True or False? a. A preorder traversal of a binary search tree processes the nodes in the tree in the exact reverse order that a postorder traversal processes them. b. An inorder traversal of a binary search tree always processes the elements of the tree in the same order, regardless of the order in which the elements were inserted. c. A preorder traversal of a binary search tree always processes the elements of the tree in the same order, regardless of the order in which the elements were inserted.
The Correct Answer and Explanation is :
Here are the answers to the statements:
a. False
A preorder traversal processes the root node first, followed by the left subtree, and then the right subtree. Postorder traversal processes the left subtree, then the right subtree, and finally the root node. While both traverse all nodes, they do so in entirely different orders and are not reverses of each other. For instance, given a binary search tree with root ( A ), left child ( B ), and right child ( C ), preorder gives ( A, B, C ), while postorder gives ( B, C, A ).
b. True
In an inorder traversal, nodes of a binary search tree (BST) are processed in ascending order of their keys (assuming the BST properties are followed). This traversal visits the left subtree first, processes the root, and then visits the right subtree. The order of insertion does not impact this traversal because the BST’s structure ensures that smaller values are in the left subtree, and larger values are in the right subtree. As a result, an inorder traversal always processes the nodes in a sorted order.
c. False
Preorder traversal visits the root node before its subtrees (root, left, right). However, the order in which elements are inserted into a BST affects its structure, which directly affects the order of nodes in a preorder traversal. For example, inserting ( 10, 5, 15 ) and ( 10, 15, 5 ) results in two different tree structures and hence different preorder traversal orders.
Explanation:
Traversal orders define the sequence in which tree nodes are visited:
- Preorder: Root → Left → Right
- Inorder: Left → Root → Right
- Postorder: Left → Right → Root
Inorder traversal’s consistency arises from the BST property, which ensures sorted ordering. Preorder and postorder depend on the tree’s structure, influenced by insertion order.