A Latin Square is a n x n grid filled by n distinct numbers each appearing exactly once in each row and column. Given an input n, we have to print a n x n matrix consisting of numbers from 1 to n each appearing exactly once in each row and each column.
Input: 3 Output: 1 2 3 3 1 2 2 3 1 Input: 5 Output: 1 2 3 4 5 5 1 2 3 4 4 5 1 2 3 3 4 5 1 2 2 3 4 5 1
Did you find any pattern in which the number are stored in a Latin Square?
- In the first row, the numbers are stored from 1 to n serially.
- the second row, the numbers are shifted to the right by one column. i.e, 1 is stored at 2nd column now and so on.
- In the third row, the numbers are shifted to the right by two columns. i.e, 1 is stored at 3rd column now and so on.
- We continue same way for remaining rows.
Note: There may be more than one possible configuration of a n x n latin square.
1 2 3 4 5 5 1 2 3 4 4 5 1 2 3 3 4 5 1 2 2 3 4 5 1
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