Which of the following statements is true regarding the time complexity of DFS?
Practice Questions
Q1
Which of the following statements is true regarding the time complexity of DFS?
O(V + E)
O(V^2)
O(E log V)
O(V log V)
Questions & Step-by-Step Solutions
Which of the following statements is true regarding the time complexity of DFS?
Step 1: Understand what DFS (Depth-First Search) is. It is an algorithm used to traverse or search through a graph or tree data structure.
Step 2: Identify the components of a graph. A graph consists of vertices (or nodes) and edges (connections between the nodes).
Step 3: Realize that during the DFS process, each vertex is visited once. This means that if there are V vertices, it will take O(V) time to visit all of them.
Step 4: Understand that DFS also explores each edge in the graph. If there are E edges, it will take O(E) time to explore all of them.
Step 5: Combine the time taken to visit all vertices and edges. The total time complexity is O(V) + O(E), which simplifies to O(V + E).
Step 6: Conclude that the statement about the time complexity of DFS being O(V + E) is true.
