# Create a matrix with alternating rectangles of O and X

Write a code which inputs two numbers m and n and creates a matrix of size m x n (m rows and n columns) in which every elements is either X or 0. The Xs and 0s must be filled alternatively, the matrix should have outermost rectangle of Xs, then a rectangle of 0s, then a rectangle of Xs, and so on.

Examples:

```Input: m = 3, n = 3
Output: Following matrix
X X X
X 0 X
X X X

Input: m = 4, n = 5
Output: Following matrix
X X X X X
X 0 0 0 X
X 0 0 0 X
X X X X X

Input:  m = 5, n = 5
Output: Following matrix
X X X X X
X 0 0 0 X
X 0 X 0 X
X 0 0 0 X
X X X X X

Input:  m = 6, n = 7
Output: Following matrix
X X X X X X X
X 0 0 0 0 0 X
X 0 X X X 0 X
X 0 X X X 0 X
X 0 0 0 0 0 X
X X X X X X X ```

We strongly recommend to minimize the browser and try this yourself first.

This question was asked in campus recruitment of Shreepartners Gurgaon. I followed the following approach.

1) Use the code for Printing Matrix in Spiral form.
2) Instead of printing the array, inserted the element ‘X’ or ‘0’ alternatively in the array.

Following is C implementation of the above approach.

```#include <stdio.h>

// Function to print alternating rectangles of 0 and X
void fill0X(int m, int n)
{
/*  k - starting row index
m - ending row index
l - starting column index
n - ending column index
i - iterator    */
int i, k = 0, l = 0;

// Store given number of rows and columns for later use
int r = m, c = n;

// A 2D array to store the output to be printed
char a[m][n];
char x = 'X'; // Iniitialize the character to be stoed in a[][]

// Fill characters in a[][] in spiral form. Every iteration fills
// one rectangle of either Xs or Os
while (k < m && l < n)
{
/* Fill the first row from the remaining rows */
for (i = l; i < n; ++i)
a[k][i] = x;
k++;

/* Fill the last column from the remaining columns */
for (i = k; i < m; ++i)
a[i][n-1] = x;
n--;

/* Fill the last row from the remaining rows */
if (k < m)
{
for (i = n-1; i >= l; --i)
a[m-1][i] = x;
m--;
}

/* Print the first column from the remaining columns */
if (l < n)
{
for (i = m-1; i >= k; --i)
a[i][l] = x;
l++;
}

// Flip character for next iteration
x = (x == '0')? 'X': '0';
}

// Print the filled matrix
for (i = 0; i < r; i++)
{
for (int j = 0; j < c; j++)
printf("%c ", a[i][j]);
printf("\n");
}
}

/* Driver program to test above functions */
int main()
{
puts("Output for m = 5, n = 6");
fill0X(5, 6);

puts("\nOutput for m = 4, n = 4");
fill0X(4, 4);

puts("\nOutput for m = 3, n = 4");
fill0X(3, 4);

return 0;
}```

Output:

```Output for m = 5, n = 6
X X X X X X
X 0 0 0 0 X
X 0 X X 0 X
X 0 0 0 0 X
X X X X X X

Output for m = 4, n = 4
X X X X
X 0 0 X
X 0 0 X
X X X X

Output for m = 3, n = 4
X X X X
X 0 0 X
X X X X ```

Time Complexity: O(mn)
Auxiliary Space: O(mn)

Please suggest if someone has a better solution which is more efficient in terms of space and time.

# GATE CS Corner    Company Wise Coding Practice

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