Solvit Alphametic Puzzle Solver
#!/usr/bin/env python
from argparse import ArgumentParser
from sympy import Symbol
from sympy import solve_linear_system
from sympy import Matrix
# from pprint import pprint
from random import sample
def ps(s, n, ex=[]):
xs = list(range(1, 10))
[xs.remove(x) for x in ex]
a = sample(xs, n)
while sum(a) != s:
a = sample(xs, n)
return list(sorted(a)), sum(a)
def main():
"""Main Entrypoint."""
ps = ArgumentParser()
ps.add_argument(
"input_file",
action="store",
help="""Solvit Input File.
The file should have the following format:
A file of 8 equations as specified in the solvit puzzle separated by
commas and the last entry in the line the corresponding sum.
a,b,c,d,20
e,f,g,h,23
j,e,f,h,18,
b,a,d,e,20
a,e,c,d,21
e,f,g,j,23
a,e,f,j,18,
j,a,d,e,20
""",
)
args = ps.parse_args()
system = read_and_parse_input_file(args.input_file)
solution, (a, b, c, d, e, f, g, h, j) = solve_puzzle(system)
# print solution
print("\n\n")
print("Solution:")
for k in solution.keys():
print("{}: {}".format(k, solution[k]))
return solution, (a, b, c, d, e, f, g, h, j)
def solve_puzzle(M):
"""Solve the puzzle given the linear system described Matrix M."""
# create symbols
a, b, c, d, e, f, g, h, j = [Symbol(x, positive=True) for x in "abcdefghj"]
# solve the system
sol = solve_linear_system(M, a, b, c, d, e, f, g, h, j)
return sol, (a, b, c, d, e, f, g, h, j)
def read_and_parse_input_file(input_file):
"""Read and parse input file.
Return a 9x10 Matrix of the equations in the file together with an
additional equation including all letters summing to 45.
"""
rows = []
with open(input_file, "r") as rf:
for line in rf.readlines():
line = line.replace("\n", "")
rows.append(line.split(","))
# transform input rows to 1 or 0
mrows = []
dhs = []
for r in rows:
cols = []
dh = dict(zip("abcdefghj", [0 for _ in range(9)]))
for c in r:
if c.lower() in dh:
dh[c.lower()] += 1
dh["sum"] = int(r[-1])
cols = [dh[k] for k in sorted(dh.keys())]
mrows.append(cols)
dhs.append(dh)
mrows.append([1 for _ in range(9)] + [45])
# print puzzle as would appear in solvit
print("Puzzle:")
for d in dhs:
for k, v in d.items():
if k != "sum":
if v != 0:
for i in range(v):
print("{} +".format(k.upper()), end=" ")
else:
print("= {}".format(d[k]))
M = Matrix(mrows)
# pprint(M)
return M
if __name__ == "__main__":
solution, (a, b, c, d, e, f, g, h, j) = main()# In terminal do:
$ pip install solvit$ git clone https://github.com/TralahM/Solvit.git
$ cd Solvit
$ pip install -e .| x1 | x2 | x3 | x4 | sum |
|---|---|---|---|---|
| C | H | G | B | 25 |
| A | J | C | D | 23 |
| G | E | F | D | 18 |
| E | H | A | F | 10 |
| C | A | G | E | 19 |
| H | J | E | H | 13 |
| G | C | F | A | 18 |
| B | D | D | F | 26 |
