Skip to content

Instantly share code, notes, and snippets.

Embed
What would you like to do?
# -*- coding: utf-8 -*-
#!/usr/bin/env python
import sys
class Polyomino(object):
def __init__(self, iterable):
self.squares = tuple(sorted(iterable))
def __repr__(self):
return "%s(%s)" % (self.__class__.__name__, repr(self.squares))
def __iter__(self):
return iter(self.squares)
def __len__(self):
return len(self.squares)
def __eq__(self, other):
return hash(self) == hash(other)
def __hash__(self):
"""Determine the one-sided key for this Poylomino"""
p = self.translate()
k = p.key()
for _ in range(3):
p = p.rotate().translate()
k = min(k, p.key())
return k
def key(self):
return hash(self.squares)
def rotate(self):
"""Return a Polyomino rotated clockwise"""
return Polyomino((-y, x) for x, y in self)
def translate(self):
"""Return a Polyomino Translated to 0,0"""
minX = min(s[0] for s in self)
minY = min(s[1] for s in self)
return Polyomino((x-minX, y-minY) for x, y in self)
def raise_order(self):
"""Return a list of higher order Polyonominos evolved from self"""
polyominoes = []
for square in self:
adjacents = (adjacent for adjacent in (
(square[0] + 1, square[1]),
(square[0] - 1, square[1]),
(square[0], square[1] + 1),
(square[0], square[1] - 1),
) if adjacent not in self)
for adjacent in adjacents:
polyominoes.append(
Polyomino(list(self) + [adjacent])
)
return polyominoes
def render(self):
"""
Returns a string map representation of the Polyomino
"""
p = self.translate()
order = len(p)
return ''.join(
["\n %s" % (''.join(
["X" if (x, y) in p.squares else "-" for x in range(order)]
)) for y in range(order)]
)
def count_polys(target):
order = 1
polyominoes = set([Polyomino(((0,0),))])
while order < target:
order += 1
next_order_polyominoes = set()
for polyomino in polyominoes:
next_order_polyominoes.update(polyomino.raise_order())
polyominoes = next_order_polyominoes
return len(polyominoes)
if __name__ == "__main__":
print count_polys(int(sys.argv[1]))
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment