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Python program to Convert a Matrix to Sparse Matrix
• Difficulty Level : Medium
• Last Updated : 30 Dec, 2020

Given a matrix with most of its elements as 0, we need to convert this matrix into a sparse matrix in Python.

Example:

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

Output: Sparse Matrix:
0 0 1
1 1 2
2 2 3
3 3 4
4 0 5

Explanation:
Here the Matrix is represented using a 2D list and the Sparse Matrix is represented in the form Row Column Value

In the Sparse Matrix the first row is `0 1 1` indicates that the value of the Matrix at row 0 and column 1 is 1.

Approach:

1. Create an empty list which will represent the sparse matrix list.
2. Iterate through the 2D matrix to find non zero elements.
3. If an element is non zero, create a temporary empty list.
4. Append the row value, column value, and the non zero element itself into the temporary list.
5. Now append the temporary list into the sparse matrix list such that the temporary list acts as a sub-list of the sparse matrix list.
6. After getting all the non zero elements from the matrix, display the sparse matrix.

The above approach has been used in `convertToSparseMatrix()` function in the below program:

 `# Python program to convert a``# matrix to sparse matrix`` ` ` ` `# function display a matrix``def` `displayMatrix(matrix):``     ` `    ``for` `row ``in` `matrix:``        ``for` `element ``in` `row:``            ``print``(element, end ``=``" "``)``        ``print``()`` ` `# function to convert the matrix ``# into a sparse matrix``def` `convertToSparseMatrix(matrix):`` ` `    ``# creating an empty sparse ``    ``# matrix list``    ``sparseMatrix ``=``[]`` ` `    ``# searching values greater ``    ``# than zero``    ``for` `i ``in` `range``(``len``(matrix)):``        ``for` `j ``in` `range``(``len``(matrix[``0``])):``            ``if` `matrix[i][j] !``=` `0` `:`` ` `                ``# creating a temporaray``                ``# sublist``                ``temp ``=` `[]`` ` `                ``# appending row value, column ``                ``# value and element into the ``                ``# sublist ``                ``temp.append(i)``                ``temp.append(j)``                ``temp.append(matrix[i][j])`` ` `                ``# appending the sublist into``                ``# the sparse matrix list``                ``sparseMatrix.append(temp)`` ` `    ``# displaying the sparse matrix``    ``print``(``"\nSparse Matrix: "``) ``    ``displayMatrix(sparseMatrix)                 `` ` `# Driver's code``# initializing a normal matrix``normalMatrix ``=``[[``1``, ``0``, ``0``, ``0``], ``               ``[``0``, ``2``, ``0``, ``0``], ``               ``[``0``, ``0``, ``3``, ``0``], ``               ``[``0``, ``0``, ``0``, ``4``], ``               ``[``5``, ``0``, ``0``, ``0``]] `` ` `# displaying the matrix``displayMatrix(normalMatrix)`` ` `# converting the matrix to sparse ``# displayMatrix ``convertToSparseMatrix(normalMatrix)       `

Output:

```0 1 0 0
0 0 2 0
0 3 0 0
0 0 5 0
0 0 0 4

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

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