What is the time complexity of Dijkstra's algorithm when using a priority queue
Practice Questions
Q1
What is the time complexity of Dijkstra's algorithm when using a priority queue implemented with a binary heap?
O(V^2)
O(E log V)
O(V log V)
O(E + V)
Questions & Step-by-Step Solutions
What is the time complexity of Dijkstra's algorithm when using a priority queue implemented with a binary heap?
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: Recognize that the algorithm processes each vertex and edge in the graph.
Step 3: Identify that a priority queue is used to efficiently get the next vertex with the smallest distance.
Step 4: Note that when using a binary heap as the priority queue, each insertion and extraction operation takes O(log V) time, where V is the number of vertices.
Step 5: Realize that for each vertex, we may need to update the distances to its neighboring vertices, which involves processing each edge.
Step 6: Count that there are E edges in the graph, and for each edge, we may perform a priority queue operation.
Step 7: Combine the operations: For each of the V vertices, we perform O(log V) operations for each of the E edges, leading to a total time complexity of O(E log V).
