#!/etc/python3.5

class PoolRoll:		#roll[roll results], rolls[count of results], successes
   roll = []
   rolls = []  # I think I need to do this for the following functions
   def rollsum(self):
     sum = 0
     for i in range (2,13):
       sum += self.rolls[i] * i
     return sum

   def newlarge(self):
     x = 12
     while x > 0:
       if self.rolls[x]:
         return x
       else:
         x += -1
     return 0
   
   def newsmall(self):
     x=2        #[0] and [1] will always be 0
     while x < 13:
       if self.rolls[x]:
         return x
       else:
         x += 1
     return 0

   def __init__( self, oldpoolroll, newdieroll, TN ):
     self.roll = oldpoolroll.roll[:]
     self.roll.append(newdieroll)
     self.rolls = oldpoolroll.rolls[:]
     self.rolls[newdieroll] += 1
     self.successes = oldpoolroll.successes
    
     if self.rollsum() < TN:
       pass    #no new successes
     else:
       large = self.newlarge()
       if self.rolls[ TN - large ]:
         self.rolls[ TN - large ] += -1
         self.rolls[large] += -1
         self.successes += 1
       else:
         total = large
         self.rolls[large] += -1
         while total < TN:
           small = self.newsmall()
           total += small
           self.rolls[small] += -1
         self.successes +=1


class Pool:
  def __init__(self, oldpool, currentpool):
    dierolls = tuple( [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] )
    self.TN = oldpool.TN
    self.pool = currentpool[:]
    self.rolls = set()
    for oldpoolroll in oldpool.rolls:
      for dieroll in dierolls:
       if dieroll <= currentpool[-1]:
        newpoolroll = PoolRoll(oldpoolroll, dieroll, TN)
        self.rolls.add( newpoolroll )

  def successes(self):
    totals = [0, 0, 0, 0, 0, 0]
    for roll in self.rolls:
      totals[roll.successes] += 1
    return( totals )

class SeedRoll:
  def __init__( self, roll ):
    self.roll = [roll]
    self.rolls = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
    self.rolls[roll] += 1
    self.successes = 0

class SeedPool:
  def __init__(self, die, TN):
    self.TN = TN
    self.pool = [die]
    self.rolls = set()
    for i in (i for i in (0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) if i <= die):
      seed = SeedRoll( i )
      self.rolls.add(seed)
  def successes(self):
    return([0, 0, 0, 0, 0, 0])

def iterate( pools, oldpool, lastpool, MAX ):
   dice = (4, 6, 8, 10, 12)
   print lastpool
   pools[str(lastpool)] = oldpool
   if len(lastpool) == MAX:
     file = open("iterative additive", "a")
     keylist = [key for key in pools if pools[key].pool[-1] == lastpool[-1]]
     for key in keylist:
       file.write("%d %s %s\n" % ( pools[key].TN, key, pools[key].successes()))
       del pools[key]
     file.close()
     return()
   else:
    for newdie in dice:
     currentpool = lastpool[:]
     if newdie <= lastpool[-1]:
      currentpool.append(newdie)
      pool = Pool(oldpool, currentpool)
      iterate( pools, pool, currentpool, MAX )

#main
MAX = 11
for TN in xrange(5,9):
  limit = ((TN-1)/2)*2
  for die in (die for die in (4, 6, 8, 10, 12) if die <= limit):
    currentpool = [die]
    seed = SeedPool(die, TN)
    pools = {}
    iterate(pools, seed, currentpool, MAX)
    del pools, seed