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 a postorder traversal, do you have enough information to reconstruct the original tree? Assume that the nodes all have unique values.

a. True
b. False

Answer 1

It is false that a binary tree can be uniquely reconstructed given only the preorder and postorder traversals, as these do not provide clear information on the left and right children.

Step-by-step explanation:

The accuracy of reconstructing an original binary tree given the preorder and postorder traversals alone is false. Preorder and postorder traversals are not enough to uniquely identify a binary tree because these traversals do not provide sufficient information about the structure of the tree. Specifically, they do not indicate which nodes are left children and which are right children. For example, given two trees with different structures but with the same set of nodes, the preorder and postorder traversals could be identical, leading to ambiguity.

In contrast, if you were given either preorder and inorder or postorder and inorder traversals, you would be able to reconstruct the binary tree uniquely, because the inorder traversal helps to determine the left and right subtree division of each node in the tree.