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

medium🪤 Complexity Trap Q13 of Q15
Tree: Depth-First Search - Sum Root to Leaf Numbers
What is the space complexity of the Morris Preorder Traversal approach for summing root-to-leaf numbers in a binary tree with n nodes?
AO(1) because Morris traversal uses threaded binary tree links without extra stack
BO(n) due to recursion stack in DFS
CO(h) where h is tree height due to implicit stack usage
DO(n) because all nodes are visited and stored temporarily
Step-by-Step Solution

  1. Step 1: Identify space usage in Morris traversal

    Morris traversal modifies tree pointers temporarily to avoid recursion or explicit stack, so no extra stack space is used.

  2. Step 2: Confirm no auxiliary data structures

    Only constant extra variables (pointers and counters) are used, so space complexity is O(1).

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Morris traversal is known for O(1) space by threading tree [OK]
Quick Trick: Morris traversal avoids recursion and stack [OK]
Common Mistakes:
MISTAKES
  • Confusing recursion stack with Morris traversal
  • Assuming O(h) due to tree height
Trap Explanation:
PITFALL
  • Candidates often assume DFS always uses O(h) stack, missing Morris traversal's pointer threading trick.
Interviewer Note:
CONTEXT
  • Tests understanding of space optimization in tree traversals beyond recursion.
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