Binary Search Tree Validation Concepts

The video tutorial explains how to determine if a binary tree is a binary search tree (BST). It begins with an introduction to the problem and discusses clarifying questions about data types and handling duplicates. A basic algorithm is presented, followed by an improved version using bounds to ensure correctness. The tutorial then provides a detailed implementation of the recursive algorithm, tests it with valid and invalid trees, and concludes with a runtime analysis, highlighting the algorithm's efficiency.

What is the primary property of a binary search tree (BST)?

• All nodes to the right of a parent node are greater, and all nodes to the left are less than or equal to the parent node.

• All nodes have unique values.

• All nodes are arranged in a complete binary tree structure.

• All nodes have at most two children.

Why is it important to clarify the type of values in the tree before implementing the BST validation algorithm?

• To decide the comparison logic for the values.

• To ensure the values are sorted.

• To determine the memory requirements.

• To choose the appropriate data structure for the tree.

In the basic algorithm for checking if a tree is a BST, what is the main limitation?

• It does not traverse the entire tree.

• It is too complex to implement.

• It does not handle duplicate values correctly.

• It does not check the bounds of the nodes.

What is the purpose of establishing bounds in the improved BST validation algorithm?

• To limit the depth of the tree.

• To ensure each node falls within a valid range.

• To optimize the traversal speed.

• To handle duplicate values.

In the improved algorithm, what should be the new minimum value when traversing to the right child of a node?

• The current node's value.

• The maximum integer value.

• The current node's left child's value.

• The current node's right child's value.

What is the base case for the recursive BST validation function?

• When the node's value is out of bounds.

• When the node has no children.

• When the node is a leaf node.

• When the node is null.

Why is it necessary to check both left and right subtrees in the BST validation algorithm?

• To verify that all nodes meet the BST properties.

• To ensure the tree is balanced.

• To find the height of the tree.

• To count the number of nodes.

What should the algorithm return if a node's value is not within the specified bounds?

• Null

• False

• The node's value

• True

What is the runtime complexity of the BST validation algorithm?

• O(log n)

• O(n^2)

• O(1)

• O(n)

Why is it important to test the algorithm with both valid and invalid trees?

• To count the number of nodes.

• To measure the algorithm's speed.

• To ensure the algorithm handles all edge cases.

• To find the height of the tree.