# C++ program to Convert a Matrix to Sparse Matrix

• Difficulty Level : Basic
• Last Updated : 11 Jul, 2022

Given a matrix with most of its elements as 0, convert this matrix to sparse matrix in C++
Examples:

```Input: Matrix:
0 1 1
1 2 2
2 1 3
3 2 5
4 3 4
Output: Sparse Matrix:
0 1 0 0
0 0 2 0
0 3 0 0
0 0 5 0
0 0 0 4
Explanation:
Here the Sparse matrix is represented
in the form Row Column Value

Hence the row 0 1 1 means that the value
of the matrix at row 0 and column 1 is 1```

Approach:

1. Get the matrix with most of its elements as 0.
2. Create a new 2D array to store the Sparse Matrix of only 3 columns (Row, Column, Value).
3. Iterate through the Matrix, and check if an element is non zero. In this case insert this element into the Sparse Matrix.
4. After each insertion, increment the value of variable length(here ‘len’). This will serve as the row dimension of the Sparse Matrix
5. Print the Dimension of the Sparse Matrix and its elements.

## CPP

 `// C++ program to convert a Matrix``// into Sparse Matrix` `#include ``using` `namespace` `std;` `// Maximum number of elements in matrix``#define MAX 100` `// Array representation``// of sparse matrix``//[][0] represents row``//[][1] represents col``//[][2] represents value``int` `data[MAX][3];` `// total number of elements in matrix``int` `len;` `// insert elements into sparse matrix``void` `insert(``int` `r, ``int` `c, ``int` `val)``{``    ``// insert row value``    ``data[len][0] = r;` `    ``// insert col value``    ``data[len][1] = c;` `    ``// insert element's value``    ``data[len][2] = val;` `    ``// increment number of data in matrix``    ``len++;``}` `// printing Sparse Matrix``void` `print()``{``    ``cout << ``"\nDimension of Sparse Matrix: "``         ``<< len << ``" x "` `<< 3;``    ``cout << ``"\nSparse Matrix: \nRow Column Value\n"``;` `    ``for` `(``int` `i = 0; i < len; i++) {` `        ``cout << data[i][0] << ``" "``             ``<< data[i][1] << ``" "``             ``<< data[i][2] << ``"\n"``;``    ``}``}` `// Driver code``int` `main()``{``    ``int` `i, j;``    ``int` `r = 5, c = 4;` `    ``// Get the matrix``    ``int` `a[r] = { { 0, 1, 0, 0 },``                    ``{ 0, 0, 2, 0 },``                    ``{ 0, 3, 0, 0 },``                    ``{ 0, 0, 5, 0 },``                    ``{ 0, 0, 0, 4 } };` `    ``// print the matrix``    ``cout << ``"\nMatrix:\n"``;``    ``for` `(i = 0; i < r; i++) {``        ``for` `(j = 0; j < c; j++) {``            ``cout << a[i][j] << ``" "``;``        ``}``        ``cout << endl;``    ``}` `    ``// iterate through the matrix and``    ``// insert every non zero elements``    ``// in the Sparse Matrix``    ``for` `(i = 0; i < r; i++)``        ``for` `(j = 0; j < c; j++)``            ``if` `(a[i][j] > 0)``                ``insert(i, j, a[i][j]);` `    ``// Print the Sparse Matrix``    ``print();` `    ``return` `0;``}`

Output:

```Matrix:
0 1 0 0
0 0 2 0
0 3 0 0
0 0 5 0
0 0 0 4

Dimension of Sparse Matrix: 5 x 3
Sparse Matrix:
Row Column Value
0 1 1
1 2 2
2 1 3
3 2 5
4 3 4```

Time complexity: O(m*n) where m is no of rows and n is no of columns of matrix

Auxiliary Space: O(MAX)

My Personal Notes arrow_drop_up