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

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

Options:

Correct Answer: O(n)

Solution:

The space complexity is O(n) due to the recursion stack, which can go as deep as the height of the tree in the worst case.

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

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

Step 1: Understand what space complexity means. It refers to the amount of memory used by an algorithm as the size of the input grows.
Step 2: Recognize that a recursive pre-order traversal of a binary tree involves calling the function multiple times for each node.
Step 3: Note that each time the function is called, it uses some space on the call stack (the memory used for function calls).
Step 4: In the worst case, the depth of the recursion stack can be as deep as the height of the tree.
Step 5: For a binary tree, the height can be as large as 'n' (the number of nodes) in the case of a skewed tree (like a linked list).
Step 6: Therefore, the maximum space used by the recursion stack can be O(n) in the worst case.
Step 7: Conclude that the space complexity of a recursive pre-order traversal of a binary tree is O(n).

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