Introduction

Path Sum II means:

  • finding all root-to-leaf paths
  • whose total sum
    equals target value

Goal:

  • explore every path
  • calculate path sum
  • store valid paths

Example:

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

Target:
22

Valid Paths:
5 → 4 → 11 → 2
5 → 8 → 4 → 5

Explanation:

Only root-to-leaf paths with target sum are stored.

This problem is one of the most important applications of:

DFS Traversal

Constraints

1 <= Number of Nodes <= 10^5

Approach : Recursive DFS + Backtracking Solution

Explanations:

Explanation:

The idea is:

  • traverse tree using DFS
  • maintain current path
  • track remaining target sum

Steps:

  1. Visit current node.
  2. Add node into path.
  3. Subtract node value from target.
  4. Check leaf condition.
  5. Store valid path.
  6. Traverse child nodes.
  7. Backtrack path.

Leaf Condition:

 left == null and right == null

Target Condition:

remainingSum == node.value

This approach:

  • uses DFS recursion
  • performs path tracking
  • uses backtracking

Dry Run

Visit:5
Remaining target:
17

Visit:
4

Remaining target:
13

Visit:
11

Remaining target:
2

Visit:
2

Target matched.

Store path:
5 → 4 → 11 → 2

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
  • Backtracking
  • Path tracking
  • Recursive tree processing
  • Binary tree analysis

Real-World Applications

Path sum concepts are used in:

  • Navigation systems
  • Route optimization
  • Financial analysis
  • Decision trees
  • Hierarchical processing

Common Beginner Mistakes

  • Forgetting backtracking
  • Incorrect target update
  • Wrong leaf node condition
  • Missing path copy operation
  • Incorrect recursion flow

Interview Tip

Interviewers often expect:

  • DFS understanding
  • recursion explanation
  • path tracking logic
  • backtracking clarity

Always explain:

  • remaining target calculation
  • recursive traversal
  • valid path storage

Related Questions

  • Root to Leaf Paths
  • Maximum Path Sum
  • Maximum Depth of Binary Tree
  • DFS Traversal
  • Binary Tree Paths

Final Takeaway

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

It teaches:

  • DFS recursion
  • path tracking
  • backtracking
  • target sum calculation

Understanding this problem builds a strong foundation for:

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