Why Path Sum Root to Leaf in Binary Tree in DSA C#?

The Big Idea

What if you could instantly know if a path in a tree adds up to your target without checking every step yourself?

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 checking every possible path manually is tiring and confusing.

The Problem

Manually adding ages along every path is slow and easy to make mistakes. You might miss some paths or add wrong numbers. It becomes impossible when the tree is big or has many branches.

The Solution

Using the "Path Sum Root to Leaf" method, a computer can quickly check all paths from the root to leaves and tell if any path adds up to the target sum. It does this by exploring each branch step-by-step, adding values as it goes, without missing any path.

Before vs After

✗ Before

int sum = 0;
// Manually add values for each path
sum = 5 + 4 + 11 + 2;
if (sum == target) return true;
// Repeat for all paths

✓ After

bool HasPathSum(TreeNode node, int targetSum) {
  if (node == null) return false;
  if (node.left == null && node.right == null) 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 in a tree matches a target sum, even in large and complex trees.

Real Life Example

Checking if a certain budget can be met by adding costs along a chain of project tasks, where each task depends on the previous one.

Key Takeaways

Manually checking paths is slow and error-prone.

Path Sum Root to Leaf uses a simple recursive check to explore all paths.

This method works efficiently even for big trees.

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