Source code: N-Queen Problem in Backtracking using C [user friendly, visual friendly, OO]

#include < stdio.h >
#include < math.h >
#include < process.h >

int board[20];
int count;

void main()
{
int n, i, j;
// n= number of queens

void queen(int row, int n);

printf("N-Queen's using Backtracking\n");
printf("Pick a number for Queen [preferably no less than 4]: ");
scanf("%d", &n);
queen(1, n);
//trace using backtrack
printf("\n\n\n\n\n");

}


/*Function to print solution of n-queen's problem*/
void print_board(int n)
{
int i, j;
printf("\n\n solution %d:\n\n", ++count);
//number of solution

for (i= 1; i<= n; i++)
{
printf("\t%d", i);
}
for (i= 1; i<= n; i++)
{
printf("\n\n%d", i);
for (j= 1; j<= n; j++)
//for n*n board
{
if (board[i] == j)
printf("\tQ");
//Queen at i,j position
else
printf("\t-");
//empty slot
}
}
}
/*Function to check for the conflicts for approaching location. returns 1 for no no conflict, 0 otherwise*/
int place(int row, int column)
{
int i;
for (i= 1; i<= row -1; i++)
{
//checking for column and diagonal conflicts
if (board[i] == column)
return 0;
else
if (abs(board[i] -column) == abs(i -row))
return 0;
}
//no conflicts hence Queen can be placed
return 1;
}


/*Function to reach and check next free slot for next possible location for the Queen*/
void queen(int row, int n)
{
int column;
for (column= 1; column<= n; column++)
{
if (place(row, column))
{
board[row]= column;
//no conflicts so place queen

if (row == n)//dead end
print_board(n);  
//printing  board configuration
else //try with next position
queen(row +1, n);
}
}
}

special thanks to course mate: Sakib Shahid.

Concrete Mathematics Exercise Solution: Chapter 5 [Binomial Coefficients]

Derivation: