Programming Contest Question: Counting Polyominos

Question

Please see my own answer, I think I did it!

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Hi,

An example question for a programming contest was to write a program that finds out ho

Answer 1

Here's some python that computes the answer. Seems to agree with Wikipedia. It isn't terribly fast because it uses lots of array searches instead of hash tables, but it still takes only a minute or so to complete.

#!/usr/bin/python                                                                                                                                                 

# compute the canonical representation of polyomino p.                                                                                                            
# (minimum x and y coordinate is zero, sorted)                                                                                                                    
def canonical(p):
  mx = min(map(lambda v: v[0], p))
  my = min(map(lambda v: v[1], p))
  return sorted(map(lambda v: (v[0]-mx, v[1]-my), p))

# rotate p 90 degrees                                                                                                                                               
def rotate(p):
  return canonical(map(lambda v: (v[1], -v[0]), p))

# add one tile to p                                                                                                                                               
def expand(p):
  result = []
  for (x,y) in p:
    for (dx,dy) in ((-1,0),(1,0),(0,-1),(0,1)):
      if p.count((x+dx,y+dy)) == 0:
        result.append(canonical(p + [(x+dx,y+dy)]))
  return result

polyominos = [[(0,0)]]

for i in xrange(1,10):
  new_polyominos = []
  for p in polyominos:
    for q in expand(p):
      dup = 0
      for r in xrange(4):
        if new_polyominos.count(q) != 0:
          dup = 1
          break
        q = rotate(q)
      if not dup: new_polyominos.append(q)
  polyominos = new_polyominos
  print i+1, len(polyominos)