The preorder traversal sequence of a binary search tree is 30, 20, 10, 15, 25, 23, 39, 35, 42. Which one of the following is the postorder traversal sequence of the same tree?

Given the preorder traversal: $[30, 20, 10, 15, 25, 23, 39, 35, 42]$.

In a Binary Search Tree (BST), the root is the first element in preorder, and elements smaller than the root form the left subtree while elements greater form the right subtree.

1. Root: $30$

   • Left Subtree (elements $< 30$): Preorder is $[20, 10, 15, 25, 23]$

   • Right Subtree (elements $> 30$): Preorder is $[39, 35, 42]$

2. Construct Left Subtree:

   • Root is $20$.

   • Left of $20$ ($< 20$): $[10, 15] \implies$ Root $10$, right child $15$.

   • Right of $20$ ($> 20$): $[25, 23] \implies$ Root $25$, left child $23$.

   • Postorder of left subtree (Left $\to$ Right $\to$ Root):

     • Left of $20$: $15, 10$

     • Right of $20$: $23, 25$

     • Combining with root $20$: $15, 10, 23, 25, 20$

3. Construct Right Subtree:

   • Root is $39$.

   • Left child ($< 39$): $35$.

   • Right child ($> 39$): $42$.

   • Postorder of right subtree: $35, 42, 39$

4. Overall Postorder Traversal:

   $$[\text{Left Subtree}] + [\text{Right Subtree}] + [\text{Root}]$$

   $$15, 10, 23, 25, 20, 35, 42, 39, 30$$

This matches option (D).