Why Two Sum in BST in DSA Typescript?

The Big Idea

What if you could find two numbers adding to your target in a tree without checking every pair?

The Scenario

Imagine you have a big family photo album sorted by year, and you want to find two photos whose years add up to a special number. You try flipping through pages one by one, checking every possible pair manually.

The Problem

Checking every pair manually takes forever because you have to look at many combinations. It's easy to miss pairs or make mistakes, especially when the album is huge.

The Solution

Using the Two Sum in BST method, you can quickly find two numbers that add up to the target by smartly using the sorted nature of the tree. This avoids checking every pair and saves a lot of time and effort.

Before vs After

✗ Before

for (let i = 0; i < arr.length; i++) {
  for (let j = i + 1; j < arr.length; j++) {
    if (arr[i] + arr[j] === target) return true;
  }
}

✓ After

function findTwoSumInBST(root, target) {
  // Use two pointers from BST inorder and reverse inorder
  // Move pointers based on sum comparison
}

What It Enables

This concept enables fast and efficient searching for pairs in sorted tree data, making complex problems simple and quick.

Real Life Example

Finding two expenses in a sorted list of transactions that add up to a specific budget limit without checking every possible pair.

Key Takeaways

Manual pair checking is slow and error-prone.

Two Sum in BST uses the tree's order to find pairs quickly.

This method saves time and reduces mistakes in searching pairs.

Practice

1. What is the main goal of the Two Sum in BST problem?

easy

A. Check if a BST is balanced

B. Find two nodes in a BST whose values add up to a target sum

C. Count the number of nodes in a BST

D. Find the maximum value in a BST

Solution

1. Step 1: Understand the problem statement

   The problem asks to find two nodes in a Binary Search Tree (BST) such that their values add up to a given target sum.

2. Step 2: Identify the goal

   The goal is to check if such a pair exists, not to find maximum, count nodes, or check balance.

3. Final Answer:

   Find two nodes in a BST whose values add up to a target sum -> Option B

4. Quick Check:

   Two Sum in BST = Find pair with target sum [OK]

Hint: Look for two values adding to target in BST [OK]

Common Mistakes:

• Confusing with finding max or min value
• Thinking it counts nodes instead of finding pairs
• Assuming it checks tree balance

2. Which TypeScript syntax correctly defines a BST node for the Two Sum problem?

easy

A. interface TreeNode { val: string; left: TreeNode; right: TreeNode; }

B. function TreeNode(val) { this.val = val; this.left = null; this.right = null; }

C. type TreeNode = { val: number; left?: TreeNode; right?: TreeNode; }

D. class TreeNode { val: number; left: TreeNode | null; right: TreeNode | null; constructor(val: number) { this.val = val; this.left = null; this.right = null; } }

Solution

1. Step 1: Check correct TypeScript class syntax for BST node

   class TreeNode { val: number; left: TreeNode | null; right: TreeNode | null; constructor(val: number) { this.val = val; this.left = null; this.right = null; } } defines a class with number value and nullable left/right children, matching BST node structure.

2. Step 2: Compare other options

   function TreeNode(val) { this.val = val; this.left = null; this.right = null; } is JavaScript function style, not TypeScript class. interface TreeNode { val: string; left: TreeNode; right: TreeNode; } uses string type for val and non-nullable children, which is incorrect. type TreeNode = { val: number; left?: TreeNode; right?: TreeNode; } uses optional properties but lacks constructor and proper null handling.

3. Final Answer:

   class TreeNode { val: number; left: TreeNode | null; right: TreeNode | null; constructor(val: number) { this.val = val; this.left = null; this.right = null; } } -> Option D

4. Quick Check:

   Correct BST node class syntax = class TreeNode { val: number; left: TreeNode | null; right: TreeNode | null; constructor(val: number) { this.val = val; this.left = null; this.right = null; } } [OK]

Hint: Use class with nullable left/right and number val [OK]

Common Mistakes:

• Using string type for node value
• Not initializing left and right to null
• Using JavaScript function instead of TypeScript class

3. Given the BST below and target = 9, what will the Two Sum function return?

    5
   / \
  3   7
 /     \
2       8

Function uses in-order traversal and a set to find pairs.

medium

A. true

B. false

C. null

D. Error

Solution

1. Step 1: Traverse BST in-order and check pairs

   In-order traversal gives sorted values: [2, 3, 5, 7, 8]. We check if target - current value exists in set.

2. Step 2: Find pair summing to 9

   Check pairs: 2 + 7 = 9 (found), so function returns true.

3. Final Answer:

   true -> Option A

4. Quick Check:

   2 + 7 = 9 found in BST [OK]

Hint: In-order traversal gives sorted list to find pairs [OK]

Common Mistakes:

• Assuming no pair without checking all nodes
• Confusing traversal order
• Ignoring set lookup for complements

4. Identify the bug in this TypeScript Two Sum in BST function snippet:

function findTarget(root: TreeNode | null, k: number): boolean {
  const set = new Set<number>();
  function dfs(node: TreeNode | null): boolean {
    if (!node) return false;
    if (set.has(k - node.val)) return true;
    set.add(node.val);
    dfs(node.left);
    dfs(node.right);
    return false;
  }
  return dfs(root);
}

medium

A. The base case should return true when node is null

B. Set is not initialized properly

C. The function returns false too early, missing true from recursive calls

D. The function should use a queue instead of recursion

Solution

1. Step 1: Analyze recursive calls and return values

   The dfs function calls dfs(node.left) and dfs(node.right) but ignores their return values, always returning false at the end.

2. Step 2: Identify missing return propagation

   If dfs(node.left) or dfs(node.right) returns true, dfs should return true immediately to propagate the success.

3. Final Answer:

   The function returns false too early, missing true from recursive calls -> Option C

4. Quick Check:

   Return recursive true results to avoid missing pairs [OK]

Hint: Return recursive calls' results to propagate true [OK]

Common Mistakes:

• Ignoring return values of recursive calls
• Returning false before checking all nodes
• Misunderstanding base case return

5. You want to optimize Two Sum in BST for large trees. Which approach best reduces time complexity while using O(h) space, where h is tree height?

hard

A. Use two pointers with iterative in-order and reverse in-order traversals simultaneously

B. Convert BST to array and use nested loops to find pairs

C. Use breadth-first search with a hash set to find pairs

D. Perform recursive DFS and store all node values in a list before checking pairs

Solution

1. Step 1: Understand space and time constraints

   We want to reduce time complexity and keep space to O(h), where h is tree height.

2. Step 2: Evaluate approaches

   Use two pointers with iterative in-order and reverse in-order traversals simultaneously uses two pointers with iterative in-order (smallest to largest) and reverse in-order (largest to smallest) traversals, allowing pair search in O(n) time and O(h) space. Other options use extra space O(n) or nested loops with O(n^2) time.

3. Final Answer:

   Use two pointers with iterative in-order and reverse in-order traversals simultaneously -> Option A

4. Quick Check:

   Two pointer BST traversal = O(n) time, O(h) space [OK]

Hint: Use two pointers with in-order and reverse in-order iterators [OK]

Common Mistakes:

• Using nested loops causing O(n^2) time
• Storing all nodes in list increasing space to O(n)
• Using BFS which uses more space than O(h)