# Find an N x N grid whose xor of every row and column is equal

Given an integer N which is a multiple of 4, the task is to find an N x N grid for which the bitwise xor of every row and column is same.

Examples:

Input: N = 4
Output:
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15

Input: N = 8
Output:
0 1 2 3 16 17 18 19
4 5 6 7 20 21 22 23
8 9 10 11 24 25 26 27
12 13 14 15 28 29 30 31
32 33 34 35 48 49 50 51
36 37 38 39 52 53 54 55
40 41 42 43 56 57 58 59
44 45 46 47 60 61 62 63

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: To solve this problem lets fix the xor of every row and column to 0 since xor of 4 consecutive numbers starting from 0 is 0. Here is an example of a 4 x 4 matrix:

0 ^ 1 ^ 2 ^ 3 = 0
4 ^ 5 ^ 6 ^ 7 = 0
8 ^ 9 ^ 10 ^ 11 = 0
12 ^ 13 ^ 14 ^ 15 = 0
and so on.

If you notice in the above example, the xor of every row and column is 0. Now we need to place the numbers in such a way that the xor of each row and column is 0.So we can divide our N x N matrix into smaller 4 x 4 matrices with N / 4 rows and columns and fill the cells in a way that the xor of every row and column is 0.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the n x n matrix ` `// that satisfies the given condition ` `void` `findGrid(``int` `n) ` `{ ` `    ``int` `arr[n][n]; ` ` `  `    ``// Initialize x to 0 ` `    ``int` `x = 0; ` ` `  `    ``// Divide the n x n matrix into n / 4 matrices ` `    ``// for each of the n / 4 rows where ` `    ``// each matrix is of size 4 x 4 ` `    ``for` `(``int` `i = 0; i < n / 4; i++) { ` `        ``for` `(``int` `j = 0; j < n / 4; j++) { ` `            ``for` `(``int` `k = 0; k < 4; k++) { ` `                ``for` `(``int` `l = 0; l < 4; l++) { ` `                    ``arr[i * 4 + k][j * 4 + l] = x; ` `                    ``x++; ` `                ``} ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Print the generated matrix ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``for` `(``int` `j = 0; j < n; j++) { ` `            ``cout << arr[i][j] << ``" "``; ` `        ``} ` `        ``cout << ``"\n"``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 4; ` ` `  `    ``findGrid(n); ` ` `  `    ``return` `0; ` `} `

 `// Java implementation of the approach ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `     `  `// Function to find the n x n matrix ` `// that satisfies the given condition ` `static` `void` `findGrid(``int` `n) ` `{ ` `    ``int` `[][]arr = ``new` `int``[n][n]; ` ` `  `    ``// Initialize x to 0 ` `    ``int` `x = ``0``; ` ` `  `    ``// Divide the n x n matrix into n / 4 matrices ` `    ``// for each of the n / 4 rows where ` `    ``// each matrix is of size 4 x 4 ` `    ``for` `(``int` `i = ``0``; i < n / ``4``; i++) ` `    ``{ ` `        ``for` `(``int` `j = ``0``; j < n / ``4``; j++)  ` `        ``{ ` `            ``for` `(``int` `k = ``0``; k < ``4``; k++)  ` `            ``{ ` `                ``for` `(``int` `l = ``0``; l < ``4``; l++)  ` `                ``{ ` `                    ``arr[i * ``4` `+ k][j * ``4` `+ l] = x; ` `                    ``x++; ` `                ``} ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Print the generated matrix ` `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``{ ` `        ``for` `(``int` `j = ``0``; j < n; j++)  ` `        ``{ ` `            ``System.out.print(arr[i][j] + ``" "``); ` `        ``} ` `        ``System.out.println(``" "``); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args) ` `{ ` `    ``int` `n = ``4``; ` `     `  `    ``findGrid(n); ` `} ` `} ` ` `  `// This code is contributed by ajit. `

 `# Python3 implementation of the approach  ` ` `  `# Function to find the n x n matrix  ` `# that satisfies the given condition  ` `def` `findGrid(n):  ` ` `  `    ``arr ``=` `[[``0` `for` `k ``in` `range``(n)]  ` `              ``for` `l ``in` `range``(n)]  ` ` `  `    ``# Initialize x to 0  ` `    ``x ``=` `0` ` `  `    ``# Divide the n x n matrix into n / 4 matrices  ` `    ``# for each of the n / 4 rows where  ` `    ``# each matrix is of size 4 x 4  ` `    ``for` `i ``in` `range``(n ``/``/` `4``):  ` `        ``for` `j ``in` `range``(n ``/``/` `4``):  ` `            ``for` `k ``in` `range``(``4``):  ` `                ``for` `l ``in` `range``(``4``):  ` `                    ``arr[i ``*` `4` `+` `k][j ``*` `4` `+` `l] ``=` `x  ` `                    ``x ``+``=` `1` ` `  `    ``# Print the generated matrix  ` `    ``for` `i ``in` `range``(n):  ` `        ``for` `j ``in` `range``(n):  ` `            ``print``(arr[i][j], end ``=` `" "``) ` `        ``print``() ` ` `  `# Driver code  ` `n ``=` `4` `findGrid(n)  ` ` `  `# This code is contributed by divyamohan123 `

 `// C# implementation of the approach ` `using` `System; ` `     `  `class` `GFG  ` `{ ` `     `  `// Function to find the n x n matrix ` `// that satisfies the given condition ` `static` `void` `findGrid(``int` `n) ` `{ ` `    ``int` `[,]arr = ``new` `int``[n, n]; ` ` `  `    ``// Initialize x to 0 ` `    ``int` `x = 0; ` ` `  `    ``// Divide the n x n matrix into n / 4 matrices ` `    ``// for each of the n / 4 rows where ` `    ``// each matrix is of size 4 x 4 ` `    ``for` `(``int` `i = 0; i < n / 4; i++) ` `    ``{ ` `        ``for` `(``int` `j = 0; j < n / 4; j++)  ` `        ``{ ` `            ``for` `(``int` `k = 0; k < 4; k++)  ` `            ``{ ` `                ``for` `(``int` `l = 0; l < 4; l++)  ` `                ``{ ` `                    ``arr[i * 4 + k, j * 4 + l] = x; ` `                    ``x++; ` `                ``} ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Print the generated matrix ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `    ``{ ` `        ``for` `(``int` `j = 0; j < n; j++)  ` `        ``{ ` `            ``Console.Write(arr[i, j] + ``" "``); ` `        ``} ` `        ``Console.WriteLine(``" "``); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main (String[] args) ` `{ ` `    ``int` `n = 4; ` `     `  `    ``findGrid(n); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

Output:
```0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
```

Time Complexity: O(N2)

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