What is the worst-case time complexity of DFS in a graph?
Practice Questions
Q1
What is the worst-case time complexity of DFS in a graph?
O(V)
O(E)
O(V + E)
O(V * E)
Questions & Step-by-Step Solutions
What is the worst-case time complexity of DFS in a graph?
Step 1: Understand what DFS (Depth-First Search) is. It is an algorithm used to explore nodes 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 during the DFS, each vertex is visited once. This means that the time taken to visit all vertices is proportional to the number of vertices, which is O(V).
Step 4: Understand that DFS also explores each edge in the graph. Since each edge is traversed once, the time taken for this is proportional to the number of edges, which is O(E).
Step 5: Combine the time taken to visit vertices and edges. Since both actions happen during the DFS, the total time complexity is O(V) + O(E).
Step 6: Conclude that the worst-case time complexity of DFS is O(V + E) because it accounts for visiting all vertices and edges in the graph.
