In a graph with V vertices and E edges, what is the time complexity of DFS?
Practice Questions
Q1
In a graph with V vertices and E edges, what is the time complexity of DFS?
O(V)
O(E)
O(V + E)
O(V * E)
Questions & Step-by-Step Solutions
In a graph with V vertices and E edges, what is the time complexity of DFS?
Step 1: Understand that DFS stands for Depth-First Search, which is a way to explore a graph.
Step 2: Know that a graph consists of vertices (V) and edges (E). Vertices are the points, and edges are the connections between them.
Step 3: Realize that during DFS, we start at a vertex and explore as far as possible along each branch before backtracking.
Step 4: When we perform DFS, we visit each vertex once. This contributes O(V) to the time complexity.
Step 5: While visiting each vertex, we also look at the edges connected to it. Since we check each edge once, this contributes O(E) to the time complexity.
Step 6: Combine the contributions from vertices and edges to get the total time complexity: O(V) + O(E) = O(V + E).
Step 7: Conclude that the time complexity of DFS is O(V + E).
