Implement N-Queens Problem Using Backtracking.

 #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 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);

  }

 }

}

Output: