Big O Complexity for Graphs: Adjacency Matrix vs Adjacency List
Graphs can be represented in two main ways: Adjacency Matrix and Adjacency List. Each method has its own pros and cons depending on how much memory it needs and how quickly it can handle different operations. 1. Space Complexity Adjacency Matrix : O(V^2) Adjacency List : O(V+E) V: Number of vertices. E: Number of edges. Adjacency Matrix requires a V×V grid, making it less efficient for sparse graphs. Adjacency List only stores edges for each vertex, making it space-efficient for sparse graphs. 2. Time Complexity: Adding a Vertex Adjacency Matrix : O(V^2) Adjacency List : O(1) Adjacency Matrix: Adding a vertex may require creating a new
Graphs can be represented in two main ways: Adjacency Matrix and Adjacency List. Each method has its own pros and cons depending on how much memory it needs and how quickly it can handle different operations.
1. Space Complexity
Adjacency Matrix : O(V^2)
Adjacency List : O(V+E)
- V: Number of vertices.
- E: Number of edges.
- Adjacency Matrix requires a V×V grid, making it less efficient for sparse graphs.
- Adjacency List only stores edges for each vertex, making it space-efficient for sparse graphs.
2. Time Complexity: Adding a Vertex
Adjacency Matrix : O(V^2)
Adjacency List : O(1)
- Adjacency Matrix: Adding a vertex may require creating a new
