Why Path Sum Root to Leaf in Binary Tree in DSA Typescript?

The Big Idea

What if you could instantly know if a path in a tree adds up to your number without guessing?

The Scenario

Imagine you have a family tree drawn on paper, and you want to find if there is a path from the oldest ancestor to a youngest family member where the ages add up to a certain number.

Doing this by looking at every possible path manually is tiring and confusing.

The Problem

Manually checking each path means you have to remember every step and sum along the way.

This is slow and easy to make mistakes, especially if the tree is big.

You might miss some paths or add numbers wrong.

The Solution

Using a program to check the tree automatically saves time and avoids mistakes.

The program walks down each path, adding numbers as it goes, and tells you if any path matches the target sum.

Before vs After

✗ Before

function checkPathSum(node, target) {
  // Manually track sums for each path
  // Very complex and error-prone
}

✓ After

function hasPathSum(node, targetSum) {
  if (!node) return false;
  if (!node.left && !node.right) return node.val === targetSum;
  return hasPathSum(node.left, targetSum - node.val) || hasPathSum(node.right, targetSum - node.val);
}

What It Enables

This lets you quickly find if any root-to-leaf path adds up to your target, even in big trees.

Real Life Example

Checking if a route in a map adds up to a certain distance, or if a decision path in a flowchart meets a target score.

Key Takeaways

Manual path checking is slow and error-prone.

Automated path sum checking walks the tree efficiently.

This helps find target sums in complex tree structures easily.

Practice

1. What does the "Path Sum Root to Leaf" problem ask you to find in a binary tree?

easy

A. The sum of all node values in the binary tree

B. If there exists a root-to-leaf path with a sum equal to a given target

C. The total number of nodes in the binary tree

D. The maximum depth of the binary tree

Solution

1. Step 1: Understand the problem statement

   The problem asks if there is any path from the root node down to any leaf node where the sum of the node values equals the target sum.

2. Step 2: Differentiate from other tree properties

   It is not about depth, total nodes, or sum of all nodes, but specifically about a path sum from root to leaf.

3. Final Answer:

   If there exists a root-to-leaf path with a sum equal to a given target -> Option B

4. Quick Check:

   Path sum means root-to-leaf sum = D [OK]

Hint: Focus on root-to-leaf paths, not entire tree sums [OK]

Common Mistakes:

• Confusing path sum with total tree sum
• Checking any path, not just root-to-leaf
• Ignoring leaf node condition

2. Which of the following TypeScript function signatures correctly represents a function to check path sum in a binary tree node defined as class TreeNode { val: number; left: TreeNode | null; right: TreeNode | null; }?

easy

A. function hasPathSum(root: number, sum: TreeNode): boolean

B. function hasPathSum(root: TreeNode, sum: string): boolean

C. function hasPathSum(root: TreeNode | null, sum: number): boolean

D. function hasPathSum(root: TreeNode | null): number

Solution

1. Step 1: Check parameter types

   The root should be a TreeNode or null (empty tree), and sum should be a number representing the target sum.

2. Step 2: Check return type

   The function returns a boolean indicating if such a path exists.

3. Final Answer:

   function hasPathSum(root: TreeNode | null, sum: number): boolean -> Option C

4. Quick Check:

   Correct types and return boolean = B [OK]

Hint: Root can be null; sum is number; return boolean [OK]

Common Mistakes:

• Swapping parameter types
• Using wrong return type
• Missing null for root parameter

3. Given the following binary tree and target sum = 22, what will the function hasPathSum(root, 22) return?

    5
   / \
  4   8
 /   / \
11  13  4
/  \      
7    2     1

medium

A. null

B. false

C. SyntaxError

D. true

Solution

1. Step 1: Identify root-to-leaf paths and their sums

   Check paths: 5->4->11->7 = 27, 5->4->11->2 = 22, 5->8->13 = 26, 5->8->4->1 = 18.

2. Step 2: Check if any path sum equals 22

   Path 5->4->11->2 sums to 22, so function returns true.

3. Final Answer:

   true -> Option D

4. Quick Check:

   Path sum 22 exists = true [OK]

Hint: Sum each root-to-leaf path, check for target [OK]

Common Mistakes:

• Ignoring leaf node condition
• Calculating sum incorrectly
• Confusing partial paths with full root-to-leaf

4. Consider this TypeScript code snippet for checking path sum:

function hasPathSum(root: TreeNode | null, sum: number): boolean {
  if (!root) return false;
  if (!root.left && !root.right) return root.val === sum;
  return hasPathSum(root.left, sum - root.val) || hasPathSum(root.right, sum - root.val);
}

What does the function return if the tree is empty (root = null) and sum is 0?

medium

A. Returns false for empty tree and sum 0

B. Causes infinite recursion

C. Throws runtime error due to null access

D. Returns true incorrectly for non-empty tree

Solution

1. Step 1: Analyze base case for empty tree

   When root is null, if (!root) returns false immediately.

2. Step 2: Confirm for sum = 0

   Empty tree has no root-to-leaf path regardless of target sum, so false is correct.

3. Final Answer:

   Returns false for empty tree and sum 0 -> Option A

4. Quick Check:

   Null root always returns false [OK]

Hint: Empty tree always returns false [OK]

Common Mistakes:

• Thinking empty tree with sum 0 should return true
• Expecting runtime error without null check
• Confusing empty tree with single-node tree

5. You want to modify the path sum function to return all root-to-leaf paths where the sum equals the target. Which approach best solves this problem?

hard

A. Use DFS to track current path and sum, collect paths when sum matches at leaf

B. Use BFS and stop at first matching path

C. Use a queue to store sums only, ignoring paths

D. Return true or false immediately when sum matches any node

Solution

1. Step 1: Understand requirement to collect all matching paths

   We need to find all root-to-leaf paths whose sums equal the target, not just check existence.

2. Step 2: Choose traversal and tracking method

   DFS (depth-first search) allows tracking the current path and sum, and collecting paths when leaf and sum match.

3. Step 3: Evaluate other options

   BFS is less natural for path tracking; queues without paths lose information; returning boolean stops early.

4. Final Answer:

   Use DFS to track current path and sum, collect paths when sum matches at leaf -> Option A

5. Quick Check:

   DFS with path tracking = A [OK]

Hint: Track path and sum with DFS to collect all matching paths [OK]

Common Mistakes:

• Using BFS without path tracking
• Stopping at first match instead of collecting all
• Ignoring leaf node condition