Introduction

Path Sum means:

  • checking whether
  • root-to-leaf path
  • equals target sum

Conditions:

  • path must start from root
  • path must end at leaf node

Example:

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

Target = 22

Output:
True

Explanation:

Path:5 → 4 → 11 → 2

Sum:
22

This problem is one of the most important applications of:

DFS Traversal

Constraints

1 <= Number of Nodes <= 10^5

Approach : Recursive DFS Solution

Explanations:

Explanation:

The idea is:

  • recursively traverse tree
  • subtract current node value
    from target

Steps:

  1. Visit current node.
  2. Reduce target sum.
  3. Check leaf node.
  4. Recurse left subtree.
  5. Recurse right subtree.

Leaf Condition:

  • node has no children
  • remaining target becomes 0

This approach:

  • uses DFS recursion
  • explores all root-to-leaf paths

Dry Run

Target:22

Visit:
5

Remaining:
17

Visit:
4

Remaining:
13

Visit:
11

Remaining:
2

Visit:
2

Remaining:
0

Leaf node reached.
Valid path found.

Practice :

Complexity Analysis :

Time Complexity:- O(n)
Explanation :
Every tree node is visited once.

Space Complexity:- O(h)
Explanation :
Recursion stack depends on tree height.

Why This Problem is Important

This problem builds the foundation for:

  • DFS traversal
  • Tree recursion
  • Root-to-leaf traversal
  • Recursive path problems
  • Binary tree processing

Real-World Applications

Path sum concepts are used in:

  • Decision trees
  • Routing systems
  • AI search systems
  • Hierarchical analysis
  • Graph traversal

Common Beginner Mistakes

  • Forgetting leaf node condition
  • Incorrect target reduction
  • Wrong recursion flow
  • Missing null checks
  • Returning incorrect boolean values

Interview Tip

Interviewers often expect:

  • DFS understanding
  • recursion explanation
  • root-to-leaf logic
  • target reduction clarity

Always explain:

  • recursive target subtraction
  • leaf node validation
  • DFS traversal flow

Related Questions

  • Same Tree
  • Tree Height
  • DFS Traversal
  • Balanced Binary Tree
  • Binary Tree Paths

Final Takeaway

The Path Sum problem is one of the most important beginner DFS tree problems.

It teaches:

  • DFS recursion
  • recursive traversal
  • root-to-leaf exploration
  • target tracking

Understanding this problem builds a strong foundation for:

  •  advanced tree problems
  • graph traversal
  • interview-level algorithms.