In a binary tree, if the in-order traversal yields the sequence [D, B, E, A, F,

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Question: In a binary tree, if the in-order traversal yields the sequence [D, B, E, A, F, C], what is the pre-order traversal?

Options:

Correct Answer: [A, B, D, E, C, F]

Solution:

The pre-order traversal can be derived from the in-order traversal and the structure of the tree, yielding [A, B, D, E, C, F].

In a binary tree, if the in-order traversal yields the sequence [D, B, E, A, F, C], what is the pre-order traversal?

In a binary tree, if the in-order traversal yields the sequence [D, B, E, A, F, C], what is the pre-order traversal?

Step 1: Understand that in-order traversal visits nodes in the order of left child, root, and then right child.
Step 2: Identify the root of the tree from the in-order sequence. The root is the first element in the pre-order traversal.
Step 3: In the given in-order sequence [D, B, E, A, F, C], the root is 'A' because it is the middle element.
Step 4: Split the in-order sequence into left and right subtrees based on the root 'A'. The left subtree is [D, B, E] and the right subtree is [F, C].
Step 5: For the left subtree [D, B, E], identify the root, which is 'B'. Split it into [D] (left) and [E] (right).
Step 6: For the right subtree [F, C], identify the root, which is 'C'. There is no left child, and 'F' is the right child.
Step 7: Combine the roots in pre-order: Start with 'A', then 'B', then 'D', then 'E', then 'C', and finally 'F'.
Step 8: The final pre-order traversal is [A, B, D, E, C, F].

Binary Tree Traversals – Understanding the different methods of traversing a binary tree, specifically in-order and pre-order traversals.
Tree Structure Reconstruction – The ability to reconstruct the binary tree structure from given traversal sequences.