What is the space complexity of a recursive depth-first traversal of a binary tr

What is the space complexity of a recursive depth-first traversal of a binary tree?

What is the space complexity of a recursive depth-first 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 binary tree is a data structure with nodes, where each node has at most two children.
Step 3: Know that a depth-first traversal means exploring as far down one branch of the tree before backtracking.
Step 4: In a recursive depth-first traversal, each function call is added to the call stack, which is a part of memory used for function calls.
Step 5: The maximum depth of the call stack during the traversal is equal to the height of the binary tree.
Step 6: In the worst case, for a skewed binary tree (like a linked list), the height can be equal to the number of nodes, n.
Step 7: Therefore, the space used by the call stack can grow up to O(n) in the worst case.
Step 8: In a balanced binary tree, the height is log(n), but we still consider the worst case for space complexity.
Step 9: Conclude that the space complexity of a recursive depth-first traversal of a binary tree is O(n) due to the call stack.

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