Introduction

Root to Leaf Paths means:

  • finding every path
  • from root node
  • to leaf node

Leaf node means:

  • node without children

Goal:

  • store all possible paths
    inside binary tree

Example:

        1      /   \
     2     3
      \
       5

Paths:
1 → 2 → 5
1 → 3

Explanation:

Every path starts from root node and ends at leaf node.

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:

  • traverse tree using DFS
  • maintain current path
  • store path at leaf node

Steps:

  1. Visit current node.
  2. Add node to path.
  3. Check leaf condition.
  4. Store complete path.
  5. Traverse left subtree.
  6. Traverse right subtree.
  7. Backtrack path.

Leaf Condition:

left == null and right == null

This approach:

  • uses DFS recursion
  • performs path tracking
  • uses backtracking

Dry Run

Visit:1

Current path:
1

Visit:
2

Current path:
1 → 2

Visit:
5

Leaf node reached.

Store:
1 → 2 → 5

Backtrack and continue.

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

Real-World Applications

Root to leaf path concepts are used in:

  • File systems
  • Route generation
  • Decision trees
  • Navigation systems
  • Hierarchical processing

Common Beginner Mistakes

  • Forgetting backtracking
  • Incorrect leaf node check
  • Missing path removal
  • Wrong recursion flow
  • Path overwrite issues

Interview Tip

Interviewers often expect:

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

Always explain:

  • path storage
  • recursive traversal
  • backtracking process

Related Questions

  • Path Sum II
  • Maximum Path Sum
  • Maximum Depth of Binary Tree
  • DFS Traversal
  • Binary Tree Paths

Final Takeaway

The Root to Leaf Paths problem is one of the most important beginner DFS tree problems.

It teaches:

  • DFS recursion
  • path tracking
  • backtracking
  • recursive tree processing

Understanding this problem builds a strong foundation for:

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