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# Java 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 = 1, 2, 3

3, 2, 1

1, 3, 2
Output:  No, Explanation : 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.

## Java

 `// Java program to check if all rows of a matrix``// are rotations of each other``class` `GFG``{` `    ``static` `int` `MAX = ``1000``;` `    ``// Returns true if all rows of mat[0..n-1][0..n-1]``    ``// are rotations of each other.``    ``static` `boolean` `isPermutedMatrix(``int` `mat[][], ``int` `n)``    ``{``        ``// Creating a string that contains``        ``// elements of first row.``        ``String str_cat = ``""``;``        ``for` `(``int` `i = ``0``; i < n; i++)``        ``{``            ``str_cat = str_cat + ``"-"` `+ String.valueOf(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` `(``int` `i = ``1``; i < n; i++)``        ``{``            ``// Store the matrix into vector in the form``            ``// of strings``            ``String curr_str = ``""``;``            ``for` `(``int` `j = ``0``; j < n; j++)``            ``{``                ``curr_str = curr_str + ``"-"` `+ String.valueOf(mat[i][j]);``            ``}` `            ``// Check if the current string is present in``            ``// the concatenated string or not``            ``if` `(str_cat.contentEquals(curr_str))``            ``{``                ``return` `false``;``            ``}``        ``}` `        ``return` `true``;``    ``}` `    ``// Drivers code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `n = ``4``;``        ``int` `mat[][] = {{``1``, ``2``, ``3``, ``4``},``        ``{``4``, ``1``, ``2``, ``3``},``        ``{``3``, ``4``, ``1``, ``2``},``        ``{``2``, ``3``, ``4``, ``1``}``        ``};``        ``if` `(isPermutedMatrix(mat, n))``        ``{``            ``System.out.println(``"Yes"``);``        ``}``        ``else``        ``{``            ``System.out.println(``"No"``);``        ``}``    ``}``}` `/* This code contributed by PrinciRaj1992 */`

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!

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