Check if all rows of a matrix are circular rotations of each other

06 Jul, 2022
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
Explanation : As 3, 2, 1 is not a rotated or 
circular permutation of 1, 2, 3
The idea is based on below article. A Program to check if strings are rotations of each other or not
Steps :  
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.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.Return true.
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.
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.
Return true.
Below is the implementation of above steps. 
C++
Java
Python3
C#
PHP
Javascript
// C++ program to check if all rows of a matrix// are rotations of each other#include <bits/stdc++.h>using namespace std;const int MAX = 1000; // Returns true if all rows of mat[0..n-1][0..n-1]// are rotations of each other.bool isPermutedMatrix( int mat[MAX][MAX], 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 + "-" + to_string(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 + "-" + to_string(mat[i][j]);         // Check if the current string is present in        // the concatenated string or not        if (str_cat.find(curr_str) == string::npos)            return false;    }     return true;} // Drivers codeint main(){    int n = 4 ;    int mat[MAX][MAX] = {{1, 2, 3, 4},        {4, 1, 2, 3},        {3, 4, 1, 2},        {2, 3, 4, 1}    };    isPermutedMatrix(mat, n)? cout << "Yes" :                              cout << "No";    return 0;}
// Java program to check if all rows of a matrix// are rotations of each otherclass 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 */
# 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 codeif __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
// C# program to check if all rows of a matrix// are rotations of each otherusing System; 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 bool 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 + "-" + mat[0,i].ToString();        }         // 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 + "-" + mat[i,j].ToString();            }             // Check if the current string is present in            // the concatenated string or not            if (str_cat.Equals(curr_str))            {                return false;            }        }         return true;    }     // Driver code    static void Main()    {        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))        {            Console.WriteLine("Yes");        }        else        {            Console.WriteLine("No");        }    }} /* This code contributed by mits */
<?php// PHP program to check if all rows of a// matrix are rotations of each other$MAX = 1000; // Returns true if all rows of mat[0..n-1][0..n-1]// are rotations of each other.function isPermutedMatrix( &$mat, $n){    // Creating a string that contains    // elements of first row.    $str_cat = "";    for ($i = 0 ; $i < $n ; $i++)        $str_cat = $str_cat . "-" .                   strval($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 = 1; $i < $n; $i++)    {        // Store the matrix into vector        // in the form of strings        $curr_str = "";        for ($j = 0 ; $j < $n ; $j++)            $curr_str = $curr_str . "-" .                        strval($mat[$i][$j]);         // Check if the current string is present        // in the concatenated string or not        if (strpos($str_cat, $curr_str))            return true;    }     return false;} // Driver Code$n = 4;$mat = array(array(1, 2, 3, 4),             array(4, 1, 2, 3),             array(3, 4, 1, 2),             array(2, 3, 4, 1));if (isPermutedMatrix($mat, $n))    echo "Yes";else    echo "No"; // This code is contributed by ita_c?>
<script> // Javascript program to check if all rows of a matrix// are rotations of each other     // Returns true if all rows of mat[0..n-1][0..n-1]// are rotations of each other.function isPermutedMatrix(mat, n){         // Creating a string that contains    // elements of first row.    let str_cat = "";    for (let i = 0; i < n; i++)    {        str_cat = str_cat + "-" +                  (mat[0][i]).toString();    }         // 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(let i = 1; i < n; i++)    {                 // Store the matrix into vector in the form        // of strings        let curr_str = "";        for(let j = 0; j < n; j++)        {            curr_str = curr_str + "-" +                       (mat[i][j]).toString();        }                 // Check if the current string is present in        // the concatenated string or not        if (str_cat.includes(curr_str))        {            return true;        }    }    return false;} // Drivers codelet n = 4;let mat = [ [ 1, 2, 3, 4 ],            [ 4, 1, 2, 3 ],            [ 3, 4, 1, 2 ],            [ 2, 3, 4, 1 ] ];             if (isPermutedMatrix(mat, n))    document.write("Yes")else    document.write("No") // This code is contributed by rag2127 </script>
Yes
Time complexity : O(n3) Auxiliary Space : O(n)
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