If a graph is represented using an adjacency matrix, what is the time complexity
Practice Questions
Q1
If a graph is represented using an adjacency matrix, what is the time complexity of BFS?
O(V + E)
O(V^2)
O(E)
O(V log V)
Questions & Step-by-Step Solutions
If a graph is represented using an adjacency matrix, what is the time complexity of BFS?
Step 1: Understand what BFS (Breadth-First Search) is. It is an algorithm used to explore nodes and edges of a graph.
Step 2: Know that an adjacency matrix is a way to represent a graph using a 2D array. If there are V vertices, the matrix will be V x V.
Step 3: Realize that in BFS, we need to explore all vertices and their connections (edges).
Step 4: For each vertex, we check all other vertices to see if there is an edge connecting them. This requires looking at each entry in the adjacency matrix.
Step 5: Since there are V vertices, and we check V entries for each vertex, the total number of checks is V * V, which is V^2.
Step 6: Therefore, the time complexity of BFS when using an adjacency matrix is O(V^2).
