In a graph represented as an adjacency list, what is the space complexity of storing the graph?
Practice Questions
1 question
Q1
In a graph represented as an adjacency list, what is the space complexity of storing the graph?
O(V)
O(E)
O(V + E)
O(V^2)
The space complexity of storing a graph in an adjacency list is O(V + E), where V is the number of vertices and E is the number of edges.
Questions & Step-by-step Solutions
1 item
Q
Q: In a graph represented as an adjacency list, what is the space complexity of storing the graph?
Solution: The space complexity of storing a graph in an adjacency list is O(V + E), where V is the number of vertices and E is the number of edges.
Steps: 6
Step 1: Understand what an adjacency list is. It is a way to represent a graph where each vertex has a list of the vertices it is connected to.
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, you need to store a list of its edges. This means you will have to store V lists for V vertices.
Step 4: Each edge in the graph connects two vertices. Therefore, you will need to store E edges in total across the lists.
Step 5: Combine the storage requirements. You need to store V lists (for the vertices) and E edges (connections), leading to a total space requirement of O(V + E).
Step 6: Conclude that the space complexity of storing a graph in an adjacency list is O(V + E).
