Pyraminx short scrambles

import sys
import collections
import copy

from db import db

# Sides
F = 0
L = 1
R = 2
D = 3

# Moves
MOVES = {
  'U': [[[F, 0], [L, 0], [R, 0]],
        [[F, 1], [L, 1], [R, 1]],
        [[F, 2], [L, 2], [R, 2]],
        [[F, 3], [L, 3], [R, 3]]],
  'L': [[[F, 4], [D, 0], [L, 8]],
        [[F, 1], [D, 2], [L, 6]],
        [[F, 5], [D, 1], [L, 7]],
        [[F, 6], [D, 5], [L, 3]]],
  'R': [[[R, 4], [D, 4], [F, 8]],
        [[R, 1], [D, 7], [F, 6]],
        [[R, 5], [D, 3], [F, 7]],
        [[R, 6], [D, 2], [F, 3]]],
  'B': [[[L, 4], [D, 8], [R, 8]],
        [[L, 1], [D, 5], [R, 6]],
        [[L, 5], [D, 6], [R, 7]],
        [[L, 6], [D, 7], [R, 3]]],
}

SOLVED = [[F] * 9, [L] * 9, [R] * 9, [D] * 9]

ALL_MOVES = list(MOVES.keys()) + [x + '\'' for x in MOVES.keys()]

def applyMove(position, move):
  subMove = move[0]
  transformations = None
  if subMove in MOVES:
    transformations = MOVES[subMove]
  elif subMove.upper() in MOVES:
    return
    #transformations = MOVES[subMove.upper()][0]
  if not transformations:
    print('ERROR: Unknown move ' + move)
    return
  if '\'' in move:
    transformations = [list(reversed(x)) for x in transformations]

  for transformation in transformations:
    saved = position[transformation[-1][0]][transformation[-1][1]]
    for i in reversed(range(len(transformation) - 1)):
      from_ = transformation[i]
      to_ = transformation[i + 1]
      position[to_[0]][to_[1]] = position[from_[0]][from_[1]]
    position[transformation[0][0]][transformation[0][1]] = saved

def executeScramble(moves):
  position = copy.deepcopy(SOLVED)
  for move in moves:
    applyMove(position, move)
  return position

def toStr(position):
  return ''.join([''.join([str(y) for y in x]) for x in position])

def positionsWithMaxDepth(num):
  scrambles = [[]]
  for i in range(num):
    for scramble in scrambles:
      if len(scramble) != i:
        continue
      for move in ALL_MOVES:
        if scramble and scramble[-1][0] == move[0]:
          continue
        scrambles += [scramble + [move]]

  out = {}
  for scramble in scrambles:
    position = toStr(executeScramble(scramble))
    if position not in out:
      out[position] = len(scramble)
  return out


positions = positionsWithMaxDepth(6)

cursor = db.cursor()
cursor.execute("SELECT competitionId, roundTypeId, groupId, isExtra, scrambleNum, scramble FROM Scrambles WHERE eventId='pyram'")

tipCounts = collections.defaultdict(lambda: 0)

for row in cursor.fetchall():
  scr = row[5].split(' ')
  numTips = len([x for x in scr if x[0] in ('u', 'l', 'r', 'b')])
  pos = toStr(executeScramble(scr))
  if pos in positions:
    if positions[pos] + numTips == 6:
      tipCounts[numTips] += 1

    if positions[pos] < 3:
      print(row)

print(tipCounts)