What is the space complexity of Depth-First Search (DFS) using recursion?
Practice Questions
Q1
What is the space complexity of Depth-First Search (DFS) using recursion?
O(V)
O(E)
O(V + E)
O(1)
Questions & Step-by-Step Solutions
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).
