Approach

When asked how to check if a binary tree is a binary search tree (BST) during an interview, it's important to provide a structured answer that demonstrates both your understanding of binary trees and your coding abilities. Here’s a clear framework to tackle this question:

1. Define a BST: Start by explaining what a binary search tree is.

2. Outline the Properties: Discuss the key properties that a binary search tree must satisfy.

3. Choose an Approach: Explain the algorithmic approach you will take.

4. Explain Your Code: Walk through your code step-by-step.

5. Consider Edge Cases: Mention any edge cases and how your code handles them.

6. Discuss Complexity: Conclude with the time and space complexity of your solution.

Key Points

• Understanding BST: A BST is a binary tree where each node has at most two children, and for any given node:

• The left subtree contains only nodes with values less than the node’s value.

• The right subtree contains only nodes with values greater than the node’s value.

• Clarity and Conciseness: Interviewers are looking for clear explanations and logical reasoning in your response.

• Algorithmic Thinking: Show your thought process when selecting your approach, whether it be recursion, iteration, or another method.

Standard Response

Here’s how you might respond to the question, "How can you write code to check if a binary tree is a binary search tree?"

class TreeNode:
 def __init__(self, value=0, left=None, right=None):
 self.value = value
 self.left = left
 self.right = right

def is_bst(node, min_value=float('-inf'), max_value=float('inf')):
 # Base case: An empty tree is a BST
 if node is None:
 return True
 
 # Check if the current node's value is within the valid range
 if not (min_value < node.value < max_value):
 return False
 
 # Recursively check the left and right subtrees
 return (is_bst(node.left, min_value, node.value) and
 is_bst(node.right, node.value, max_value))

Explanation of the Code

• TreeNode Class: The TreeNode class defines the structure of the nodes in the binary tree.

• is_bst Function: This function checks whether the binary tree rooted at node is a BST.

• Base Case: If the node is None, return True (an empty tree is a BST).

• Value Check: Ensure the current node's value is between minvalue and maxvalue.

• Recursive Check: Call is_bst for the left child with updated max value and for the right child with updated min value.

• Edge Cases: This code handles:

• Completely empty trees.

• Trees with a single node.

• Trees with duplicate values (which are not allowed in a strict BST).

• Time Complexity: The time complexity is O(n) since we are visiting every node once.

• Space Complexity: The space complexity is O(h) where h is the height of the tree, which is the space used by the recursion stack.

Tips & Variations

Common Mistakes to Avoid

• Ignoring Edge Cases: Always consider cases like an empty tree, a tree with one node, or trees with duplicate values.

• Incorrect Value Ranges: Ensure that you are correctly maintaining the min and max values as you traverse the tree.

Alternative Ways to Answer

• Iterative Approach: You could also use an iterative method with a stack to avoid recursion.

Role-Specific Variations

• Technical Positions: Focus on the efficiency of your solution and discuss trade-offs.

• Managerial Roles: Emphasize your ability to lead a team in implementing data structures effectively.

• Creative Positions: Discuss innovative ways to visualize or explain the BST properties.

Follow-Up Questions

• Can you explain how this would change with a self-balancing tree?

• How does this solution scale with very large binary trees?

• Can you implement this in another programming language?

Conclusion

By following this structured approach to answering the