What is the time complexity of the depth-first search (DFS) algorithm in a graph

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Question: What is the time complexity of the depth-first search (DFS) algorithm in a graph?

Options:

Correct Answer: O(V + E)

Solution:

DFS also explores all vertices (V) and edges (E), resulting in a time complexity of O(V + E).

What is the time complexity of the depth-first search (DFS) algorithm in a graph?

What is the time complexity of the depth-first search (DFS) algorithm in a graph?

Step 1: Understand that a graph consists of vertices (points) and edges (connections between points).
Step 2: Recognize that depth-first search (DFS) is an algorithm used to explore all the vertices and edges in a graph.
Step 3: Note that during the DFS process, each vertex is visited once.
Step 4: Also note that each edge is considered once when exploring the graph.
Step 5: Combine the visits to vertices and edges: since there are V vertices and E edges, the total work done is proportional to V + E.
Step 6: Conclude that the time complexity of the DFS algorithm is O(V + E).

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