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What is the space complexity of recursive tree traversals?

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Question: What is the space complexity of recursive tree traversals?

Options:

  1. O(n)
  2. O(log n)
  3. O(1)
  4. O(n log n)

Correct Answer: O(log n)

Solution: 

The space complexity of recursive tree traversals is O(h), where h is the height of the tree. In the worst case of a skewed tree, this can be O(n), but for balanced trees, it is O(log n).

What is the space complexity of recursive tree traversals?

Practice Questions

Q1
What is the space complexity of recursive tree traversals?
  1. O(n)
  2. O(log n)
  3. O(1)
  4. O(n log n)

Questions & Step-by-Step Solutions

What is the space complexity of recursive tree traversals?
  • Step 1: Understand what space complexity means. It refers to the amount of memory space required by an algorithm as a function of the input size.
  • Step 2: Recognize that recursive tree traversals use the call stack to keep track of function calls.
  • Step 3: Identify that the maximum depth of the call stack is determined by the height of the tree (h).
  • Step 4: Realize that for a balanced tree, the height (h) is approximately log(n), where n is the number of nodes.
  • Step 5: Understand that in the worst case, if the tree is skewed (like a linked list), the height (h) can be equal to n.
  • Step 6: Conclude that the space complexity for recursive tree traversals is O(h), which can be O(log n) for balanced trees and O(n) for skewed trees.
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