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#
// 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.
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