Tree: Depth-First Search - Path Sum III (Any Path)
What is the space complexity of the recursive prefix sum DFS solution for Path Sum III on a balanced binary tree with n nodes?
What is the space complexity of the recursive prefix sum DFS solution for Path Sum III on a balanced binary tree with n nodes?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze recursion stack space
Recursion stack depth is O(h), which is O(log n) for balanced tree, O(n) worst case.Step 2: Analyze prefix sum map space
Prefix sum map stores up to O(n) entries in worst case.Step 3: Combine space usage
Total space is O(h) + O(n), dominated by O(n).Final Answer:
Option B -> Option BQuick Check:
Space is O(n) due to recursion stack and prefix map [OK]
Quick Trick: Prefix sum map + recursion stack -> O(n) space [OK]
Common Mistakes:
MISTAKES- Ignoring recursion stack space
- Assuming O(1) space for prefix sums
Trap Explanation:
PITFALL- Candidates often forget recursion stack space or assume prefix sums use no extra space.
Interviewer Note:
CONTEXT- Tests understanding of auxiliary space including recursion stack and hash map.
Master "Path Sum III (Any Path)" in Tree: Depth-First Search
Want More Practice?
15+ quiz questions · All difficulty levels · Free
Free Signup - Practice All QuestionsMore Tree: Depth-First Search Quizzes