Sort the matrix row-wise and column-wise

Given a n x n matrix. The problem is to sort the matrix row-wise and column wise.

Examples: 

Input : mat[][] = { {4, 1, 3},
 {9, 6, 8},
 {5, 2, 7} }
Output : 1 3 4
 2 5 7
 6 8 9

Input : mat[][] = { {12, 7, 1, 8},
 {20, 9, 11, 2},
 {15, 4, 5, 13},
 {3, 18, 10, 6} } 
Output : 1 5 8 12
 2 6 10 15
 3 7 11 18
 4 9 13 20

Approach: Following are the steps:

1. Sort each row of the matrix.
2. Get transpose of the matrix.
3. Again sort each row of the matrix.
4. Again get transpose of the matrix.

Algorithm for sorting each row of matrix using C++ STL sort(): 

for (int i = 0 ; i < n; i++)
 sort(mat[i], mat[i] + n);

Algorithm for getting transpose of the matrix: 

for (int i = 0; i < n; i++) {
 for (int j = i + 1; i < n; i++) {
 int temp = mat[i][j];
 mat[i][j] = mat[j][i];
 mat[j][i] = temp;
 }
}

Implementation:

Original Matrix:
4 1 3 
9 6 8 
5 2 7 

Matrix After Sorting:
1 3 4 
2 5 7 
6 8 9 

Time Complexity: O(n²log₂n). 
Auxiliary Space: O(1). Since no extra space has been taken.