarrow 30 \rightarrow 15 \rightarrow 10$ , which contains $4$ edges.

Final answer

Common trap

Counting the number of nodes (5) on the path instead of the number of edges (4).

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2025 Computer Science and Information Technology - Session 2 (CS2)
Question: 35 of 65
Section: Computer Science and Information Technology

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