What is the time complexity of performing a breadth-first search (BFS) on a grap
Practice Questions
Q1
What is the time complexity of performing a breadth-first search (BFS) on a graph?
O(V)
O(E)
O(V + E)
O(V * E)
Questions & Step-by-Step Solutions
What is the time complexity of performing a breadth-first search (BFS) on a graph?
Step 1: Understand what BFS is. BFS is a way to explore all the nodes (or vertices) in a graph level by level.
Step 2: Identify the components of a graph. 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 BFS, each vertex is visited once. This means we will look at all V vertices.
Step 4: Understand that for each vertex, we may need to look at all its edges to find connected vertices. This means we will also consider all E edges.
Step 5: Combine the two parts. Since we visit each vertex and check each edge, the total time taken is proportional to the number of vertices plus the number of edges.
Step 6: Write the final time complexity. The time complexity of BFS is O(V + E).
