If a graph has V vertices and E edges, what is the space complexity of Dijkstra'
Practice Questions
Q1
If a graph has V vertices and E edges, what is the space complexity of Dijkstra's algorithm?
O(V)
O(E)
O(V + E)
O(V^2)
Questions & Step-by-Step Solutions
If a graph has V vertices and E edges, what is the space complexity of Dijkstra's algorithm?
Step 1: Understand that Dijkstra's algorithm is used to find the shortest path in a graph.
Step 2: Identify that a graph consists of vertices (V) and edges (E).
Step 3: Recognize that the graph can be represented using an adjacency list, which stores all the edges for each vertex.
Step 4: Note that the adjacency list requires space proportional to the number of vertices (V) and edges (E), hence it takes O(V + E) space.
Step 5: Additionally, Dijkstra's algorithm uses a distance array to keep track of the shortest distance from the source vertex to each vertex, which also requires O(V) space.
Step 6: Combine the space requirements: O(V) for the distance array and O(V + E) for the adjacency list, resulting in O(V + E) overall space complexity.
