Python Program to Sort the matrix row-wise and column-wise

Given a n x n matrix. The problem is to sort the matrix row-wise and column wise.
Examples: 
 

Input : mat[][] = { {4, 1, 3},
                    {9, 6, 8},
                    {5, 2, 7} }
Output : 1 3 4
         2 5 7
         6 8 9

Input : mat[][] = { {12, 7, 1, 8},
                    {20, 9, 11, 2},
                    {15, 4, 5, 13},
                    {3, 18, 10, 6} } 
Output : 1 5 8 12
         2 6 10 15
         3 7 11 18
         4 9 13 20

Approach: Following are the steps:
 

1. Sort each row of the matrix.
2. Get transpose of the matrix.
3. Again sort each row of the matrix.
4. Again get transpose of the matrix.

Algorithm for getting transpose of the matrix: 
 

for (int i = 0; i < n; i++) {
    for (int j = i + 1; i < n; i++) {
        int temp = mat[i][j];
        mat[i][j] = mat[j][i];
        mat[j][i] = temp;
    }
}

# Python 3 implementation to
# sort the matrix row-wise
# and column-wise
MAX_SIZE = 10

# function to sort each
# row of the matrix
def sortByRow(mat, n):
    for i in range (n):
        
        # sorting row number 'i'
        for j in range(n-1):
            if mat[i][j] > mat[i][j + 1]:
                temp = mat[i][j]
                mat[i][j] = mat[i][j + 1]
                mat[i][j + 1] = temp

# function to find
# transpose of the matrix
def transpose(mat, n):
    for i in range (n):
        for j in range(i + 1, n):

            # swapping element at
            # index (i, j) by element
            # at index (j, i)
            t = mat[i][j]
            mat[i][j] = mat[j][i]
            mat[j][i] = t

# function to sort
# the matrix row-wise
# and column-wise
def sortMatRowAndColWise(mat, n):
    
    # sort rows of mat[][]
    sortByRow(mat, n)

    # get transpose of mat[][]
    transpose(mat, n)

    # again sort rows of mat[][]
    sortByRow(mat, n)

    # again get transpose of mat[][]
    transpose(mat, n)

# function to print the matrix
def printMat(mat, n):
    for i in range(n):
        for j in range(n):
            print(str(mat[i][j] ), end = " ")
        print();
        
# Driver Code
mat = [[ 4, 1, 3 ],
    [ 9, 6, 8 ],
    [ 5, 2, 7 ]]
n = 3

print("Original Matrix:")
printMat(mat, n)

sortMatRowAndColWise(mat, n)

print("
Matrix After Sorting:")
printMat(mat, n)

# This code is contributed
# by ChitraNayal

Output: 
 

Original Matrix:
4 1 3
9 6 8
5 2 7

Matrix After Sorting:
1 3 4
2 5 7
6 8 9

Time Complexity: O(n²log₂n). 
Auxiliary Space: O(1). Please refer complete article on Sort the matrix row-wise and column-wise for more details!

Approach 2: Using NumPy

The NumPy code uses the numpy library to sort the matrix rows and transpose the matrix. The NumPy method looks considerably simple. 

• np.sort() function is used to sort each row of the matrix and mat.transpose() is used to find the transpose of the matrix. 
• The sortMatRowAndColWise function first sorts each row of the matrix using sortByRow function, then finds the transpose of the matrix and again sorts each row of the matrix and finds the transpose. 
• The printMat function is used to print the matrix.

Note: Install numpy in python using the following command: pip install numpy

Below is the code for the above approach: 

import numpy as np

# function to sort each row of the matrix
def sortByRow(mat):
    return np.sort(mat, axis=1)

# function to sort the matrix row-wise and column-wise
def sortMatRowAndColWise(mat):
    # sort rows of mat[][]
    mat = sortByRow(mat)

    # get transpose of mat[][]
    mat = mat.transpose()

    # again sort rows of mat[][]
    mat = sortByRow(mat)

    # again get transpose of mat[][]
    mat = mat.transpose()

    return mat

# function to print the matrix
def printMat(mat):
    print(mat)

# Driver Code
mat = np.array([[ 4, 1, 3 ],
                [ 9, 6, 8 ],
                [ 5, 2, 7 ]])

print("Original Matrix:")
printMat(mat)

mat = sortMatRowAndColWise(mat)

print("Matrix After Sorting:")
printMat(mat)

# This code is contributed by adityasha4x71

Output: 

Time Complexity: O(n^2 log n), where n is the number of elements in the matrix.

Auxiliary Space: O(n^2), as it creates a copy of the transposed matrix.