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# 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 ` `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

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## Javascript

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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.