What is the time complexity of finding the shortest path in an unweighted graph
Practice Questions
Q1
What is the time complexity of finding the shortest path in an unweighted graph using BFS?
O(n)
O(n^2)
O(m + n)
O(log n)
Questions & Step-by-Step Solutions
What is the time complexity of finding the shortest path in an unweighted graph using BFS?
Step 1: Understand what BFS (Breadth-First Search) is. It is an algorithm used to explore nodes and edges in a graph.
Step 2: Identify the components of a graph: 'n' represents the number of vertices (or nodes) and 'm' represents the number of edges (connections between nodes).
Step 3: Realize that BFS visits each vertex once and checks each edge once to explore the graph.
Step 4: Calculate the total time taken by BFS. Since it visits all 'n' vertices and checks all 'm' edges, the total time complexity is O(m + n).
Step 5: Conclude that the time complexity of finding the shortest path in an unweighted graph using BFS is O(m + n).
