What is the worst-case time complexity of DFS for a graph represented as an adja
Practice Questions
Q1
What is the worst-case time complexity of DFS for a graph represented as an adjacency list?
O(V + E)
O(V^2)
O(E)
O(V log V)
Questions & Step-by-Step Solutions
What is the worst-case time complexity of DFS for a graph represented as an adjacency list?
Step 1: Understand what DFS (Depth-First Search) is. It is an algorithm used to explore nodes and edges of a graph.
Step 2: Know that a graph can be represented in different ways. One common way is using an adjacency list, which lists all the neighbors for each node.
Step 3: Identify the components of the graph: V represents the number of vertices (or nodes) in the graph, and E represents the number of edges (connections between nodes).
Step 4: Realize that in DFS, we visit each vertex once and explore all its edges. This means we will look at every vertex and every edge in the graph.
Step 5: Calculate the time taken: Visiting each vertex takes O(V) time, and exploring all edges takes O(E) time.
Step 6: Combine the time taken for vertices and edges: The total time complexity is O(V) + O(E), which simplifies to O(V + E).
Step 7: Conclude that the worst-case time complexity of DFS for a graph represented as an adjacency list is O(V + E).
