Tree: Depth-First Search - Path Sum II (All Root-to-Leaf Paths)
What is the time complexity of the iterative DFS solution for finding all root-to-leaf paths with a given sum in a binary tree with N nodes and maximum path length L?
What is the time complexity of the iterative DFS solution for finding all root-to-leaf paths with a given sum in a binary tree with N nodes and maximum path length L?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Solution:
Step 1: Identify operations per node
Each node is visited once, but path copying of length up to L occurs when pushing onto stack.Step 2: Calculate total complexity
Copying paths of length L for up to N nodes leads to O(N * L) time complexity.Final Answer:
Option C -> Option CQuick Check:
Path copying dominates, so complexity is O(N * L) [OK]
Quick Trick: Path copying causes O(N * L), not just O(N) [OK]
Common Mistakes:
MISTAKES- Assuming O(N) ignoring path copying
- Confusing with quadratic complexity from unrelated operations
Trap Explanation:
PITFALL- O(N) looks right but ignores path list copying cost; O(N^2) is too high without nested loops
Interviewer Note:
CONTEXT- Tests understanding of hidden costs in path tracking during DFS
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