What is the space complexity of Dijkstra's algorithm when using a priority queue
Practice Questions
Q1
What is the space complexity of Dijkstra's algorithm when using a priority queue?
O(V)
O(E)
O(V + E)
O(V log V)
Questions & Step-by-Step Solutions
What is the space complexity of Dijkstra's algorithm when using a priority queue?
Step 1: Understand what Dijkstra's algorithm does. It finds the shortest path from a starting vertex to all other vertices in a graph.
Step 2: Identify the components that Dijkstra's algorithm uses. It uses a priority queue to keep track of the vertices to explore based on their current shortest distance.
Step 3: Recognize that the algorithm needs to store information for each vertex. This includes the shortest distance from the starting vertex to each vertex.
Step 4: Count the number of vertices in the graph. Let's call this number V.
Step 5: Realize that the priority queue will store each vertex at least once, which means it will need space proportional to the number of vertices.
Step 6: Conclude that the space needed for storing distances and the priority queue is O(V), since it grows linearly with the number of vertices.
