# C Program to Solve the Magic Squares Puzzle without Recursion

This is a C Program to solve the magic squares puzzle without using recursion.

Problem Description

The following C program, using iteration, finds the magic square for a given odd sized number.

Problem Solution

A magic square is an arrangement of numbers from 1 to n^2 in an [n x n] matrix, with each number occurring exactly once, and such that the sum of the entries of any row, any column, or any main diagonal is the same.

Program/Source Code

Here is the source code of the C program to display a linked list in reverse. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

```/*
* C Program to Solve the Magic Squares Puzzle without using
* Recursion
*/
#include <stdio.h>

void magicsq(int, int [][10]);

int main( )
{
int size;
int a[10][10];

printf("Enter the size: ");
scanf("%d", &size);
if (size % 2 == 0)
{
printf("Magic square works for an odd numbered size\n");
}
else
{
magicsq(size, a);
}
return 0;
}

void magicsq(int size, int a[][10])
{
int sqr = size * size;
int i = 0, j = size / 2, k;

for (k = 1; k <= sqr; ++k)
{
a[i][j] = k;
i--;
j++;

if (k % size == 0)
{
i += 2;
--j;
}
else
{
if (j == size)
{
j -= size;
}
else if (i < 0)
{
i += size;
}
}
}
for (i = 0; i < size; i++)
{
for (j = 0; j < size; j++)
{
printf("%d  ", a[i][j]);
}
printf("\n");
}
printf("\n");
}```
Program Explanation

In this C Program, we are reading the size of an array using ‘size’ variable. If condition statement is used to check whether the size is odd numbered size or even numbered size. If the size is even numbered then magic square will not work for an even numbered and exit the program.

Otherwise, if the condition is false, then enter the size is odd numbered size, hence magic square works for an odd numbered size. Execute the else statement. The magicsq() function is used to find the magic square for a given odd sized number.

Using for loop arrange the numbers from 1 to n^2 in an [n x n] matrix. If else condition statement is used to check that each number is occurring exactly once. Hence the sum of the entries of any row, any column, or any main diagonal is the same. Using for loop print the magic squares puzzle.

Runtime Test Cases
```\$ cc pgm27.c
\$ a.out
Enter the size: 6
Magic square works for an odd numbered size

\$ a.out
Enter the size: 5
17  24  1  8  15
23  5  7  14  16
4  6  13  20  22
10  12  19  21  3
11  18  25  2  9```

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