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What is the time complexity of the Morris preorder traversal algorithm on a binary tree with n nodes?

medium🪤 Complexity Trap Q5 of Q15
Tree: Depth-First Search - Binary Tree Preorder Traversal
What is the time complexity of the Morris preorder traversal algorithm on a binary tree with n nodes?
AO(n log n) due to repeated threading
BO(n^2) because of nested loops in threading
CO(n) because each edge is visited at most twice
DO(log n) since traversal is balanced
Step-by-Step Solution
Solution:

  1. Step 1: Analyze edge visits

    Each edge is visited at most twice: once to create thread, once to remove it.

  2. Step 2: Total operations proportional to nodes

    Since edges are n-1, total operations are O(n).

  3. Final Answer:

    Option C -> Option C

  4. Quick Check:

    Linear time traversal with threading [OK]
Quick Trick: Each edge visited twice -> O(n) [OK]
Common Mistakes:
MISTAKES
  • Assuming nested loops cause O(n^2) complexity
Trap Explanation:
PITFALL
  • Candidates confuse inner loops with repeated full traversals, inflating complexity.
Interviewer Note:
CONTEXT
  • Tests understanding of Morris traversal time complexity.
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