Sparse array in C++

In this article, we will discuss the sparse array in C++ with its example.

A sparse array represents a data array in which many of the elements contain a value of zero. As a result, in a full array, the majority of the components have non-zero values or are "full" of numbers. In computer data handling, a sparse array may be handled differently from a dense array.

Sparse array properties:

• A sparse array has most of its entries with the same value (the standard value is zero/Null).
• Sparse matrices are arrays in which the majority of the elements are zero.
• A sparse array is one with no contiguous indexes beginning at zero.
• When there are fewer non-zero elements, sparse arrays can be used instead of arrays. Sparse arrays use less space to store each component and can save time in computation.

Example:

[[1 0 1],

[0 2 0],

[0 3 0]]

Why a sparse array is preferred over a simple array for storing elements:

Storage: When there are a majority of zero elements and the fewest non-zero elements, we choose a sparse array instead of a simple array since it uses a smaller amount of memory to store all of the elements. Something other than zero elements is stored in the sparse array.

Computation Time: Because we only keep non-zero components in the sparse array, traversing just non-zero components takes less time for computation.

Sparse Array Representation:

There are two ways to express sparse arrays:

1. Linked List Representation
2. Array Representation

1. Representation of an Array:

A sparse array is represented by a 2-D array with three rows: Row, Column, and Value.

Row: The starting position of the row containing non-zero elements.

Column: The number that represents the index of the column containing the non-zero element.

Value: A non-zero value found in the (Row, Columns) index.

2. Representation of Linked Lists:

Each of the nodes in a sparse array is represented by four fields: Row, Column, Value, and Next node.

Row: It is the starting position of the row containing non-zero elements.

Column: The value of the index of the column containing the non-zero element.

Value: A non-zero value found in the (Row, Column) index.

Next Node: It saves a subsequent node's address.

Algorithm

Filename: SparseArray.cpp

Output:

The given matrix is:
1 0 9 
3 0 0 
1 0 0 
The total number of zeros in the given array are 5
The given array is a sparse array.