Tree: Depth-First Search - Binary Tree Maximum Path Sum
You need to find the maximum sum of values along any path in a binary tree where the path can start and end at any node. Which algorithmic pattern best fits this problem?
You need to find the maximum sum of values along any path in a binary tree where the path can start and end at any node. Which algorithmic pattern best fits this problem?
easy🔍 Pattern Recognition Q1 of Q15
Step-by-Step Solution
Solution:
Step 1: Identify problem constraints
The path can start and end at any node, and negative values exist, so simple BFS or topological sort won't capture all paths.Step 2: Recognize suitable traversal
Postorder DFS allows computing max gain from left and right subtrees before combining at current node, enabling global max tracking.Final Answer:
Option A -> Option AQuick Check:
Postorder DFS with global max is standard for max path sum [OK]
Quick Trick: Max path sum needs postorder DFS with global max tracking [OK]
Common Mistakes:
MISTAKES- Using BFS misses subtree combinations
- Topological sort applies only to DAGs, not trees
- Counting paths instead of sums
Trap Explanation:
PITFALL- Candidates often confuse longest path with max sum or try BFS, which can't handle negative values or arbitrary start/end nodes.
Interviewer Note:
CONTEXT- Tests candidate's ability to recognize tree DFS pattern for max path sums.
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