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puzzle_1904_Jan_26_19.py
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puzzle_1904_Jan_26_19.py
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'''Solving a 1 to 9 puzzle
https://twitter.com/1to9puzzle
January 26, 2019'''
import random
from itertools import permutations, product
class Square(object):
def __init__(self,numList):
self.numList = numList
def add(self, B):
'''adds matrices A and B and returns a list
of all possible differences between given numbers'''
nums = list(range(1, 10))
# list for choices of numbers
terms = []
# add and subtract all pairs
for i in range(9):
this_term = []
term = self.numList[i] + B[i]
if term in nums:
this_term.append(term)
term = self.numList[i] - B[i]
if term in nums:
this_term.append(term)
# put all choices in terms list
terms.append(this_term)
final_output = []
output = []
choices = []
for i, t in enumerate(terms):
if len(t) == 0:
pass # same number in s1 and diff
if len(t) == 1:
output.append(t[0])
else:
# record which terms have choices
choices.append(i)
output.append(t)
data = product([0, 1], repeat=len(choices))
'''This produces (0,0,0),(0,0,1) and so on'''
while True:
try:
p = next(data)
output_list = [] # one list
j = 0
for i, t in enumerate(output):
if i in choices:
# insert the choices
output_list.append(t[p[j]])
j += 1
else:
output_list.append(t)
if len(output_list) != 9:
continue
wrong = False
for n in output_list:
if output_list.count(n) > 1:
wrong = True
break
if wrong:
continue
final_output.append(output_list)
except:
break
# print(final_output)
return final_output
class Puzzle(object):
def __init__(self,dark_squares,given):
self.dark = dark_squares
self.given = given
#squares
self.s1 = Square([0 for i in range(9)])
self.s1.numList[4] = self.given[0]
self.s2 = Square([0 for i in range(9)])
self.s2.numList[4] = self.given[1]
self.s3 = Square([0 for i in range(9)])
self.s3.numList[4] = self.given[2]
self.s4 = Square([0 for i in range(9)])
self.s4.numList[4] = self.given[3]
self.board = []
self.solutions = []
self.s2_list = []
self.s3_list = []
self.s4_list = []
def printBoard(self):
'''Prints out board for inspection'''
# put together in a board
self.board = [self.s1.numList[:3] + self.s2.numList[:3],
self.s1.numList[3:6] + self.s2.numList[3:6],
self.s1.numList[6:] + self.s2.numList[6:],
self.s4.numList[:3] + self.s3.numList[:3],
self.s4.numList[3:6] + self.s3.numList[3:6],
self.s4.numList[6:] + self.s3.numList[6:]]
for row in self.board:
for c in row:
print(c,end = ',')
print()
print()
def solve(self):
wrong = False #we're not wrong yet!
# Generate a starting square
g = permutations([1, 2, 4, 5, 6, 7, 8, 9])
count_right = 0
while True:
# for i in range(10):
try:
# generate list of numbers
self.s1 = Square(list(next(g)))
# insert 3 in middle square
self.s1.numList = self.s1.numList[:4] + [self.given[0]] + self.s1.numList[4:]
# add s1 and the first difference list
# print("s1:", self.s1)
# print("d0:", self.dark[0])
s2_list = self.s1.add(self.dark[0])
for s2 in s2_list:
# print("s2:",s2)
if not s2:
continue
if check_rows(self.s1.numList, s2):
self.solutions.append([Square(self.s1.numList), Square(s2)])
except StopIteration:
break
#solution pairs for s1 and s2 are in the self.solutions list. There were 64 solutions so far
print("solutions:", len(self.solutions))
for solution in self.solutions:
s2 = solution[1]
s3_list = s2.add(dark[1])
#s3 = Square(s3_list)
# print(s3_list)
for s3 in s3_list:
if not s3:
continue
if s3[4] != 9:
continue
# print("s3:", s3)
# for n in s3:
# if s3.count(n) > 1:
# wrong = True
# break
if wrong:
continue
s3_square = Square(s3)
solution.append(s3_square)
#There's only 1 solution left
for solution in self.solutions:
if len(solution) == 3:
self.s1 = solution[0]
self.s2 = solution[1]
self.s3 = solution[2]
#self.printBoard()
s4_list = self.s3.add(dark[2])
for s4 in s4_list:
if not s4:
continue
if s4[4] != 4:
continue
#print(s4)
self.s4 = Square(s4)
solution.append(self.s4)
self.printBoard()
# dark squares
dark = [[3, 3, 2,
3, 4, 4,
3, 2, 6],
[5, 2, 5, 2, 2, 5, 7, 3, 1],
[6, 4, 1, 4, 5, 7, 5, 4, 4],
[4, 1, 2, 1, 1, 6, 1, 1, 3]]
given = [3, 7, 9, 4]
def check_rows(A,B):
'''Checks two flat lists for repeats in rows
Returns False if there's a repeat'''
stacked_list = []
for i in range(3):
#stacked_list.append([])
stacked_list.append(A[3*i:3*(i+1)]+B[3*i:3*(i+1)])
for row in stacked_list:
for num in row:
if row.count(num) > 1:
return False
return True
### Program starts here ###
p = Puzzle(dark,given)
p.solve()
p.printBoard()