In binary search trees, how may pre-order traversal be most efficiently utilized?

How does a balanced binary search tree improve upon the standard binary search tree in terms of operations and efficiency?

How may the advantages of pre-order traversal in binary search trees be maximised?

In the binary search tree, write a function that takes in a root, p, and checks whether the tree rooted in p is a binary search tree or not. What is the time complexity of your function? def is_bst(self, p: Node):

What is the most popular application of in-order traversal in binary search trees? Please don't just copy and paste someone else's answer it will result in automatic thumbs down.

1. Stack 2. Queue 3. Singly-linked list 4. Binary search tree 5. AVL tree 6. Priority queue 7. Hash table Can be used as an auxiliary data structure for expression evaluation with a binary tree.   Often implemented with complete binary trees satisfying a partial order property.   Data is not ordered, but insertion and search are expected to take O(1) time.   Data is fully ordered, insertion, removal and search are guaranteed to be less than O(n) time.

What is the most popular application of in-order traversal in binary search trees?

Data Structure/Operation Stack/Push Balanced Binary Search Tree/Delete Binary Heap/DeleteMin Hash Table/Find Vector/push_back Binary Heap/Insert Balanced Binary Search Tree/Delete Queue/pop Vector/Find Linked List/InsertAtHead Hash Table/Insert Average Complexity in Big-O 0 (1)

In binary search trees, what is one of the most significant applications that makes use of pre-order traversal?