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

Practice Questions

Q1
What is the time complexity of the depth-first search (DFS) algorithm in a graph?
  1. O(V + E)
  2. O(V)
  3. O(E)
  4. O(V^2)

Questions & Step-by-Step Solutions

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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