Path Sum Root to Leaf in Binary Tree in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does "Path Sum Root to Leaf" mean in a binary tree?

It means checking if there is a path from the top (root) of the tree down to any leaf (end node) where the sum of all node values equals a given number.

beginner

In the context of path sum, what is a leaf node?

A leaf node is a node in the binary tree that has no children. It is the end of a path.

intermediate

Why do we subtract the current node's value from the target sum when moving down the tree?

Because we want to check if the remaining sum can be found in the subtree below. Subtracting helps track how much sum is left to find.

beginner

What is the base case when checking for path sum in a binary tree?

When we reach a leaf node, we check if the remaining sum equals the leaf's value. If yes, the path sum exists.

intermediate

How does recursion help in solving the path sum problem?

Recursion helps by checking each node's children with the updated sum, breaking the problem into smaller parts until reaching leaves.

What is the first step when checking for a path sum in a binary tree?

A Add the current node's value to the sum

B Check if the node has two children

C Return true immediately

D Check if the current node is null

We first check if the current node is null to avoid errors and to know when to stop recursion.

When do we confirm that a path sum exists?

A When the sum equals the leaf node's value

B When the root node value equals the sum

C When the sum is zero at any node

D When the sum is negative

We confirm the path sum exists if at a leaf node, the remaining sum equals the leaf's value.

What happens if the current node is not a leaf and the sum does not match?

A Return true

B Return false

C Check left and right children with updated sum

D Stop the program

We continue checking both children with the sum reduced by the current node's value.

Which data structure is naturally used to solve the path sum problem?

A Stack

B Recursion (call stack)

C Queue

D Hash map

Recursion uses the call stack to explore paths from root to leaves.

If the tree is empty, what should the path sum function return?

A False

B Null

C Sum value

D True

If the tree is empty (null root), no path exists, so return false.

Explain how to check if a binary tree has a root-to-leaf path with a given sum.

Think about walking down the tree and updating the sum.

Describe the role of recursion in solving the path sum problem in a binary tree.

Recursion helps explore all paths 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