from Numberjack import *

# N-Queens

# The N-Queens problem is the probelm of placing N queens on an N x N chess
# board such that no two queens are attacking each other. A queen is attacking
# another if it they are on the same row, same column, or same diagonal.

def get_model(N):
queens = VarArray(N, N)
model = Model(
AllDiff(queens),
AllDiff([queens[i] + i for i in range(N)]),
AllDiff([queens[i] - i for i in range(N)])
)
return queens, model

def solve(param):
queens, model = get_model(param['N'])
solver.setHeuristic(param['heuristic'], param['value'])
solver.setVerbosity(param['verbose'])
solver.setTimeLimit(param['tcutoff'])
solver.solve()

out = ''
if solver.is_sat() and param['print'] == 'yes':
out += print_chessboard(queens)
out += ('\nNodes: ' + str(solver.getNodes()))
return out

def print_chessboard(queens):
out = '+---' * len(queens) + '+\n'
for queen in queens:
out += ('|   '*queen.get_value()+'| Q |'+'   |'*(len(queens)-1-queen.get_value())+'\n'+'+---'*len(queens)+'+\n')
return out

default = {'solver': 'Mistral', 'N': 6, 'heuristic': 'MinDomainMinVal',
'print': 'yes', 'value': 'Lex', 'verbose': 0, 'tcutoff': 30}

if __name__ == '__main__':
param = input(default)
print solve(param)