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What is the time complexity of the optimal DFS with early stopping solution for the Path Sum problem on a binary tree with n nodes?

medium🪤 Complexity Trap Q5 of Q15
Tree: Depth-First Search - Path Sum
What is the time complexity of the optimal DFS with early stopping solution for the Path Sum problem on a binary tree with n nodes?
AO(n)
BO(log n)
CO(n^2)
DO(n * W) where W is targetSum
Step-by-Step Solution
Solution:

  1. Step 1: Analyze DFS traversal

    DFS visits each node once, so base complexity is O(n).

  2. Step 2: Consider early stopping effect

    Early stopping can reduce work but worst case still visits all nodes, so O(n).

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    DFS linear in nodes -> O(n) [OK]
Quick Trick: DFS visits each node once -> O(n) time [OK]
Common Mistakes:
MISTAKES
  • Confusing with DP complexity involving targetSum
  • Assuming quadratic due to recursion
Trap Explanation:
PITFALL
  • Candidates often think targetSum affects complexity multiplicatively, but it does not here.
Interviewer Note:
CONTEXT
  • Tests understanding of DFS time complexity with pruning.
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