C Program for N Queens Problem Using Backtracking

N Queens Problem is a famous puzzle in which n-queens are to be placed on a nxn chess board such that no two queens are in the same row, column or diagonal. In this tutorial I am sharing the C program to find solution for N Queens problem using backtracking. Below animation shows the solution for 8 queens problem using backtracking.

Also Read: C Program for Tower of Hanoi Problem

8 Queens Problem Using Backtracking

C Program for N Queens Problem Using Backtracking

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