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What is the time complexity of the optimal greedy postorder traversal solution for the Binary Tree Cameras problem on a tree with n nodes?

medium🪤 Complexity Trap Q5 of Q15
Tree: Depth-First Search - Binary Tree Cameras
What is the time complexity of the optimal greedy postorder traversal solution for the Binary Tree Cameras problem on a tree with n nodes?
AO(n^2) due to checking coverage states multiple times per node
BO(n) because each node is visited once in postorder traversal
CO(n log n) due to recursive calls and state checks
DO(2^n) because of exploring all camera placement combinations
Step-by-Step Solution
Solution:

  1. Step 1: Analyze traversal

    The algorithm visits each node exactly once in a postorder DFS.

  2. Step 2: Check constant work per node

    At each node, constant time operations determine coverage state and camera placement.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Linear time due to single DFS traversal [OK]
Quick Trick: Single DFS traversal -> O(n) time [OK]
Common Mistakes:
MISTAKES
  • Confusing with brute force exponential or quadratic complexity
Trap Explanation:
PITFALL
  • Candidates often overestimate complexity due to recursion or state checks.
Interviewer Note:
CONTEXT
  • Tests understanding of DFS traversal complexity in tree problems
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