The preorder traversal of a binary search tree is 15, 10, 12, 11, 20, 18, 16, 19. Which one of the following is the postorder traversal of the tree?

Given the preorder traversal of a Binary Search Tree (BST):

In a BST, all elements in the left subtree are smaller than the root, and all elements in the right subtree are greater than the root.

1. Root: $15$

2. Left Subtree of $15$: elements less than $15 \implies [10, 12, 11]$

   • Root is $10$.

   • Right child of $10$ is $12$.

   • Left child of $12$ is $11$.

3. Right Subtree of $15$: elements greater than $15 \implies [20, 18, 16, 19]$

   • Root is $20$.

   • Left child of $20$ is $18$.

   • Left child of $18$ is $16$; right child of $18$ is $19$.

Now, perform Postorder traversal (Left $\to$ Right $\to$ Root):

• Postorder of left subtree of $15$: $11, 12, 10$

• Postorder of right subtree of $15$: $16, 19, 18, 20$

• Root: $15$

Combining these gives the complete postorder traversal:

Therefore, option (B) is correct.