Provide the result of post-order traversal of the following Binary Search Tree (BST) as a sequence of nodes.

Question

BlackTom AI · Accepted Answer

To determine the post-order traversal, I’ll break down the BST into its left and right subtrees and then combine the results in the standard post-order way (left, right, root).

Option analysis begins with the given question and answer set. The question asks for the post-order traversal of the BST shown in the diagram.

Option a. 5, 2, 1, 3, 8, 6, 7, 9, 10
- This sequence starts with the root 5, which would be incorrect for post-order since the root should appear last. It looks more like a preorder or a misordered traversal, not post-order.

Option b. 1, 3, 2, 7, 6, 10, 9, 8, 5
- This matches the standard post-order result when visiting left subtree first (1, 3, 2), then right subtree (7, 6, 10, 9, 8), and finally the root (5). The left subtree of the root yields 1, 3, 2; the right subtree yields 7, 6, 10, 9, 8; and then 5 is appended at the end. This aligns with the tree structure shown.

Option c. 5, 2, 8, 1, 3, 6, 9, 7, 10
- This sequence begins with the root 5 and interleaves subtree roots (2, 8) early, which is not consistent with post-order. It resembles a mixture of preorder-like prefixes and subtrees in an incorrect order, so it’s not a valid post-order for this tree.

Option d. 1, 2, 3, 5, 6, 7, 8, 9, 10
- This ends with an increasing sequence and places 5 before many nodes, which contradicts post-order where the root should come last. It also doesn’t respect the hierarchical relationships in the right subtree (7 under 6 under 8 under 5) as required by post-order traversal.

Putting it together, the correct post-order sequence for the BST depicted is obtained by listing the left subtree nodes first (1, 3, 2), then the right subtree nodes (7, 6, 10, 9, 8), and finally the root (5). The reasoning for each option highlights the typical post-order constraints: left-before-right-before-root, and preserving the subtree structures as shown in the diagram.

FIT1008-FIT2085_S1_2025 Week 11 Workshop Quiz

Provide the result of post-order traversal of the following Binary Search Tree (BST) as a sequence of nodes.

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