Tree: Depth-First Search - Invert Binary Tree
What is the space complexity of the optimal recursive approach to invert a binary tree, assuming the tree has n nodes and height h?
What is the space complexity of the optimal recursive approach to invert a binary tree, assuming the tree has n nodes and height h?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Identify auxiliary space usage in recursion
The algorithm uses recursion, so the call stack depth is proportional to the height h of the tree.Step 2: Distinguish between in-place operations and recursion stack
Swapping pointers is in-place (O(1) per node), but recursion stack space is O(h), not O(n).Final Answer:
Option D -> Option DQuick Check:
Recursion stack dominates space, proportional to tree height h [OK]
Quick Trick: Recursion stack space depends on tree height, not node count [OK]
Common Mistakes:
MISTAKES- Confusing in-place operation with O(1) total space
- Assuming queue-based BFS space applies to recursive DFS
- Counting node swaps as extra space
Trap Explanation:
PITFALL- Many think in-place means O(1) total space ignoring recursion stack, or confuse BFS queue space with DFS recursion space.
Interviewer Note:
CONTEXT- Tests understanding of recursion stack space vs in-place pointer swaps.
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