# Sort the matrix row-wise and column-wise using Python

In this article, we will learn a python program to sort the matrix row-wise and column-wise.

Assume we have taken an input MxM matrix. We will now sort the given input matrix row-wise and column-wise using the nested for loop.

## Algorithm (Steps)

Following are the Algorithms/steps to be followed to perform the desired task. −

• Create a function sortingMatrixByRow() to sort each row of matrix i.e, row-wise by accepting input matrix, m(no of rows) as arguments.

• Inside the function, use the for loop to traverse through the rows of a matrix.

• Use Another nested for loop to traverse through all the columns of the current row.

• Use the if conditional statement to check whether the current element is greater than the next element.

• Swap the elements using a temporary variable if the condition is true.

• Create another function transposeMatrix() to get the transpose of a matrix by accepting the input matrix, m(no of rows) as arguments.

• Use the for loop, to traverse through the rows of a matrix.

• Use another nested for loop to traverse through the form (row +1) column to the end of the columns.

• Swap the current row, column element with the column, row element.

• Create a function sortMatrixRowandColumn() to sort the matrix row and column-wise by accepting the input matrix, m(no of rows) as arguments.

• Inside the function, call the above-defined sortingMatrixByRow() function to sort the rows of an input matrix.

• Call the above-defined transposeMatrix() function to get the transpose of an input matrix.

• Once again sort the rows of an input matrix by calling the above-defined sortingMatrixByRow() function.

• Once again getting the transpose of an input matrix by calling the above-defined transposeMatrix() function.

• Create a function printingMatrix() to print the matrix by traversing through rows and columns of a matrix using nested for loop.

• Create a variable to store the input matrix.

• Create another variable to store input m(no of rows) value

• Call the above-defined printingMatrix() function to print the input matrix.

• Call the above-defined sortMatrixRowandColumn() function by passing the input matrix, m values to it to sort the matrix row and column-wise.

• Print the resultant input matrix after sorting row and column-wise by calling the above-defined printingMatrix() function.

## Example

The following program returns the sorted matrix by row and column-wise for the given input matrix using nested for loops −

# creating a function for sorting each row of matrix row-wise
def sortingMatrixByRow(inputMatrix, m):
#  traversing till the length of rows of a matrix
for p in range(m):
# Sorting the current row
for q in range(m-1):
# checking whether the current element is greater than the next element
if inputMatrix[p][q] >inputMatrix[p][q + 1]:
# swapping the elements using a temporary variable
# if the condition is true
tempVariable = inputMatrix[p][q]
inputMatrix[p][q] = inputMatrix[p][q + 1]
inputMatrix[p][q + 1] = tempVariable

# creating a function to get the transpose of a matrix
# by accepting the input matrix, m values as arguments
def transposeMatrix(inputMatrix, m):
# traversing through the rows of a matrix
for p in range(m):
# Traversing from row +1 column to last column
for q in range(p + 1, m):
# Swapping the element at index (p,q) with (q,p)
temp = inputMatrix[p][q]
inputMatrix[p][q] = inputMatrix[q][p]
inputMatrix[q][p] = temp

# creating a function for sorting the matrix rows column-wise
def sortMatrixRowandColumn(inputMatrix, m):
# sorting the rows of an input matrix by
# calling the above defined sortingMatrixByRow() function
sortingMatrixByRow(inputMatrix, m)
# getting the transpose of an input matrix by
# calling the above defined transposeMatrix() function
transposeMatrix(inputMatrix, m)
# once again sorting the rows of an input matrix by
# calling the above defined sortingMatrixByRow() function
sortingMatrixByRow(inputMatrix, m)
# once again getting the transpose of an input matrix(So we sorted the columns)
transposeMatrix(inputMatrix, m)

# creating a function to print the matrix
def printingMatrix(inputMatrix, rows):
# Traversing in the rows of the input matrix
for i in range(rows):
# Traversing in the columns corresponding to the current row
# of the input matrix
for j in range(rows):
print(inputMatrix[i][j], end=" ")
# Printing a new line to separate the rows
print()
# input matrix
inputMatrix = [[2, 6, 5],
[1, 9, 8],
[7, 3, 10]]

# input m value representing 3x3 matrix
# (dimensions)
m = 3
print("Input Matrix:")
# printing the input matrix by calling the above
# printingMatrix() function
printingMatrix(inputMatrix, m)
# calling the above defined sortMatrixRowandColumn() function
# by passing the input matrix, m values to it to
# sort the matrix row and column-wise
sortMatrixRowandColumn(inputMatrix, m)
# printing the input matrix after sorting row and column-wise
# by calling the above printingMatrix() function
print("Input Matrix after sorting row and column-wise:")
printingMatrix(inputMatrix, m)


## Output

On execution, the above program will generate the following output −

Input Matrix:
2 6 5
1 9 8
7 3 10
Input Matrix after sorting row and column-wise:
1 5 6
2 7 9
3 8 10


Time Complexity − O(n^2 log2n)

Auxiliary Space − O(1)

## Conclusion

In this article, we learned how to use Python to sort the given matrix both row- and column-wise. Additionally, we learned how to transpose the given matrix and how to sort the matrix by rows using nested for loops (rather than utilizing the built-in sort() method).