Question at position 27 Given a binary tree of height 3 with 5 nodes and the postorder traversal ABCDE Which node is the root?BCEDA单项选择题
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Question

Question at position 27 Given a binary tree of height 3 with 5 nodes and the postorder traversal ABCDE Which node is the root?BCEDA

BlackTom AI · Accepted Answer

First, let's restate what's given: we have a binary tree of height 3 with 5 nodes, and the postorder traversal is ABCDE. In postorder traversal, nodes are visited in the order: left subtree, right subtree, then the root. Therefore, the last symbol in the postorder sequence must be the root of the entire tree.

Option B: If B were the root, the traversal would have to end with B, since the last visited node in postorder is the root. But the given postorder ends with E, so B cannot be the root. This makes option B incorrect.

Option C: Similarly, if C were the root, the last element of the postorder would be C. The provided sequence ends with E, so C cannot be the root. This option is invalid.

Option E: If E is the root, it aligns perfectly with the fundamental property of postorder traversal: the root appears last. Since the sequence ends with E, E is a coherent root candidate for the entire tree. This matches the core rule of postorder.

Option D: If D were the root, the last element would be D in postorder, which contradicts the given final element E. Hence D cannot be the root.

Option A: If A were the root, the postorder would end with A, not E, which again contradicts the provided sequence. Therefore A is not the root.

In summary, evaluating each option against the defining feature of postorder traversal (root is last), only the choice that places E at the end remains consistent with the traversal ABCDE, while all other options place a different node as the last element and thus as root.

Question at position 27 Given a binary tree of height 3 with 5 nodes and the postorder traversal ABCDE Which node is the root?BCEDA单项选择题

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