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

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

Options:

Correct Answer: O(h)

Solution:

The space complexity of a recursive preorder traversal is O(h), where h is the height of the tree due to the call stack.

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

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

Step 1: Understand what a binary tree is. A binary tree is a data structure where each node has at most two children, referred to as the left child and the right child.
Step 2: Learn what a preorder traversal is. In a preorder traversal, you visit the root node first, then the left subtree, and finally the right subtree.
Step 3: Recognize that recursion uses a call stack. When you call a function recursively, each call adds a new layer to the call stack.
Step 4: Identify the height of the tree (h). The height of a binary tree is the number of edges on the longest path from the root to a leaf node.
Step 5: Realize that during a recursive preorder traversal, the maximum number of function calls on the call stack at any time is equal to the height of the tree (h).
Step 6: Conclude that the space complexity, which measures how much memory is used, is O(h) because the space used by the call stack is proportional to the height of the tree.

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