In-order traversal of a binary search tree (BST) always gives a sorted sequence of the values, regardless of the tree's exact structure. The reason is that in-order traversal visits the left subtree, then the node itself, and finally the right subtree. As per the property of a BST, all elements in the left subtree are smaller than the node, and all elements in the right subtree are larger than the node.
An AVL tree is a self-balancing binary search tree, and the in-order traversal of an AVL tree also gives a sorted sequence of values. This is because the AVL tree maintains the same property as the BST, i.e., all elements in the left subtree are smaller than the node, and all elements in the right subtree are larger than the node.
So, when a BST is converted into an AVL tree, the in-order traversal of both trees will yield the same sequence of values.
On the other hand, pre-order and post-order traversals depend on the exact structure of the tree, not just on the relative ordering of the values. Since the process of converting a BST into an AVL tree may involve rotations that change the tree's structure, the pre-order and post-order traversals of the AVL tree and the original BST might not be the same. Therefore, options b and c are incorrect.
