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The n-queens problem Description The n queens: place n queens on an nxn chessboard so that none of them can be eaten in one move. Further explanation of this example:
'Xpress Python Reference Manual'
Source Files n_queens.py # # 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) # What's the largest number of queens we can place on the chessboard? p.setObjective(xp.Sum(x), sense=xp.maximize) 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('') | |||||||||

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