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What is the auxiliary space complexity of the iterative preorder traversal using a stack on a binary tree with height h?

medium🪤 Complexity Trap Q6 of Q15
Tree: Depth-First Search - Binary Tree Preorder Traversal
What is the auxiliary space complexity of the iterative preorder traversal using a stack on a binary tree with height h?
AO(log n) always, regardless of tree shape
BO(n) because all nodes are pushed onto the stack
CO(1) since no recursion is used
DO(h) because stack stores nodes along the path
Step-by-Step Solution
Solution:

  1. Step 1: Understand stack usage

    Stack stores nodes along the current path; max size equals tree height h.

  2. Step 2: Relate height to n

    Height h can be up to n in skewed trees, so space is O(h).

  3. Final Answer:

    Option D -> Option D

  4. Quick Check:

    Stack size depends on height, which varies by tree shape [OK]
Quick Trick: Stack size equals tree height [OK]
Common Mistakes:
MISTAKES
  • Assuming stack holds all nodes simultaneously
  • Assuming height is always log n
Trap Explanation:
PITFALL
  • Candidates confuse total nodes with max stack size, picking O(n) or O(log n) incorrectly.
Interviewer Note:
CONTEXT
  • Tests understanding of space usage in iterative traversal.
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