Question at position 19 Given a binary tree of height 3 with 5 nodes and the preorder traversal ABCDE Which nodes must be the rootCABDE

Question

BlackTom AI · Accepted Answer

Begin by restating the information we have: the tree is binary, height 3, contains 5 nodes, and the preorder traversal is ABCDE.
In a preorder traversal, the first element visited is the root of the tree. Therefore, the root must be the first symbol in the sequence, which is 'A'.
Now evaluate each answer option against this fact:
- Option C: If the root were C, the preorder would need to start with C, but the given preorder starts with A. Hence C cannot be the root.
- Option A: This option asserts 'A' as the root. Since preorder begins with A, this is consistent with the traversal and thus a valid root candidate. It matches the fundamental property of preorder.
- Option B: If B were the root, the preorder would start with B, conflicting with the provided ABCDE. Therefore B cannot be the root.
- Option D: A root of D would imply a preorder starting with D, which is not the case here, so D is incorrect.
- Option E: Similarly, root E would produce a preorder beginning with E, contradicting ABCDE, so E cannot be the root.
Overall, only the option whose text is 'A' aligns with the rule that the preorder's first element is the root, while all other options conflict with the given traversal.

Question at position 19 Given a binary tree of height 3 with 5 nodes and the preorder traversal ABCDE Which nodes must be the rootCABDE

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