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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
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?
AUse a depth-first search with postorder traversal to compute maximum gains from subtrees and track global max path sum.
BUse a breadth-first search to find the longest path and sum node values along it.
CUse dynamic programming on tree nodes to count the number of paths with maximum sum.
DUse a topological sort to order nodes and then find maximum path sums.
Step-by-Step Solution
Solution:

  1. 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.

  2. 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.

  3. Final Answer:

    Option A -> Option A

  4. Quick 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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