ernie.WPI.EDU> cat queens.C

// file queens.C, cs2223, D97/98 //
// class 26 - N-queens problem

// 24Apr98 NW, First version

// include
#include "headers.h"

// global value
unsigned long int counter; // count iterations
vector <int> column; // the column vector

// prototype
int queens(int, int); // check partial solution of N-queens problem

// main
int main ()
   {
   
   while (1)
      {
      int n;
      cout << endl << "enter a value of n: ";
      cin >> n;
      if (n <= 0) return 0; // exit criterion
      
      column.resize(n); // resize the column vector
      for (int i = 0; i < n; i++) column[i] = i; // fill the vector
      counter = 0;
      if (queens(0, n)) // found a solution
         {
         cout << "this solution was found in " << counter << " tests" << endl;
         for (int i = 0; i < n; i++) cout << setw(3) << column[i];
         cout << endl;
         }
      else 
         {
         cout << "no solution could be found in " << counter << " tests" << endl;
         }
      }
   } // end main()

int queens(int k, int n) // N-queens test
   { // n is the length of the vector, k is the position to begin testing
   if (k == n) return 1; // checking is complete - the solution has been found 
   for (int j = k; j < n; j++) // otherwise, permute and check the following queens
      {
      int temp = column[k]; column[k] = column[j]; column[j] = temp; // swap
      int conflicts = 0; // flag to keep track of conflicts
       if (k != 0) for (int i = k-1; i >= 0; i--) // don't need to check when k == 0
         {
         counter++; // keep track of diagonal tests
         if ((column[i] == column[k] - (k - i)) || (column[i] == column[k] + (k - i))) // conflict
            {
            conflicts = 1;
            break; // no need to look further
            }
         }
         if (!conflicts && queens(k+1, n)) return 1; // solution found
      temp = column[k]; column[k] = column[j]; column[j] = temp; // not found, swap back
      }
   return 0; // no solution found
   } // end queens()


// Copyright 1998 Norman Wittels

ernie.WPI.EDU> g++ queens.C

ernie.WPI.EDU> a.out

enter a value of n: 1
this solution was found in 0 tests
  0

enter a value of n: 2
no solution could be found in 2 tests

enter a value of n: 3
no solution could be found in 8 tests

enter a value of n: 4
this solution was found in 18 tests
  1  3  0  2

enter a value of n: 5
this solution was found in 14 tests
  0  2  4  1  3

enter a value of n: 6
this solution was found in 165 tests
  1  3  5  0  2  4

enter a value of n: 7
this solution was found in 52 tests
  0  2  4  6  1  3  5

enter a value of n: 8
this solution was found in 1032 tests
  0  4  7  5  2  6  1  3

enter a value of n: 9
this solution was found in 494 tests
  0  2  5  7  1  3  8  6  4

enter a value of n: 10
this solution was found in 1391 tests
  0  2  5  7  9  4  8  1  3  6

enter a value of n: 15
this solution was found in 37279 tests
  0  2  4  1  9 11 13  3 12  8  5 14  6 10  7

enter a value of n: 20
this solution was found in 8519585 tests
  0  2  4  1  3 12 14 11 17 19 16  8 15 18  7  9  6 13  5 10

enter a value of n: -3
ernie.WPI.EDU>