# Python3 Program to Check if all rows of a matrix are circular rotations of each other

Given a matrix of n*n size, the task is to find whether all rows are circular rotations of each other or not.

Examples:

Input: mat[][] = 1, 2, 3

3, 1, 2

2, 3, 1
Output:  Yes,All rows are rotated permutation of each other.
Input: mat[3][3] = 1, 2, 3

3, 2, 1

1, 3, 2
Output:  No,As 3, 2, 1 is not a rotated or circular permutation of 1, 2, 3

The idea is based on the below article.
A Program to check if strings are rotations of each other or not

Steps :

1. Create a string of first row elements and concatenate the string with itself so that string search operations can be efficiently performed. Let this string be str_cat.
2. Traverse all remaining rows. For every row being traversed, create a string str_curr of current row elements. If str_curr is not a substring of str_cat, return false.
3. Return true.

Below is the implementation of the above steps.

## Python3

 `# Python3 program to check if all rows ``# of a matrix are rotations of each other ` `MAX` `=` `1000` `# Returns true if all rows of mat[0..n-1][0..n-1] ``# are rotations of each other. ``def` `isPermutedMatrix(mat, n) :``    ` `    ``# Creating a string that contains ``    ``# elements of first row. ``    ``str_cat ``=` `""``    ``for` `i ``in` `range``(n) :``        ``str_cat ``=` `str_cat ``+` `"-"` `+` `str``(mat[``0``][i])` `    ``# Concatenating the string with itself ``    ``# so that substring search operations ``    ``# can be performed on this ``    ``str_cat ``=` `str_cat ``+` `str_cat` `    ``# Start traversing remaining rows ``    ``for` `i ``in` `range``(``1``, n) :``        ` `        ``# Store the matrix into vector ``        ``# in the form of strings ``        ``curr_str ``=` `""``        ` `        ``for` `j ``in` `range``(n) :``            ``curr_str ``=` `curr_str ``+` `"-"` `+` `str``(mat[i][j])` `        ``# Check if the current string is present ``        ``# in the concatenated string or not ``        ``if` `(str_cat.find(curr_str)) : ``            ``return` `True``            ` `    ``return` `False` `# Driver code ``if` `__name__ ``=``=` `"__main__"` `:``    ``n ``=` `4``    ``mat ``=` `[[``1``, ``2``, ``3``, ``4``], ``           ``[``4``, ``1``, ``2``, ``3``], ``           ``[``3``, ``4``, ``1``, ``2``], ``           ``[``2``, ``3``, ``4``, ``1``]] ``    ` `    ``if` `(isPermutedMatrix(mat, n)):``        ``print``(``"Yes"``)``    ``else` `:``        ``print``(``"No"``)``        ` `# This code is contributed by Ryuga`

Output
```Yes
```

Time complexity: O(n3
Auxiliary Space: O(n)

Please refer complete article on Check if all rows of a matrix are circular rotations of each other for more details!

Previous
Next