Tree: Depth-First Search - Sum Root to Leaf Numbers
What is the auxiliary space complexity of a recursive DFS approach for summing root-to-leaf numbers in a binary tree with height h?
What is the auxiliary space complexity of a recursive DFS approach for summing root-to-leaf numbers in a binary tree with height h?
medium📊 Complexity Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand recursion stack usage
Recursive DFS uses call stack proportional to tree height.Step 2: Define height h
Height h is the longest root-to-leaf path length.Step 3: Auxiliary space complexity
Auxiliary space is O(h) due to recursion depth.Final Answer:
Option C -> Option CQuick Check:
Recursion depth equals tree height [OK]
Quick Trick: Recursive DFS space equals tree height [OK]
Common Mistakes:
MISTAKES- Assuming O(n) space due to all nodes stored
- Confusing auxiliary space with total space
- Ignoring recursion stack depth
Trap Explanation:
PITFALL- Confusing total nodes with recursion stack space leads to O(n) mistake.
Interviewer Note:
CONTEXT- Tests understanding of recursion space complexity in tree traversal.
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