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What is the time complexity of the Morris Preorder Traversal approach for summing root-to-leaf numbers in a binary tree with n nodes?

medium🪤 Complexity Trap Q5 of Q15
Tree: Depth-First Search - Sum Root to Leaf Numbers
What is the time complexity of the Morris Preorder Traversal approach for summing root-to-leaf numbers in a binary tree with n nodes?
AO(n log n)
BO(log n)
CO(n^2)
DO(n)
Step-by-Step Solution
Solution:

  1. Step 1: Analyze Morris traversal visits each node

    Morris traversal visits each node at most twice, once to create threads and once to remove them.

  2. Step 2: Conclude linear time complexity

    Since each edge is traversed at most twice, total time is O(n).

  3. Final Answer:

    Option D -> Option D

  4. Quick Check:

    Morris traversal is O(n) time [OK]
Quick Trick: Morris traversal is linear time [OK]
Common Mistakes:
MISTAKES
  • Assuming O(n^2) due to nested loops
  • Confusing with recursive DFS complexity
Trap Explanation:
PITFALL
  • Candidates often think the inner while loop causes quadratic time, but it only traverses edges once.
Interviewer Note:
CONTEXT
  • Tests understanding of Morris traversal time complexity.
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