Separate a Tree Level by Level

car = lambda lst: lst[0]
cdr = lambda lst: lst[1:]

'''
depth: returns the maximum nesting level of a list

Given:
  ls, a list

Result:
  an integer
'''
def depth(ls):
  if not ls:
    return 0
  elif isinstance(car(ls),list):
    return max(depth(car(ls))+1,depth(cdr(ls)))
  else:
    return max(1,depth(cdr(ls)))

'''
strip: returns the list elements of a list

Given:
  ls, a list

Result:
  ls, the modified list
'''
def strip(ls, top):
  if top:
    for item in top:
      if item in ls:
        ls.remove(item)
  elif cdr(ls):
    ls = car(ls) + strip(cdr(ls), top) # case like [[1], ...]
  else:
    ls = car(ls) # case like [[1]]
  return ls

'''
level: returns the top level elements of a list

Given:
  ls, a list

Result:
  a new list
'''
def level(ls):
  if not ls:
    return []
  elif not isinstance(car(ls),list):
    return [car(ls)] + level(cdr(ls))
  else:
    return level(cdr(ls))

'''
levelize: returns a list of lists, each list is contains the items of a level

Given:
  ls, a list

Result:
  a new list
'''
def levelize(ls):
  result = []
  a = list(ls)
  for i in range(2*depth(ls)):
    if not i%2:
      result.append(level(a))
    a = strip(a, level(a))
  return result
    
'''
level: returns the top level elements of a list

Given:
  ls, a list

Result:
  a new list
'''
def level(ls):
  if not ls:
    return []
  elif not isinstance(car(ls),list):
    return [car(ls)] + level(cdr(ls))
  else:
    return level(cdr(ls))

'''
levelize: returns a list of lists, each list is contains the items of a level

Given:
  ls, a list

Result:
  a new list
'''
def levelize(ls):
  result = []
  a = list(ls)
  for i in range(2*depth(ls)):
    if not i%2:
      result.append(level(a))
    a = strip(a, level(a))
  return result

print levelize([1,[2,6,[3,5,[4,[]],[]],[7,[]]]])

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