TTrave_2
Consider the post-order traversal of the following BST. Note that visiting the node is actually printing the node. Which node is printed 5th?

Question

TTrave_2
Consider the post-order traversal of the following BST. Note that  visiting the node is actually printing the node. Which node is printed 5th?

BlackTom AI · Accepted Answer

To analyze a post-order traversal, recall the rule: visit left subtree, then right subtree, then the node itself (root).
Option by option, we consider where each value would appear in a standard BST post-order sequence, noting that the exact order depends on the specific shape of the BST in the diagram.
- Option 100: If 100 were a leaf in the left subtree, it would typically be one of the earliest nodes visited in post-order, often printed before nodes higher up in the tree. It being the 5th would require a very particular subtree structure; without that structure, it is less likely to consistently appear exactly as the 5th.
- Option 300: Given the provided answer is 300, this option would align with a scenario where 300 is encountered after finishing the left subtree and part of the right subtree, before printing the root of a higher-level subtree. In many BST shapes, the root of a smaller subtree in the left region or the first node in a specific right-subtree path can end up as the 5th in post-order.
- Option 775: In a BST post-order, large values such as 775 are often located in the right subtree. If 775 were deeply nested as a right-right path, it might appear later in the sequence, potentially closer to the end, but not typically as the 5th unless the subtree structure is very constrained.
- Option 201: As an intermediate value, 201 could appear after finishing its own left subtree and possibly its right subtree, but whether it lands exactly fifth depends on how many nodes precede it in post-order within its own subtrees. Without the diagram, we can’t pin it as the 5th with certainty.
- Option 750: Similar to 775, 750 would usually belong to the right subtree’s region. Its position in post-order would depend on how many nodes lie in its left/right subtrees before it; being precisely the 5th is not guaranteed across all BST shapes.
In summary, because post-order prints all nodes in the left subtree first, then the right subtree, and finally the root, the exact 5th element is determined by the specific shape of the BST. The given correct answer being 300 indicates that in this particular BST diagram, 300 is the node that appears after completing its left and part of its right subtree, but before the parent/root of its enclosing subtree. The other options would require alternative subtree configurations to occupy the 5th position, which does not match the presented BST in this question.

TTrave_2 Consider the post-order traversal of the following BST. Note that visiting the node is actually printing the node. Which node is printed 5th?

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