Consider the following tree: 14 / \ 2 11 / \ / \ 1 3 10 30 / / 7 40 What is the order of nodes visited using a post-order traversal?

Question

Consider the following tree: 14 /  \  2  11 / \ / \ 1  3  10 30 /  /  7  40 What is the order of nodes visited using a post-order traversal?

BlackTom AI · Accepted Answer

First, I restate the problem to ensure we’re aligned: we have a binary tree with root 14, left child 2, right child 11; the left subtree 2 has children 1 and 3; the right subtree 11 has left child 10 and right subtree 30, which itself has left child 7 and right child 40. The question asks for the post-order traversal, which visits left subtree, then right subtree, and finally the node itself.

Starting with the left subtree of the root (rooted at 2):
- Visit left subtree of 2, which is node 1. Since 1 has no children, 1 is visited first.
- Then visit right subtree of 2, which is node 3. Since 3 has no children, 3 is visited next.
- Finally visit the node 2 itself after its children, so the left-subtree sequence ends as: 1, 3, 2.

Now consider the right subtree of the root (rooted at 11):
- The left child of 11 is 10, with no children, so 10 is visited first in this subtree.
- The right subtree of 11 is rooted at 30. We must first traverse its left subtree; node 30’s left child is 7 with no children, so 7 is visited.
- Then traverse 30’s right subtree, which is node 40 with no children, so 40 is visited.
- After visiting both children of 30, we visit 30 itself, giving the sequence 7, 40, 30 for the right child’s subtree.
- After completing the left and right subtrees of 11, we visit 11 itself, yielding the right-subtree sequence: 10, 7, 40, 30, 11.

Combining the two major subtrees under the root: we concatenate the left-subtree result (1, 3, 2) with the right-subtree result (10, 7, 40, 30, 11), and finally visit the root 14.

Thus, the overall post-order sequence should be: 1, 3, 2, 10, 7, 40, 30, 11, 14.

In the provided option, the sequence is given as 1, 3, 2, 7, 10, 40, 30, 11, 14. The discrepancy occurs at the portion after 2: the correct order processes 10 before 7 (since 10 is the left child of 11, and 7 is in the left subtree of 30, which is in the right subtree of 11). Therefore, placing 7 before 10 does not respect the left-right-root ordering required by post-order traversal.

To summarize the sources of confusion: (a) post-order requires finishing left subtree before touching right subtree, (b) within a subtree, you fully process left subtree, then right subtree, then the node, and (c) the right subtree rooted at 11 contains 10 on the left and 30 on the right; within that right subtree, 7 (left of 30) and 40 (right of 30) must be processed before 30, and 10 must come before 11 as part of the right-subtree processing. The misplacement of 10 and 7 in the option violates these rules.

Consider the following tree: 14 / \ 2 11 / \ / \ 1 3 10 30 / / 7 40 What is the order of nodes visited using a post-order traversal?单项选择题

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