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

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

Options:

Correct Answer: O(V + E)

Solution:

DFS explores all vertices (V) and edges (E) in the graph, leading to a time complexity of O(V + E).

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

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

Step 1: Understand that a graph consists of vertices (nodes) and edges (connections between nodes).
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, each vertex is visited once, which contributes to the time complexity.
Step 4: Also, during the DFS, each edge is explored once, which adds to the time complexity as well.
Step 5: Combine the contributions from vertices and edges to determine the total time complexity.
Step 6: Conclude that the time complexity of DFS is O(V + E), where V is the number of vertices and E is the number of edges.

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