Sort a Matrix in all way increasing order
Last Updated :
13 Sep, 2023
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 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
# 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
<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>
Time Complexity : O(N*N log N)
Auxiliary Space : (N*N), since N*N extra space has been taken.
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