- A sparse array (or sparse vector) is a data structure where most elements are zero, so instead of storing all positions, we only store the non-zero entries. This saves memory and makes operations faster when the data is extremely sparse.
- A sparse matrix extends the same idea to 2D grids. Instead of keeping an entire R × C table full of zeros, each row stores only its non-zero column entries. This makes it efficient for scientific computing, graphs, and machine-learning workloads where matrices are huge but mostly empty.
1- Sparse arrays and sparse matrices play a crucial role in modern computing when dealing with large datasets containing predominantly zero values. Their key advantages include:
2- Memory Efficiency: Only non-zero elements are stored, significantly reducing memory requirements compared to dense structures.
3- Computational Performance: Algorithms operate exclusively on meaningful data, avoiding unnecessary computations on zeros.
4- Scalability: Enable handling of extremely large vectors and matrices that would be infeasible to store in dense format.
5- Efficient Mathematical Operations: Support fast addition, dot products, and matrix–vector multiplication, particularly in sorted or structured representations.
6- Applicability in Advanced Domains: Essential in scientific computing, optimization problems, graph algorithms, and machine-learning workloads where sparse data is common.
| Operation | Sorted List (default) | Unsorted List (fast insert) |
|---|---|---|
get(index) |
O(k) | O(k) |
set(index, value) |
O(k) | O(1) |
erase(index) |
O(k) | O(k) |
iterate all nnz |
Θ(k) | Θ(k) |
add(other) |
Θ(k1 + k2) | O(k1 * k2) |
dot(other) |
Θ(k1 + k2) | O(k1 * k2) |
| Memory | O(k) nodes + overhead | O(k) nodes + overhead |
| Operation | Complexity (default sorted rows) |
|---|---|
get(r,c) |
O(k_row) |
set(r,c) |
O(k_row) |
erase(r,c) |
O(k_row) |
iterate all entries |
Θ(nnz) |
matrix × vector (y = Ax) |
Θ(nnz) |
add(A,B) |
Θ(nnz_A + nnz_B) |
transpose |
Θ(nnz) |
| Memory | O(nnz) nodes + per-row heads |
Clone the repository to your local machine using Git:
git clone https://github.com/OMar-Adelll/SparseNet.git
cd SparseNet- Author: Omar Adel Youssef
- Repo: SparseNet