n-queens in Fusion

In a nice post on LinkedIn by Alireza Soroudi the author presents a short GAMS integer model for the classical n-queens puzzle: place the maximal number of non-attacking queens on an $n\times n$ chessboard.

We couldn't resist writing it up in Python Fusion as well.

	from mosek.fusion import *
	import numpy as np
	import sys
	n = int(sys.argv[1])
	M = Model()
	x = M.variable("x", [n,n], Domain.binary())
	M.objective(ObjectiveSense.Maximize, Expr.sum(x))
	M.constraint(Expr.sum(x, 0), Domain.lessThan(1))
	M.constraint(Expr.sum(x, 1), Domain.lessThan(1))
	for k in range(-n+1,n):
	M.constraint(Expr.dot(x, np.diag([1]*(n-abs(k)), k)), Domain.lessThan(1))
	M.constraint(Expr.dot(x, np.fliplr(np.diag([1]*(n-abs(k)), k))), Domain.lessThan(1))
	M.solve()
	print(np.array2string(np.fromiter(
	map(lambda u: '\u2655' if u>0.5 else '_', x.level()), dtype='<U1').reshape((n,n)),
	formatter={'str_kind': lambda u: u}))

view raw nqueens.py hosted with ❤ by GitHub

And here is the solution we get for $n=8$:

[[_ ♕ _ _ _ _ _ _]

 [_ _ _ _ _ ♕ _ _]

 [♕ _ _ _ _ _ _ _]

 [_ _ _ _ _ _ ♕ _]

 [_ _ _ ♕ _ _ _ _]

 [_ _ _ _ _ _ _ ♕]

 [_ _ ♕ _ _ _ _ _]

  [_ _ _ _ ♕ _ _ _]]