Lego buying

lego.py

import sys

try:
  N = int(sys.argv[1]) # number of characters, the only input!
  assert N >= 1
except:
  N = 16
  print "Defaulting to", N, "characters."
  print "You could also supply a different number as argument 1."

print "Let's see how many ways we can buy all", N, "characters, having bought B..."
print "bought (B): (ways to get all " + str(N) + ") / (ways to buy any B) = (% good)"

success_rate = 0.0
collex = [0] * (N+1)
collex[1] = 1
buy = 1
denom = 1

while success_rate < 50.0 or buy < 10:
  new = [0] * (N+1)
  new[1] = 1

  for k in range(2,N+1):
    new[k] += collex[k-1] * (N-k+1) # ways to get a new one
    new[k] += collex[k] * k         # ways to get a duplicate

  collex = new
  buy += 1
  denom *= N

  if buy >= N: # gotta have at least N
    success_rate = float(collex[N]) / float(denom) * 100.0
    print "bought", buy, ":", collex[N], "/", denom, "=", str(success_rate) + "%"