# 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}
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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}
```
```// 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;
}
```

Output:

```0 1 2
3 4 5
6 8 9
```

Time Complexity : O(N*N log N)
Auxiliary Space : (N*N)

# GATE CS Corner    Company Wise Coding Practice

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