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 sorting each row of matrix using C++ STL sort():

for (int i = 0 ; i < n; i++)
    sort(mat[i], mat[i] + n);

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;
    }
}

Implementation:

C++

// C++ implementation to sort the matrix row-wise
// and column-wise
#include <bits/stdc++.h>

using namespace std;

#define MAX_SIZE 10

// function to sort each row of the matrix
void sortByRow(int mat[MAX_SIZE][MAX_SIZE], int n)
{
    for (int i = 0; i < n; i++)

        // sorting row number 'i'
        sort(mat[i], mat[i] + n);
}

// function to find transpose of the matrix
void transpose(int mat[MAX_SIZE][MAX_SIZE], int n)
{
    for (int i = 0; i < n; i++)
        for (int j = i + 1; j < n; j++)

            // swapping element at index (i, j)
            // by element at index (j, i)
            swap(mat[i][j], mat[j][i]);
}

// function to sort the matrix row-wise
// and column-wise
void sortMatRowAndColWise(int mat[MAX_SIZE][MAX_SIZE],
                                               int 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
void printMat(int mat[MAX_SIZE][MAX_SIZE], int n)
{
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++)
            cout << mat[i][j] << " ";
        cout << endl;
    }
}

// Driver program to test above
int main()
{
    int mat[MAX_SIZE][MAX_SIZE] = { { 4, 1, 3 },
                            { 9, 6, 8 },
                            { 5, 2, 7 } };
    int n = 3;

    cout << "Original Matrix:\n";
    printMat(mat, n);

    sortMatRowAndColWise(mat, n);

    cout << "\nMatrix After Sorting:\n";
    printMat(mat, n);

    return 0;
}

Java

// Java implementation to sort the
// matrix row-wise and column-wise
import java.util.Arrays;

class GFG
{
    static final int MAX_SIZE=10;

    // function to sort each row of the matrix
    static void sortByRow(int mat[][], int n)
    {
        for (int i = 0; i < n; i++)

            // sorting row number 'i'
            Arrays.sort(mat[i]);
    }

    // function to find transpose of the matrix
    static void transpose(int mat[][], int n)
    {
        for (int i = 0; i < n; i++)
            for (int j = i + 1; j < n; j++)
                {
                // swapping element at index (i, j)
                // by element at index (j, i)
                int temp=mat[i][j];
                mat[i][j]=mat[j][i];
                mat[j][i]=temp;
                }
    }

    // function to sort the matrix row-wise
    // and column-wise
    static void sortMatRowAndColWise(int mat[][],int 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
    static void printMat(int mat[][], int n)
    {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++)
                System.out.print(mat[i][j] + " ");
            System.out.println();
        }
    }

    // Driver code
    public static void main (String[] args)
    {
        int mat[][] = { { 4, 1, 3 },
                        { 9, 6, 8 },
                        { 5, 2, 7 } };
        int n = 3;

        System.out.print("Original Matrix:\n");
        printMat(mat, n);

        sortMatRowAndColWise(mat, n);

        System.out.print("\nMatrix After Sorting:\n");
        printMat(mat, n);
    }
}

// This code is contributed by Anant Agarwal.

Python 3

# 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("\nMatrix After Sorting:")
printMat(mat, n)

# This code is contributed
# by ChitraNayal

C#

// C# implementation to sort the
// matrix row-wise and column-wise
using System;

class GFG
{
    // function to sort each
    // row of the matrix
    static void sortByRow(int [,]mat,
                          int n)
    {

    // sorting row number 'i'
    for (int i = 0; i < n ; i++)
        {
        for(int j = 0;
                j < n - 1; j++)
        {
            if(mat[i, j] > mat[i, j + 1])
            {

                var temp = mat[i, j];
                mat[i, j] = mat[i, j + 1];
                mat[i, j + 1] = temp;

            }
        }
        }
    }

    // function to find transpose
    // of the matrix
    static void transpose(int [,]mat,
                          int n)
    {
        for (int i = 0; i < n; i++)
            for (int j = i + 1;
                     j < n; j++)
                {

                    // swapping element at
                    // index (i, j) by
                    // element at index (j, i)
                    var temp = mat[i, j];
                    mat[i, j] = mat[j, i];
                    mat[j, i] = temp;
                }
    }

    // function to sort
    // the matrix row-wise
    // and column-wise
    static void sortMatRowAndColWise(int [,]mat,
                                     int 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
    static void printMat(int [,]mat, int n)
    {
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < n; j++)
                Console.Write(mat[i, j] + " ");
            Console.Write("\n");
        }
    }

    // Driver code
    public static void Main ()
    {
        int [,]mat = {{4, 1, 3},
                      {9, 6, 8},
                      {5, 2, 7}};
        int n = 3;

        Console.Write("Original Matrix:\n");
        printMat(mat, n);

        sortMatRowAndColWise(mat, n);

        Console.Write("\nMatrix After Sorting:\n");
        printMat(mat, n);
    }
}

// This code is contributed
// by ChitraNayal

PHP

<?php
// PHP implementation to sort
// the matrix row-wise and
// column-wise
$MAX_SIZE = 10;

// function to sort each
// row of the matrix
function sortByRow(&$mat, $n)
{
    for ($i = 0; $i < $n; $i++)

        // sorting row number 'i'
        sort($mat[$i]);
}

// function to find
// transpose of the matrix
function transpose(&$mat, $n)
{
    for ($i = 0; $i < $n; $i++)
    {
        for ($j = $i + 1;
             $j < $n; $j++)
        {
            // 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
function 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
function printMat(&$mat, $n)
{
    for ($i = 0; $i < $n; $i++)
    {
        for ($j = 0; $j < $n; $j++)
            echo $mat[$i][$j] . " ";
        echo "\n";
    }
}

// Driver Code
$mat = array(array( 4, 1, 3 ),
             array( 9, 6, 8 ),
             array( 5, 2, 7 ));
$n = 3;

echo "Original Matrix:\n";
printMat($mat, $n);

sortMatRowAndColWise($mat, $n);

echo "\nMatrix After Sorting:\n";
printMat($mat, $n);

// This code is contributed
// by ChitraNayal
?>

Javascript

<script>
// Javascript implementation to sort the
// matrix row-wise and column-wise

    let  MAX_SIZE=10;

    // function to sort each row of the matrix
    function sortByRow(mat,n)
    {
        for (let i = 0; i < n; i++)

            // sorting row number 'i'
            mat[i].sort(function(a,b){return a-b;});
    }

    // function to find transpose of the matrix
    function transpose(mat,n)
    {
        for (let i = 0; i < n; i++)
            for (let j = i + 1; j < n; j++)
                {
                // swapping element at index (i, j)
                // by element at index (j, i)
                let temp=mat[i][j];
                mat[i][j]=mat[j][i];
                mat[j][i]=temp;
                }
    }

    // function to sort the matrix row-wise
    // and column-wise
    function 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
    function printMat(mat,n)
    {
        for (let i = 0; i < n; i++) {
            for (let j = 0; j < n; j++)
                document.write(mat[i][j] + " ");
            document.write("<br>");
        }
    }

    // Driver code
    let mat = [[ 4, 1, 3 ],
       [ 9, 6, 8 ],
       [ 5, 2, 7 ]];

    let n = 3;
    document.write("Original Matrix:<br>");
    printMat(mat, n);

    sortMatRowAndColWise(mat, n);

    document.write("\nMatrix After Sorting:<br>");
    printMat(mat, n);
    // This code is contributed by avanitrachhadiya2155
</script>

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). Since no extra space has been taken.