Two Sum in Binary Search Tree (BST) 🎯

Welcome to this comprehensive guide on finding the two sum problem in a Binary Search Tree (BST)! We'll walk through the problem, understand why it's important, and learn how to solve it with practical examples. Let's dive in!

Introduction 📝

In this lesson, we'll learn to find a pair of nodes in a Binary Search Tree (BST) that add up to a given sum. This problem is a common question during technical interviews and is an essential concept in data structures and algorithms.

Prerequisites 💡

Before diving into the Two Sum problem in BST, make sure you're familiar with the following topics:

Problem Statement 📝

Given a Binary Search Tree (BST) and an integer targetSum, find a pair of nodes in the tree whose values add up to the targetSum.

Solution Approach 💡

To solve the Two Sum problem in a BST, we can use the Inorder Traversal property of BSTs and recursion.

Traverse the BST in Inorder (Left -> Root -> Right)
Maintain a variable currentSum and compare each node's value with targetSum - currentSum. If they are equal, we've found the desired pair.
If currentSum + node.value is less than targetSum, update currentSum and move to the right subtree.
If currentSum + node.value is greater than targetSum, move to the left subtree.
Repeat the process until the entire BST is traversed or we find the desired pair.

Example 💡

Let's consider the following BST:

To find a pair that adds up to 9, we'll traverse the tree as follows:

Start from the root (5). Since targetSum - 5 (i.e., 4) is greater than 2 (3, the left child of 5), move to the left subtree.
Traverse the left subtree and find 3. Since targetSum - 3 (i.e., 6) is less than 5 (the right child of 3), move to the right subtree.
Find 2 in the right subtree of 3. Since targetSum - 2 (i.e., 7) is less than 7 (the right child of 3), move to the right subtree.
Find 4 in the right subtree of 7. Since targetSum - 4 (i.e., 5) equals the current node's value (4), we've found the desired pair (4, 5).

Code Example 💡

Here's a Python implementation of the Two Sum problem in a BST:

python

class Node:
    def __init__(self, key):
        self.left = None
        self.right = None
        self.val = key

def findPairWithGivenSum(root, targetSum):
    def helper(node, currentSum):
        if not node:
            return False

        if currentSum < targetSum:
            return helper(node.right, currentSum + node.val)

        if currentSum > targetSum:
            return helper(node.left, currentSum + node.val)

        return True

    return helper(root, 0)

# Test the function
root = Node(5)
root.left = Node(3)
root.right = Node(7)
root.left.left = Node(2)
root.left.right = Node(4)
root.right.left = Node(6)
root.right.right = Node(8)

print(findPairWithGivenSum(root, 9))  # True (Found: (4, 5))

Quiz 💡

That's it for today! By learning how to solve the Two Sum problem in a Binary Search Tree, you've taken a significant step towards mastering important data structures and algorithms concepts. Keep practicing and happy coding! 🤖✨