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What is the time complexity of the iterative postorder traversal using one stack and a pointer on a binary tree with n nodes?

medium🪤 Complexity Trap Q13 of Q15
Tree: Depth-First Search - Binary Tree Postorder Traversal
What is the time complexity of the iterative postorder traversal using one stack and a pointer on a binary tree with n nodes?
AO(n log n) due to repeated stack operations
BO(n) but with O(h) auxiliary space where h is tree height
CO(n^2) because of nested while loops
DO(n) because each node is visited and processed once
Step-by-Step Solution

  1. Step 1: Analyze node visits

    Each node is pushed and popped exactly once, so operations proportional to n.

  2. Step 2: Confirm no nested repeated work

    Inner loops traverse down left children, but total iterations over all nodes sum to n.

  3. Final Answer:

    Option D -> Option D

  4. Quick Check:

    Linear time complexity matches traversal of all nodes once [OK]
Quick Trick: Each node processed once -> O(n) time [OK]
Common Mistakes:
MISTAKES
  • Assuming nested loops multiply to n^2
  • Confusing auxiliary space with time
Trap Explanation:
PITFALL
  • Nested loops may look like O(n^2), but total iterations over all nodes sum to O(n).
Interviewer Note:
CONTEXT
  • Checks understanding of complexity beyond superficial loop nesting.
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