The n-queens problem

#
# Example using the Xpress Python interface
#
# The n queens: place n queens on an nxn chessboard so that none of
# them can be eaten in one move.
#

from __future__ import print_function

import xpress as xp

n = 8 # the size of the chessboard
N = range (n)

# create a "dictionary" of variables, i.e. a mapping from all tuples
# (i,j) to a variable.

x = {(i,j): xp.var (vartype = xp.binary, name='q{0}_{1}'.format (i,j)) for i in N for j in N}

vertical   = [xp.Sum (x[i,j] for i in N) <= 1 for j in N]
horizontal = [xp.Sum (x[i,j] for j in N) <= 1 for i in N]

diagonal1  = [xp.Sum (x[k-j,j] for j in range (max(0,k-n+1), min(k+1,n))) <= 1 for k in range (1,2*n-2)]
diagonal2  = [xp.Sum (x[k+j,j] for j in range (max(0,-k),    min(n-k,n))) <= 1 for k in range (2-n,n-1)]

p = xp.problem()

p.addVariable   (x)
p.addConstraint (vertical, horizontal, diagonal1, diagonal2)
p.setObjective  (xp.Sum (x), sense = xp.maximize) # What's the largest number of queens we can place on the chessboard?

p.solve ()

for i in N:
    for j in N:
        if p.getSolution (x[i,j]) == 1:
            print ('@', sep='', end='')
        else:
            print ('.', sep='', end='')
    print ('')