# 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}

`// 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; ` `} ` |

*chevron_right*

*filter_none*

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 contribute.geeksforgeeks.org or mail your article to contribute@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.

## Recommended Posts:

- Sort even and odd placed elements in increasing order
- Python | Sort Tuples in Increasing Order by any key
- Sort even-placed elements in increasing and odd-placed in decreasing order
- Sort only non-prime numbers of an array in increasing order
- Sort all even numbers in ascending order and then sort all odd numbers in descending order
- Sorting rows of matrix in descending order followed by columns in ascending order
- Sorting rows of matrix in ascending order followed by columns in descending order
- Check if it is possible to make the given matrix increasing matrix or not
- Rearrange all elements of array which are multiples of x in increasing order
- Print array elements in alternatively increasing and decreasing order
- Sort first k values in ascending order and remaining n-k values in descending order
- Shortest path to traverse all the elements of a circular array in increasing order
- Longest Increasing Path in Matrix
- Check if the given matrix is increasing row and column wise
- Find trace of matrix formed by adding Row-major and Column-major order of same matrix