What is the space complexity of a recursive in-order traversal of a binary tree?

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Question: What is the space complexity of a recursive in-order traversal of a binary tree?

Options:

Correct Answer: O(log n)

Solution:

The space complexity is O(h) where h is the height of the tree, which is O(log n) for balanced trees.

What is the space complexity of a recursive in-order traversal of a binary tree?

What is the space complexity of a recursive in-order 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: Recognize that in-order traversal of a binary tree means visiting the left child, then the current node, and finally the right child.
Step 3: Note that in a recursive function, each function call uses some space on the call stack.
Step 4: Identify that the maximum number of function calls on the call stack at any time is equal to the height of the tree.
Step 5: Define the height of the tree (h). For a balanced binary tree, the height is approximately log(n), where n is the number of nodes.
Step 6: Conclude that the space complexity for the recursive in-order traversal is O(h), which is O(log n) for balanced trees.

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