What is the space complexity of Depth-First Search (DFS) using recursion?

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Question: What is the space complexity of Depth-First Search (DFS) using recursion?

Options:

Correct Answer: O(V)

Solution:

The space complexity of DFS using recursion is O(V) due to the call stack that can go as deep as the number of vertices in the worst case.

What is the space complexity of Depth-First Search (DFS) using recursion?

What is the space complexity of Depth-First Search (DFS) using recursion?

Step 1: Understand what Depth-First Search (DFS) is. It is an algorithm used to explore nodes and edges of a graph.
Step 2: Recognize that DFS can be implemented using recursion, which means it calls itself to explore deeper into the graph.
Step 3: Identify that each time a function is called in recursion, it uses some space in memory, which is stored in a structure called the call stack.
Step 4: Realize that in the worst case, the depth of the recursion can go as deep as the number of vertices (V) in the graph, especially in a linear structure like a linked list.
Step 5: Conclude that the maximum space used by the call stack during the DFS process is proportional to the number of vertices, which gives us a space complexity of O(V).

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