In a graph represented by an adjacency list, what is the space complexity?

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Question: In a graph represented by an adjacency list, what is the space complexity?

Options:

Correct Answer: O(V + E)

Solution:

The space complexity of a graph represented by an adjacency list is O(V + E), where V is the number of vertices and E is the number of edges.

In a graph represented by an adjacency list, what is the space complexity?

In a graph represented by an adjacency list, what is the space complexity?

Step 1: Understand what an adjacency list is. It is a way to represent a graph where each vertex has a list of its neighboring vertices.
Step 2: Identify the components of the graph. V represents the number of vertices (or nodes) in the graph, and E represents the number of edges (connections between the vertices).
Step 3: Realize that for each vertex, we need to store a list of its edges. This means we will have to store information for all V vertices.
Step 4: For each edge in the graph, we need to store it in the adjacency list. This means we will also have to account for all E edges.
Step 5: Combine the storage requirements. The total space needed is the sum of the space for vertices (O(V)) and the space for edges (O(E)).
Step 6: Conclude that the overall space complexity of a graph represented by an adjacency list is O(V + E).

Graph Representation – Understanding how graphs can be represented using adjacency lists, which store lists of adjacent vertices for each vertex.
Space Complexity – Analyzing the amount of memory required to store the graph structure based on the number of vertices and edges.