If a graph has V vertices and E edges, what is the worst-case time complexity of
Practice Questions
Q1
If a graph has V vertices and E edges, what is the worst-case time complexity of Dijkstra's algorithm using an adjacency matrix?
O(V^2)
O(E log V)
O(V + E)
O(V^3)
Questions & Step-by-Step Solutions
If a graph has V vertices and E edges, what is the worst-case time complexity of Dijkstra's algorithm using an adjacency matrix?
Step 1: Understand that Dijkstra's algorithm is used to find the shortest path from a starting vertex to all other vertices in a graph.
Step 2: Know that an adjacency matrix is a way to represent a graph where we use a 2D array to show the connections (edges) between vertices.
Step 3: Realize that in an adjacency matrix, to find the shortest path, we need to check each vertex to see which one has the smallest distance that hasn't been processed yet.
Step 4: Since there are V vertices, we will need to check each vertex to find the minimum distance, which takes O(V) time.
Step 5: We repeat this process for each vertex, leading to a total of V iterations, each taking O(V) time.
Step 6: Therefore, the total time complexity is O(V) for each of the V vertices, resulting in O(V * V) or O(V^2) overall.
