What is the worst-case time complexity of DFS on a graph?
Practice Questions
Q1
What is the worst-case time complexity of DFS on a graph?
O(V + E)
O(V^2)
O(E)
O(V)
Questions & Step-by-Step Solutions
What is the worst-case time complexity of DFS on a graph?
Step 1: Understand what DFS (Depth-First Search) is. It is an algorithm used to explore all the vertices and edges of a graph.
Step 2: Identify the components of a graph. A graph consists of vertices (V) and edges (E). Vertices are the points, and edges are the connections between them.
Step 3: Realize that in the worst-case scenario, DFS will visit every vertex in the graph. This means it will take O(V) time.
Step 4: Also, understand that DFS will traverse every edge in the graph. This adds O(E) time to the total.
Step 5: Combine the time taken to visit all vertices and edges. This gives us O(V) + O(E).
Step 6: Conclude that the worst-case time complexity of DFS is O(V + E).
