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 using an adjacency list?

Options:

Correct Answer: O(V + E)

Solution:

The space complexity of Dijkstra\'s algorithm using an adjacency list is O(V + E) due to the storage of vertices and edges.

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

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

Step 1: Understand that a graph consists of vertices (V) and edges (E). Vertices are the points in the graph, and edges are the connections between those points.
Step 2: Recognize that an adjacency list is a way to represent a graph. In this representation, each vertex has a list of the vertices it is connected to by edges.
Step 3: Realize that to store the graph using an adjacency list, you need space for all the vertices and space for all the edges.
Step 4: The space needed for the vertices is O(V) because you need to store each vertex once.
Step 5: The space needed for the edges is O(E) because you need to store each edge once in the adjacency list.
Step 6: Combine the space for vertices and edges to get the total space complexity: O(V) + O(E) = O(V + E).
Step 7: Conclude that the space complexity of Dijkstra's algorithm using an adjacency list is O(V + E).

Graph Representation – Understanding how graphs can be represented using adjacency lists, which store vertices and their corresponding edges.
Space Complexity – Analyzing the amount of memory required by an algorithm in relation to the input size, specifically for Dijkstra's algorithm.
Dijkstra's Algorithm – A shortest path algorithm that operates on weighted graphs, requiring knowledge of its implementation details.