Tree: Depth-First Search - Symmetric Tree (DFS Approach)
What is the space complexity of the optimized recursive DFS approach for checking if a binary tree is symmetric, assuming the tree has n nodes and height h?
What is the space complexity of the optimized recursive DFS approach for checking if a binary tree is symmetric, assuming the tree has n nodes and height h?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Solution:
Step 1: Identify recursion stack usage
The recursive calls go as deep as the height of the tree, so the recursion stack uses O(h) space.Step 2: Confirm no additional data structures store all nodes
The algorithm does not use queues or arrays to store nodes; it only uses call stack and local variables.Final Answer:
Option A -> Option AQuick Check:
Recursion stack space depends on tree height, not total nodes [OK]
Quick Trick: Recursion stack space = tree height, not total nodes [OK]
Common Mistakes:
MISTAKES- Confusing BFS queue space with DFS recursion stack
- Assuming O(n) space due to node storage
- Ignoring recursion stack space
Trap Explanation:
PITFALL- Candidates often pick O(n) thinking all nodes are stored, but recursion stack is only O(h).
Interviewer Note:
CONTEXT- Checks understanding of recursion stack space vs auxiliary data structures.
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