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hidato_reg_csp.py
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hidato_reg_csp.py
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from cspbase import *
import itertools
def get_satisfying_tuples(vars, reduced_domain, max):
var_doms = []
new_tuples = []
for var in vars:
if type(var) is int:
continue
if len(var.cur_domain()) == 1:
var_doms.append(var.cur_domain())
else:
var_doms.append(reduced_domain)
sat_tuples = [tup for tup in itertools.product(*var_doms) if len(set(tup)) == len(tup) and (tup[0]+1 in tup and tup[0] -1 in tup)]
if 1 in reduced_domain or max in reduced_domain:
if 1 in reduced_domain and max in reduced_domain:
new_tuples = [tup for tup in itertools.product(*var_doms) if len(set(tup)) == len(tup) and ((tup[0] ==1 and 2 in tup) or tup[0] == max and max-1 in tup)]
elif 1 in reduced_domain:
new_tuples = [tup for tup in itertools.product(*var_doms) if len(set(tup)) == len(tup) and tup[0] ==1 and 2 in tup]
elif max in reduced_domain:
new_tuples = [tup for tup in itertools.product(*var_doms) if len(set(tup)) == len(tup) and tup[0] == max and max-1 in tup]
return list(set(sat_tuples + new_tuples))
def make_var_doms(vars):
var_doms = []
for var in vars:
if type(var) is int:
continue
if len(var.cur_domain()) == 1:
var_doms.append(var.cur_domain())
else:
var_doms.append(reduced_domain)
return var_doms
def first_last_sat_tuples(vars, reduced_domain):
var_doms = []
for var in vars:
if type(var) is int:
continue
if len(var.cur_domain()) == 1:
var_doms.append(var.cur_domain())
else:
var_doms.append(reduced_domain)
sat_tuples = [tup for tup in itertools.product(*var_doms) if len(set(tup)) == len(tup) and (tup[0]+1 in tup or tup[0] -1 in tup)]
return sat_tuples
def single_row(initial_grid):
max_num = 0
initial_nums = []
for i in range(len(initial_grid)):
if initial_grid[i] != -2:
max_num += 1
if initial_grid[i] != -1:
initial_nums.append(initial_grid[i])
initial_nums.sort()
whole_dom = [k for k in range(1, max_num+1)]
reduced_domain = list(set(whole_dom) - set(initial_nums))
reduced_domain.sort()
# Assign domain to each variable
variable_array = []
for i in range(len(initial_grid)):
if initial_grid[i] == -1:
variable_array.append(Variable('{}'.format(i), whole_dom))
elif initial_grid[i] == -2:
variable_array.append(0)
else:
variable_array.append(Variable('{}'.format(i),[initial_grid[i]]))
# Constraints
cons = []
if len(variable_array) == 1:
numbrix_csp = CSP('Numbrix', variable_array)
return numbrix_csp, variable_array
for i in range (len(variable_array)):
vars = []
if variable_array[i] == 0:
continue
# if left edge
if i == 0:
vars.append(variable_array[i])
if variable_array[i+1] != 0:
vars.append(variable_array[i+1])
# if right edge
elif i == len(variable_array) - 1:
vars.append(variable_array[i])
if variable_array[i-1] != 0:
vars.append(variable_array[i-1])
# anywhere else
else:
vars.append(variable_array[i])
if variable_array[i-1] != 0:
vars.append(variable_array[i-1])
if variable_array[i+1] != 0:
vars.append(variable_array[i+1])
con = Constraint('R{}'.format(i), vars)
sat_tuples = get_satisfying_tuples(vars, reduced_domain, max_num)
if len(sat_tuples) == 0:
if (vars[0].cur_domain()[0] == 1 and len(vars[0].cur_domain()) == 1) or (vars[0].cur_domain()[0] == max_num and len(vars[0].cur_domain()) == 1):
sat_tuples = first_last_sat_tuples(vars, reduced_domain)
if len(sat_tuples) == 0:
sat_tuples.append([1])
con.add_satisfying_tuples(sat_tuples)
cons.append(con)
flattened_var = [val for val in variable_array if val != 0]
# binary not equal constraints for all pairs
for i in range(len(flattened_var)):
for j in range(i+1, len(flattened_var)):
vars = []
var_doms = []
flag = False
vars.append(flattened_var[i])
vars.append(flattened_var[j])
con = Constraint('R{}'.format(i), vars)
for var in vars:
if type(var) is int:
flag = True
continue
if len(var.cur_domain()) == 1:
var_doms.append(var.cur_domain())
else:
var_doms.append(reduced_domain)
if not flag:
sat_tuples = [tup for tup in itertools.product(*var_doms) if tup[0] != tup[1]]
con.add_satisfying_tuples(sat_tuples)
cons.append(con)
numbrix_csp = CSP('Numbrix', flattened_var)
for c in cons:
numbrix_csp.add_constraint(c)
return numbrix_csp, variable_array
def single_column(initial_grid):
max_num = 0
initial_nums = []
for i in range(len(initial_grid)):
if initial_grid[i][0] != -2:
max_num += 1
if initial_grid[i][0] != -1:
initial_nums.append(initial_grid[i][0])
initial_nums.sort()
whole_dom = [k for k in range(1, max_num+1)]
reduced_domain = list(set(whole_dom) - set(initial_nums))
reduced_domain.sort()
# Assign domain to each variable
variable_array = []
for i in range(len(initial_grid)):
if initial_grid[i][0] == -1:
variable_array.append(Variable('{}'.format(i), whole_dom))
elif initial_grid[i][0] == -2:
variable_array.append(0)
else:
variable_array.append(Variable('{}'.format(i),[initial_grid[i][0]]))
# Constraints
cons = []
if len(variable_array) == 1:
numbrix_csp = CSP('Numbrix', variable_array)
return numbrix_csp, variable_array
for i in range (len(variable_array)):
vars = []
if variable_array[i] == 0:
continue
# if left edge
if i == 0:
vars.append(variable_array[i])
if variable_array[i+1] != 0:
vars.append(variable_array[i+1])
# if right edge
elif i == len(variable_array) - 1:
vars.append(variable_array[i])
if variable_array[i-1] != 0:
vars.append(variable_array[i-1])
# anywhere else
else:
vars.append(variable_array[i])
if variable_array[i-1] != 0:
vars.append(variable_array[i-1])
if variable_array[i+1] != 0:
vars.append(variable_array[i+1])
con = Constraint('R{}'.format(i), vars)
sat_tuples = get_satisfying_tuples(vars, reduced_domain, max_num)
if len(sat_tuples) == 0:
if (vars[0].cur_domain()[0] == 1 and len(vars[0].cur_domain()) == 1) or (vars[0].cur_domain()[0] == max_num and len(vars[0].cur_domain()) == 1):
sat_tuples = first_last_sat_tuples(vars, reduced_domain)
if len(sat_tuples) == 0:
sat_tuples.append([1])
con.add_satisfying_tuples(sat_tuples)
cons.append(con)
flattened_var = [val for val in variable_array if val != 0]
# binary not equal constraints for all pairs
for i in range(len(flattened_var)):
for j in range(i+1, len(flattened_var)):
vars = []
var_doms = []
flag = False
vars.append(flattened_var[i])
vars.append(flattened_var[j])
con = Constraint('R{}'.format(i), vars)
for var in vars:
if type(var) is int:
flag = True
continue
if len(var.cur_domain()) == 1:
var_doms.append(var.cur_domain())
else:
var_doms.append(reduced_domain)
if not flag:
sat_tuples = [tup for tup in itertools.product(*var_doms) if tup[0] != tup[1]]
con.add_satisfying_tuples(sat_tuples)
cons.append(con)
numbrix_csp = CSP('Numbrix', flattened_var)
for c in cons:
numbrix_csp.add_constraint(c)
return numbrix_csp, variable_array
def numbrix_model_1(initial_grid):
# single row case
if type(initial_grid[0]) is int:
numbrix_csp, variable_array = single_row(initial_grid)
return numbrix_csp, variable_array
if len(initial_grid[0]) == 1:
numbrix_csp, variable_array = single_column(initial_grid)
return numbrix_csp, variable_array
max_num = 0
# store initially given numbers from grid in this array
initial_numbers = []
# Calculate the maximum number that that will be on the grid
for i in range(len(initial_grid)):
for j in range(len(initial_grid[i])):
if initial_grid[i][j] != -2:
max_num += 1
if initial_grid[i][j] != -1:
initial_numbers.append(initial_grid[i][j])
initial_numbers.sort()
whole_domain = [k for k in range (1, max_num+1)]
reduced_domain = list(set(whole_domain) - set(initial_numbers))
reduced_domain.sort()
# Assign a domain to each variable
variable_array = []
for i in range(len(initial_grid)):
vars = []
for j in range (len(initial_grid[i])):
if initial_grid[i][j] == -1:
vars.append(Variable('{}, {}'.format(i, j), [k for k in range(1, max_num + 1)]))
elif initial_grid[i][j] == -2:
vars.append(0)
else:
vars.append(Variable('{}, {}'.format(i, j), [initial_grid[i][j]]))
variable_array.append(vars)
# Adjacent constraints
cons = []
for i in range(len(initial_grid)):
for j in range(len(initial_grid[0])):
vars = []
if variable_array[i][j] == 0:
continue
# if number on top edge
if i == 0:
# if number in top left corner
if j == 0:
if variable_array[i][j] !=0:
vars.append(variable_array[i][j])
if variable_array[i+1][j] !=0:
vars.append(variable_array[i+1][j])
if variable_array[i][j+1] !=0:
vars.append(variable_array[i][j+1])
if variable_array[i+1][j+1] !=0:
vars.append(variable_array[i+1][j+1])
con = Constraint('R{}'.format(i), vars)
# if number in top right corner
elif j == len(initial_grid[i]) - 1:
if variable_array[i][j] !=0:
vars.append(variable_array[i][j])
if variable_array[i+1][j] !=0:
vars.append(variable_array[i+1][j])
if variable_array[i][j-1] !=0:
vars.append(variable_array[i][j-1])
if variable_array[i+1][j-1] !=0:
vars.append(variable_array[i+1][j-1])
con = Constraint('R{}'.format(i), vars)
# otherwise just on top edge
else:
if variable_array[i][j] !=0:
vars.append(variable_array[i][j])
if variable_array[i+1][j] !=0:
vars.append(variable_array[i+1][j])
if variable_array[i][j-1] !=0:
vars.append(variable_array[i][j-1])
if variable_array[i][j+1] !=0:
vars.append(variable_array[i][j+1])
if variable_array[i+1][j+1] !=0:
vars.append(variable_array[i+1][j+1])
if variable_array[i+1][j-1] !=0:
vars.append(variable_array[i+1][j-1])
con = Constraint('R{}'.format(i), vars)
# # # if number on bottom edge of grid
elif i == len(initial_grid) - 1:
# if number in bottom left corner
if j == 0:
if variable_array[i][j] !=0:
vars.append(variable_array[i][j])
if variable_array[i-1][j] !=0:
vars.append(variable_array[i-1][j])
if variable_array[i][j+1] !=0:
vars.append(variable_array[i][j+1])
if variable_array[i-1][j+1] !=0:
vars.append(variable_array[i-1][j+1])
con = Constraint('R{}'.format(i), vars)
# if number in bottom right corner
elif j == len(initial_grid[i]) -1:
if variable_array[i][j] !=0:
vars.append(variable_array[i][j])
if variable_array[i-1][j] !=0:
vars.append(variable_array[i-1][j])
if variable_array[i][j-1] !=0:
vars.append(variable_array[i][j-1])
if variable_array[i-1][j-1] !=0:
vars.append(variable_array[i-1][j-1])
con = Constraint('R{}'.format(i), vars)
# otherwise just on bottom edge
else:
if variable_array[i][j] !=0:
vars.append(variable_array[i][j])
if variable_array[i-1][j] !=0:
vars.append(variable_array[i-1][j])
if variable_array[i][j-1] !=0:
vars.append(variable_array[i][j-1])
if variable_array[i][j+1] !=0:
vars.append(variable_array[i][j+1])
if variable_array[i-1][j+1] !=0:
vars.append(variable_array[i-1][j+1])
if variable_array[i-1][j-1] !=0:
vars.append(variable_array[i-1][j-1])
con = Constraint('R{}'.format(i), vars)
# if the number is on the left or right edge (corners already taken care of)
elif j == 0 or j == len(initial_grid[i]) - 1:
# number is on left edge
if j == 0:
if variable_array[i][j] !=0:
vars.append(variable_array[i][j])
if variable_array[i-1][j] !=0:
vars.append(variable_array[i-1][j])
if variable_array[i+1][j] !=0:
vars.append(variable_array[i+1][j])
if variable_array[i][j+1] !=0:
vars.append(variable_array[i][j+1])
if variable_array[i-1][j+1] !=0:
vars.append(variable_array[i-1][j+1])
if variable_array[i+1][j+1] !=0:
vars.append(variable_array[i+1][j+1])
con = Constraint('R{}'.format(i), vars)
# number is on right edge
elif j == len(initial_grid[i]) - 1:
if variable_array[i][j] !=0:
vars.append(variable_array[i][j])
if variable_array[i-1][j] !=0:
vars.append(variable_array[i-1][j])
if variable_array[i+1][j] !=0:
vars.append(variable_array[i+1][j])
if variable_array[i][j-1] !=0:
vars.append(variable_array[i][j-1])
if variable_array[i-1][j-1] !=0:
vars.append(variable_array[i-1][j-1])
if variable_array[i+1][j-1] !=0:
vars.append(variable_array[i+1][j-1])
con = Constraint('R{}'.format(i), vars)
# anywhere else on the grid (won't be on an edge)
else:
if variable_array[i][j] !=0:
vars.append(variable_array[i][j])
if variable_array[i-1][j] !=0:
vars.append(variable_array[i-1][j])
if variable_array[i+1][j] !=0:
vars.append(variable_array[i+1][j])
if variable_array[i][j-1] !=0:
vars.append(variable_array[i][j-1])
if variable_array[i][j+1] !=0:
vars.append(variable_array[i][j+1])
if variable_array[i-1][j-1] !=0:
vars.append(variable_array[i-1][j-1])
if variable_array[i-1][j+1] !=0:
vars.append(variable_array[i-1][j+1])
if variable_array[i+1][j-1] !=0:
vars.append(variable_array[i+1][j-1])
if variable_array[i+1][j+1] !=0:
vars.append(variable_array[i+1][j+1])
con = Constraint('R{}'.format(i), vars)
sat_tuples = get_satisfying_tuples(vars, reduced_domain, max_num)
if len(sat_tuples) == 0:
if (vars[0].cur_domain()[0] == 1 and len(vars[0].cur_domain()) == 1) or (vars[0].cur_domain()[0] == max_num and len(vars[0].cur_domain()) == 1):
sat_tuples = first_last_sat_tuples(vars, reduced_domain)
if len(sat_tuples) == 0:
sat_tuples.append([1])
con.add_satisfying_tuples(sat_tuples)
cons.append(con)
# ******All diff constraints take too long******
# var = []
# var_doms = []
# for i in range(len(variable_array)):
# for j in range(len(variable_array[i])):
# vars.append(variable_array[i][j])
#
# con = Constraint('R{}'.format(i), vars)
#
# for var in vars:
# if len(var.cur_domain()) == 1:
# var_doms.append(var.cur_domain())
# else:
# var_doms.append(reduced_domain)
#
# sat_tuples = [tup for tup in itertools.product(*var_doms) if len(set(tup)) == len(tup)]
# con.add_satisfying_tuples(sat_tuples)
# cons.append(con)
flattened_var = [val for sublist in variable_array for val in sublist if val != 0]
# binary not equal constraints for all pairs
for i in range(len(flattened_var)):
for j in range(i+1, len(flattened_var)):
vars = []
var_doms = []
flag = False
vars.append(flattened_var[i])
vars.append(flattened_var[j])
con = Constraint('R{}'.format(i), vars)
for var in vars:
if type(var) is int:
flag = True
continue
if len(var.cur_domain()) == 1:
var_doms.append(var.cur_domain())
else:
var_doms.append(reduced_domain)
if not flag:
sat_tuples = [tup for tup in itertools.product(*var_doms) if tup[0] != tup[1]]
con.add_satisfying_tuples(sat_tuples)
cons.append(con)
numbrix_csp = CSP('Numbrix', flattened_var)
for c in cons:
numbrix_csp.add_constraint(c)
return numbrix_csp, variable_array