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Sort a Matrix in all way increasing order

  • Difficulty Level : Basic
  • Last Updated : 23 Dec, 2021

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}

 

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

C#




// 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)
This article is contributed by Shivam Pradhan (anuj_charm). If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


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