What is the space complexity of a recursive depth-first search (DFS) on a binary

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Question: What is the space complexity of a recursive depth-first search (DFS) on a binary tree?

Options:

Correct Answer: O(n)

Solution:

The space complexity is O(n) due to the recursion stack in the worst case when the tree is skewed.

What is the space complexity of a recursive depth-first search (DFS) on a binary tree?

What is the space complexity of a recursive depth-first search (DFS) on 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 a recursive depth-first search (DFS) uses a call stack to keep track of function calls.
Step 3: In a binary tree, each node can have up to two children. The depth of the tree affects how many function calls are on the stack at once.
Step 4: In the worst case, if the binary tree is skewed (like a linked list), the maximum depth of the tree can be equal to the number of nodes, n.
Step 5: When the tree is skewed, the recursion stack can grow to hold all n nodes, leading to a space complexity of O(n).
Step 6: In a balanced binary tree, the maximum depth is log(n), but we focus on the worst case for space complexity.

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