Sort a Matrix in all way increasing order

Given a square matrix of order N*N having distinct elements, the task is to sort given matrix in such a way that its rows, columns and both diagonals (diagonal and anti-diagonal) are in increasing order.

Examples:

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

Input : arr[2][2] = {0, 4,
                     5, 2}                    
Output :{0, 2,
         4, 5}

Sorting any matrix in a way that its rows, columns and main diagonal are in increasing order is easy. If we consider matrix elements in sequence according to row-major order and sort the sequence, we get the desired result.

Example: arr[2][2] : {1, 2
                      3, 4}
Rows in increasing order:  {1,2} and {3,4}
Columns in increasing order:  {1,3} and {2,4}
Diagonal in increasing order:  {1,4}
Anti-diagonal in increasing order:  {2,3}

Implementation:

CPP

// C++ program to sort matrix in all-way
#include<bits/stdc++.h>
using namespace std;
#define N 3

// Sorts a matrix in increasing order
void sortAllWay(int arr[][N])
{
    // Consider matrix elements (in row major
    // order) and sort the sequence.
    int *ptr = (int *)arr;
    sort(ptr, ptr+N*N);
}

// driver program
int main()
{
    int arr[N][N] = {1, 0, 3,
                     2, 5, 6,
                     9, 4, 8};
    sortAllWay(arr);


    // print resultant matrix
    for (int i=0; i<N; i++)
    {
        for (int j=0; j<N; j++)
            cout << arr[i][j] << " ";
        cout <<"\n";
    }

    return 0;
}

Java

// Java program to sort matrix in all-way
import java.util.*;

class GFG{
static final int N =  3;

// Sorts a matrix in increasing order
static int[][] sortAllWay(int arr[][])
{
  
    // Consider matrix elements (in row major
    // order) and sort the sequence.
    int []ar = new int[arr.length*arr.length];
    int k = 0;
    for(int i = 0; i < arr.length; i++) {
        for(int j = 0; j < arr.length; j++) {
            ar[k] = arr[i][j];
            k++;
        }
    }
    Arrays.sort(ar);
    k = 0;
    for(int i = 0; i < arr.length; i++) {
        for(int j = 0; j < arr.length; j++) {
            arr[i][j] = ar[k];
            k++;
        }
    }
    return arr;
}

// Driver program
public static void main(String[] args)
{
    int arr[][] = {{1, 0, 3},
    { 2, 5, 6},
    {   9, 4, 8}};
    arr = sortAllWay(arr);

    // print resultant matrix
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j < N; j++)
            System.out.print(arr[i][j] + " ");
        System.out.println();
    }
}
}

// This code is contributed by umadevi9616

Python3

# Python program to sort matrix in all-way
N = 3;

# Sorts a matrix in increasing order
def sortAllWay(arr):

    # Consider matrix elements (in row major
    # order) and sort the sequence.
    ar = [0 for i in range(len(arr) * len(arr))];
    k = 0;
    for i in range(len(arr)):
        for j in range(len(arr)):
            ar[k] = arr[i][j];
            k += 1;
    
    ar.sort();
    k = 0;
    for i in range(len(arr)):
        for j in range(len(arr)):
            arr[i][j] = ar[k];
            k += 1;
    
    return arr;

# Driver program
if __name__ == '__main__':
    arr = [[ 1, 0, 3 ],[ 2, 5, 6 ],[ 9, 4, 8 ]] ;
    arr = sortAllWay(arr);

    # print resultant matrix
    for i in range(N):
        for j in range(N):
            print(arr[i][j], end=" ");
        print();
    
# This code IS contributed by umadevi9616

// C# program to sort matrix in all-way
using System;

public class GFG {
  static readonly int N = 3;

  // Sorts a matrix in increasing order
  static int[,] sortAllWay(int [,]arr) {

    // Consider matrix elements (in row major
    // order) and sort the sequence.
    int[] ar = new int[arr.GetLength(0) * arr.GetLength(1)];
    int k = 0;
    for (int i = 0; i < arr.GetLength(0); i++) {
      for (int j = 0; j < arr.GetLength(1); j++) {
        ar[k] = arr[i,j];
        k++;
      }
    }
    Array.Sort(ar);
    k = 0;
    for (int i = 0; i < arr.GetLength(0); i++) {
      for (int j = 0; j < arr.GetLength(1); j++) {
        arr[i,j] = ar[k];
        k++;
      }
    }
    return arr;
  }

  // Driver program
  public static void Main(String[] args) {
    int [,]arr = { { 1, 0, 3 }, { 2, 5, 6 }, { 9, 4, 8 } };
    arr = sortAllWay(arr);

    // print resultant matrix
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++)
        Console.Write(arr[i,j] + " ");
      Console.WriteLine();
    }
  }
}

// This code is contributed by umadevi9616

JavaScript

<script>
 
// Javascript program to sort matrix in all-way
var N = 3;

// Sorts a matrix in increasing order
function sortAllWay(arr)
{
    // Consider matrix elements (in row major
    // order) and sort the sequence.
    arr.sort((a,b)=>a-b);
    return arr;
}

// driver program
var arr = [1, 0, 3,
                 2, 5, 6,
                 9, 4, 8];
arr = sortAllWay(arr);
// print resultant matrix
for(var i=0; i<N; i++)
{
    for (var j=0; j<N; j++)
        document.write(arr[N*i+j] + " ");
    document.write("<br>");
}

// This code is contributed by rutvik_56.

</script>

Output

0 1 2 
3 4 5 
6 8 9

Time Complexity : O(N*N log N)
Auxiliary Space : (N*N), since N*N extra space has been taken.

Sort a Matrix in all way increasing order

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