Tree: Depth-First Search - Binary Tree Maximum Path Sum
What is the time complexity of the optimal recursive postorder traversal algorithm for computing the maximum path sum in a binary tree with n nodes?
What is the time complexity of the optimal recursive postorder traversal algorithm for computing the maximum path sum in a binary tree with n nodes?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze traversal
The algorithm visits each node once in postorder traversal.Step 2: Compute complexity
Each node's max_gain is computed once, with constant work per node, so total time is O(n).Final Answer:
Option D -> Option DQuick Check:
Single DFS traversal over n nodes is O(n) [OK]
Quick Trick: DFS visits each node once -> O(n) time [OK]
Common Mistakes:
MISTAKES- Assuming O(n^2) due to path enumeration
- Confusing with DP on weights or capacities
- Thinking recursion adds extra overhead
Trap Explanation:
PITFALL- Candidates often think enumerating all paths causes O(n^2), but optimal DFS avoids that by computing gains bottom-up.
Interviewer Note:
CONTEXT- Tests understanding of DFS time complexity in tree problems.
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