If a graph has V vertices and E edges, what is the space complexity of Dijkstra'

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Question: If a graph has V vertices and E edges, what is the space complexity of Dijkstra\'s algorithm?

Options:

Correct Answer: O(V + E)

Solution:

The space complexity of Dijkstra\'s algorithm is O(V + E) due to the storage of the graph\'s adjacency list and the distance array.

If a graph has V vertices and E edges, what is the space complexity of Dijkstra's algorithm?

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.

Graph Representation – Understanding how graphs can be represented using adjacency lists and the implications for space complexity.
Dijkstra's Algorithm – Knowledge of Dijkstra's algorithm and its requirements for storing distances and graph structure.
Space Complexity – Understanding how to analyze the space complexity of algorithms based on their data structures.