Sort the given matrix

Given a m x n matrix. The problem is to sort the given matrix in strict order. Here strict order means that the matrix is sorted in a way such that all elements in a row are sorted in increasing order and for row ‘i’, where 1 <= i <= m-1, the first element is greater than or equal to the last element of row 'i-1'.

Examples: 

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

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

Naive Approach - O(mn Log mn) Time and O(mn) Space

We first store the matrix elements in a m x n sized 1D array, then sort the array and finally copy the elements back to the matrix,

Sorted Matrix Will be:
1 2 3 
4 5 6 
7 8 9 

Time Complexity: O(mnlog₂mn)
Auxiliary Space: O(mn) for the auxiliary 1D array.

Treating the Given Array as 1D Array - O(1) Space

The idea is to treat the 2D-Array as a 1D-Array to sort the matrix without using extra space. This can also be explained with the help of the following example. 

For Example:

There is a 2*2 Matrix with 4 elements,
The idea is to treat the elements of the matrix
as 1D Array of 4 elements.
1 2
3 4

As In the given matrix each element can be accessed as -
1st Element - 0th Row, 0th Col
2nd Element - 0th Row, 1st Col
3rd Element - 1st Row, 0th Col
4th Element - 1st Row, 1st Col 

So, for Accessing i^th element of the matrix, the relation can be defined as:

I^th Element of the Matrix = Mat[ i / n ][ i % n ]  
Where n is number of columns

Please refer Sort the given Matrix | Memory Efficient Approach for implementation