NQueens Problem.c

#include<stdio.h>
#include<math.h>
#include<stdlib.h>
 
int board[20],count;
 
int main()
{
int n,i,j;
void queen(int row,int n);
 
printf(" - N Queens Problem Using Backtracking -");
printf("\n\nEnter the  Number of Queens : ");
scanf("%d",&n);
queen(1,n);
return 0;
}
 
//function for printing the solution
void print(int n)
{
int i,j;
printf("\n\nSolution %d : \n\n",++count);
 
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 nxn board
  {
   if(board[i]==j)
    printf("\tQ"); //queen at i,j position
   else
    printf("\t-"); //empty slot
  }
}
}
 
/*funtion to check conflicts
If no conflict for desired postion returns 1 otherwise returns 0*/
int place(int row,int column)
{
int i;
for(i=1;i<=row-1;++i)
{
  //checking column and digonal conflicts
  if(board[i]==column)
   return 0;
  else
   if(abs(board[i]-column)==abs(i-row))
    return 0;
}
 
return 1; //no conflicts
}
 
//function to check for proper positioning of 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(n); //printing the board configuration
   else //try queen with next position
    queen(row+1,n);
  }
}
}