Question

If you are given the order of the nodes as visited by a preorder traversal and the order of the nodes as visited by an inorder traversal, do you have enough information to reconstruct the original tree? Assume that the nodes all have unique values.

True
False

Answer 1

Given the preorder and inorder traversal sequences of a binary tree where all nodes have unique values, it is indeed possible to reconstruct the original tree. The preorder list identifies the root, while the inorder list enables division into left and right subtrees, facilitating a recursive reconstruction.

Step-by-step explanation:

The question asks whether having the order of nodes from a preorder traversal and an inorder traversal is sufficient to reconstruct the original binary tree. The answer is True. Given these two sequences and knowing each node has a unique value, you can reconstruct the original binary tree. The first node in the preorder list is the root of the tree. In the inorder list, the nodes to the left of the root are part of the left subtree, and nodes to the right are part of the right subtree. This information can be used recursively to rebuild the entire tree structure.

Steps to Reconstruct a Binary Tree

1. Identify the root node from the preorder sequence.
2. Locate the root node in the inorder sequence.
3. Divide the inorder sequence into left and right subtrees based on the root node's position.
4. Recursively apply steps 1-3 for the subtrees using the corresponding preorder segments.

This method is guaranteed to reconstruct the original tree structure if all node values are unique.