Path Sum Root to Leaf in Binary Tree in DSA C# - 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 root node down to any leaf node where the sum of all node values equals a given number.

beginner

What is a leaf node in a binary tree?

A leaf node is a node that has no children, meaning both its left and right pointers are null.

intermediate

In the path sum problem, why do we subtract the current node's value from the target sum as we go down the tree?

Because we want to check if the remaining sum can be found in the subtree. Subtracting the current node's value updates the target for the next nodes.

intermediate

What is the base case when using recursion to solve the path sum problem?

When the current node is null, return false because no path exists. When the current node is a leaf, check if its value equals the remaining sum.

beginner

How do you know if a path sum exists in a binary tree?

If any path from root to leaf adds up exactly to the target sum, return true; otherwise, return false after checking all paths.

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

A Check leaf nodes first

B Add all node values

C Check if the root is null

D Subtract the sum from the root value

We first check if the root is null because if it is, no path exists.

When do you return true in the path sum problem?

A When the current node is a leaf and its value equals the remaining sum

B When the tree has more than one node

C When the sum is greater than the node value

D When the current node is null

We return true only if we reach a leaf node and the sum matches exactly.

What does it mean if no path sums to the target?

A Return the root value

B Return true

C Return the sum of all nodes

D Return false

If no path matches the sum, the answer is false.

Which traversal method is commonly used to solve the path sum problem?

A Breadth-first search

B Depth-first search

C Inorder traversal

D Level order traversal

Depth-first search is used to explore each path from root to leaf.

What happens to the target sum as you move down the tree?

A It decreases by the node value

B It stays the same

C It increases by the node value

D It resets to zero

The target sum decreases by the current node's value as we move down.

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 base cases needed when implementing the path sum check recursively.

Consider what happens at the end of a path and when there is no node.

Practice

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

easy

A. The total number of nodes in the binary tree

B. The maximum depth of the binary tree

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

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

Solution

1. Step 1: Understand the problem statement

   The problem asks to check if any path from the root node down to any leaf node sums up exactly to a given target value.

2. Step 2: Identify what is being checked

   We are not asked for maximum depth, total nodes, or sum of all nodes, but specifically for a path sum equal to the target.

3. Final Answer:

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

4. Quick Check:

   Path sum check = If there exists a root-to-leaf path with a sum equal to a given target [OK]

Hint: Look for a path from root to leaf matching target sum [OK]

Common Mistakes:

• Confusing path sum with total tree sum
• Checking any path, not just root-to-leaf
• Looking for maximum depth instead

2. Which of the following C# method signatures correctly represents a function to check path sum in a binary tree node class?

easy

A. public bool HasPathSum(TreeNode root, int targetSum)

B. public int HasPathSum(TreeNode root, int targetSum)

C. public void HasPathSum(TreeNode root, int targetSum)

D. public string HasPathSum(TreeNode root, int targetSum)

Solution

1. Step 1: Determine the return type for path sum check

   The function should return true or false indicating if such a path exists, so return type must be bool.

2. Step 2: Check method signature correctness

   public bool HasPathSum(TreeNode root, int targetSum) returns bool and takes root node and target sum as parameters, matching the problem requirements.

3. Final Answer:

   public bool HasPathSum(TreeNode root, int targetSum) -> Option A

4. Quick Check:

   Return type bool for yes/no check = public bool HasPathSum(TreeNode root, int targetSum) [OK]

Hint: Return bool for yes/no path sum check [OK]

Common Mistakes:

• Using int or void return type instead of bool
• Returning string instead of boolean
• Incorrect parameter types or order

3. Given the following binary tree and targetSum = 22, what will the method HasPathSum(root, 22) return?

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

medium

A. Runtime error

B. true

C. null

D. false

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 the method returns true.

3. Final Answer:

   true -> Option B

4. Quick Check:

   Path sum 22 exists = true [OK]

Hint: Sum each root-to-leaf path to find target [OK]

Common Mistakes:

• Ignoring leaf node condition
• Summing partial paths not ending at leaf
• Miscomputing sums of nodes

4. The following C# code attempts to check path sum but has a bug. What is the error?

public bool HasPathSum(TreeNode root, int targetSum) {
    if (root == null) return false;
    if (root.left == null && root.right == null) return root.val == targetSum;
    return HasPathSum(root.left, targetSum - root.val) || HasPathSum(root.right, targetSum - root.val);
}

medium

A. No bug; code works correctly

B. Should check for null root after subtracting value

C. Incorrect base case for leaf node check

D. Missing return statement in recursive calls

Solution

1. Step 1: Analyze base cases and recursion

   Code returns false if root is null, correctly handles leaf node by comparing value to targetSum, and recursively checks left and right subtrees with updated targetSum.

2. Step 2: Confirm correctness of logic

   All conditions and recursive calls are correct and return statements are present.

3. Final Answer:

   No bug; code works correctly -> Option A

4. Quick Check:

   Code logic matches problem requirements = No bug; code works correctly [OK]

Hint: Check base cases and recursive returns carefully [OK]

Common Mistakes:

• Forgetting to subtract node value from targetSum
• Missing return keyword in recursion
• Incorrect leaf node condition

5. You want to find all root-to-leaf paths in a binary tree where the sum of node values equals a target sum. Which approach best extends the path sum check to collect all such paths?

hard

A. Sum all nodes and compare to target sum once traversal ends

B. Use BFS and stop at first path matching the sum

C. Use recursion without tracking path, just return true/false

D. Use DFS with a list to track current path and add to result when sum matches at leaf

Solution

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

   We need to find all root-to-leaf paths with sum equal to target, so we must track the current path during traversal.

2. Step 2: Choose the correct traversal and tracking method

   DFS with a list to store nodes along the current path allows backtracking and collecting all valid paths when leaf and sum conditions are met.

3. Final Answer:

   Use DFS with a list to track current path and add to result when sum matches at leaf -> Option D

4. Quick Check:

   Track paths with DFS and list = Use DFS with a list to track current path and add to result when sum matches at leaf [OK]

Hint: Track path nodes during DFS to collect all valid paths [OK]

Common Mistakes:

• Using BFS which is less natural for path tracking
• Not tracking path nodes, only sums
• Stopping at first found path instead of all