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

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

Options:

Correct Answer: O(V + E)

Solution:

The space complexity of a graph represented as 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 as an adjacency list, what is the space complexity?

In a graph represented as 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 connected vertices (neighbors).
Step 2: Identify the components of the graph. V represents the number of vertices (nodes) in the graph, and E represents the number of edges (connections between nodes).
Step 3: Realize that for each vertex, we need to store a list of its edges. This means we need space for all vertices and all edges.
Step 4: Calculate the space needed for vertices. We need O(V) space for the vertices themselves.
Step 5: Calculate the space needed for edges. We need O(E) space for the edges since each edge connects two vertices.
Step 6: Combine the space for vertices and edges. The total space needed is O(V) + O(E), which simplifies to O(V + E).
Step 7: Conclude that the space complexity of a graph represented as 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.