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What is the space complexity of a recursive inorder traversal of a binary tree?

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Question: What is the space complexity of a recursive inorder traversal of a binary tree?

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 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 a balanced tree, it is O(log n).

What is the space complexity of a recursive inorder traversal of a binary tree?

Practice Questions

Q1
What is the space complexity of a recursive inorder traversal of a binary tree?
  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 a recursive inorder traversal of a binary tree?
  • 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: Know that a recursive function uses the call stack to keep track of function calls. Each recursive call adds a new layer to the stack.
  • Step 3: In an inorder traversal of a binary tree, the function calls itself for the left child, processes the current node, and then calls itself for the right child.
  • Step 4: The maximum number of recursive calls that can be on the stack at the same time is equal to the height of the tree (h).
  • Step 5: If the tree is balanced, the height (h) is approximately log(n), where n is the number of nodes. Thus, the space complexity is O(log n).
  • Step 6: If the tree is skewed (like a linked list), the height (h) can be equal to the number of nodes (n). In this case, the space complexity is O(n).
  • Step 7: Conclude that the space complexity of a recursive inorder traversal is O(h), where h is the height of the tree.
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