"itertools" --- Funções que criam iteradores para laços eficientes
******************************************************************

======================================================================

Esse módulo implementa diversos blocos de construção de *iterator*
building blocks inspirados por construções de  APL, Haskell, e SML.
Cada uma foi reformulada de forma adequada para Python.

Esse módulo padroniza um conjunto central de ferramentas rápidas e de
uso eficiente da memória, que podem ser utilizadas sozinhas ou
combinadas. Juntas, eles formam uma "álgebra de iteradores" tornando
possível construir ferramentas sucintas e eficientes em Python puro.

Por exemplo, SML fornece uma ferramenta para tabulação: "tabulate(f)"
que produz uma sequência "f(0), f(1), ...".  O mesmo efeito pode ser
obtido em Python combinando "map()" e "count()" para formar "map(f,
count())".

Essa ferramentas e suas equivalências embutidas também trabalham bem
com as funções de alta velocidade do módulo "operator" module. Por
exemplo, o operador de multiplicação pode ser mapeado em dois vetores
para criar um produto escalar eficiente: "sum(map(operator.mul,
vector1, vector2))".

**Iteradores infinitos:**

+--------------------+-------------------+---------------------------------------------------+-------------------------------------------+
| Iterador           | Argumentos        | Resultado                                         | Exemplo                                   |
|====================|===================|===================================================|===========================================|
| "count()"          | start, [step]     | start, start+step, start+2*step, ...              | "count(10) --> 10 11 12 13 14 ..."        |
+--------------------+-------------------+---------------------------------------------------+-------------------------------------------+
| "cycle()"          | p                 | p0, p1, ... ultimo elemento de p, p0, p1, ...     | "cycle('ABCD') --> A B C D A B C D ..."   |
+--------------------+-------------------+---------------------------------------------------+-------------------------------------------+
| "repeat()"         | elem [,n]         | elem, elem, elem, ... repete infinitamente ou até | "repeat(10, 3) --> 10 10 10"              |
|                    |                   | n vezes                                           |                                           |
+--------------------+-------------------+---------------------------------------------------+-------------------------------------------+

**Iteradores terminando na sequencia de entrada mais curta:**

+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| Iterador                     | Argumentos                   | Resultado                                         | Exemplo                                                       |
|==============================|==============================|===================================================|===============================================================|
| "accumulate()"               | p [,func]                    | p0, p0+p1, p0+p1+p2, ...                          | "accumulate([1,2,3,4,5]) --> 1 3 6 10 15"                     |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "chain()"                    | p, q, ...                    | p0, p1, ... último elemento de p, q0, q1, ...     | "chain('ABC', 'DEF') --> A B C D E F"                         |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "chain.from_iterable()"      | iterável                     | p0, p1, ... último elemento de p, q0, q1, ...     | "chain.from_iterable(['ABC', 'DEF']) --> A B C D E F"         |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "compress()"                 | data, selectors              | (d[0] if s[0]), (d[1] if s[1]), ...               | "compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F"               |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "dropwhile()"                | pred, seq                    | seq[n], seq[n+1], iniciando quando pred for falsa | "dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1"             |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "filterfalse()"              | pred, seq                    | elementos de seq onde pred(elem) é falso          | "filterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8"         |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "groupby()"                  | iterable[, key]              | sub-iteradores agrupados pelo valor de key(v)     |                                                               |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "islice()"                   | seq, [start,] stop [, step]  | elementos de seq[start:stop:step]                 | "islice('ABCDEFG', 2, None) --> C D E F G"                    |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "starmap()"                  | func, seq                    | func(*seq[0]), func(*seq[1]), ...                 | "starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000"          |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "takewhile()"                | pred, seq                    | seq[0], seq[1], enquanto pred é falso             | "takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4"               |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "tee()"                      | it, n                        | n iteradores it independentes                     |                                                               |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+
| "zip_longest()"              | p, q, ...                    | (p[0], q[0]), (p[1], q[1]), ...                   | "zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-"    |
+------------------------------+------------------------------+---------------------------------------------------+---------------------------------------------------------------+

**Iteradores combinatórios:**

+------------------------------------------------+----------------------+---------------------------------------------------------------+
| Iterador                                       | Argumentos           | Resultado                                                     |
|================================================|======================|===============================================================|
| "product()"                                    | p, q, ... [repeat=1] | produto cartesiano, equivalente a laços "for" aninhados       |
+------------------------------------------------+----------------------+---------------------------------------------------------------+
| "permutations()"                               | p[, r]               | tuplas de tamanho r, com todas ordenações possíveis, sem      |
|                                                |                      | elementos repetidos                                           |
+------------------------------------------------+----------------------+---------------------------------------------------------------+
| "combinations()"                               | p, r                 | tuplas de tamanho r, ordenadas, sem elementos repetidos       |
+------------------------------------------------+----------------------+---------------------------------------------------------------+
| "combinations_with_replacement()"              | p, r                 | tuplas de tamanho r, ordenadas, com elementos repetidos       |
+------------------------------------------------+----------------------+---------------------------------------------------------------+
| "product('ABCD', repeat=2)"                    |                      | "AA AB AC AD BA BB BC BD CA CB CC CD DA DB DC DD"             |
+------------------------------------------------+----------------------+---------------------------------------------------------------+
| "permutations('ABCD', 2)"                      |                      | "AB AC AD BA BC BD CA CB CD DA DB DC"                         |
+------------------------------------------------+----------------------+---------------------------------------------------------------+
| "combinations('ABCD', 2)"                      |                      | "AB AC AD BC BD CD"                                           |
+------------------------------------------------+----------------------+---------------------------------------------------------------+
| "combinations_with_replacement('ABCD', 2)"     |                      | "AA AB AC AD BB BC BD CC CD DD"                               |
+------------------------------------------------+----------------------+---------------------------------------------------------------+


Funções de itertools
====================

Todas as funções a seguir constroem e retorna iteradores. Algumas
fornecem fluxos de tamanhos infinitos, assim elas devem ser acessados
somente por funções ou laços que interrompem o fluxo.

itertools.accumulate(iterable[, func])

   Make an iterator that returns accumulated sums, or accumulated
   results of other binary functions (specified via the optional
   *func* argument).  If *func* is supplied, it should be a function
   of two arguments. Elements of the input *iterable* may be any type
   that can be accepted as arguments to *func*. (For example, with the
   default operation of addition, elements may be any addable type
   including "Decimal" or "Fraction".) If the input iterable is empty,
   the output iterable will also be empty.

   Aproximadamente equivalente a:

      def accumulate(iterable, func=operator.add):
          'Return running totals'
          # accumulate([1,2,3,4,5]) --> 1 3 6 10 15
          # accumulate([1,2,3,4,5], operator.mul) --> 1 2 6 24 120
          it = iter(iterable)
          try:
              total = next(it)
          except StopIteration:
              return
          yield total
          for element in it:
              total = func(total, element)
              yield total

   Existem diversos usos para o argumento *func*.  Ele pode ser
   definido como a função "min()" calcular um valor mínimo, "max()"
   para um valor máximo, ou "operator.mul()" para calcular um produto.
   Tabelas de amortização podem ser construídas acumulando juros e
   aplicando pagamentos.  Relações de recorrência de primeira ordem
   podem ser modeladas fornecendo o valor inicial no iterável e usando
   somente o valor total acumulado no argumento *func*:

      >>> data = [3, 4, 6, 2, 1, 9, 0, 7, 5, 8]
      >>> list(accumulate(data, operator.mul))     # running product
      [3, 12, 72, 144, 144, 1296, 0, 0, 0, 0]
      >>> list(accumulate(data, max))              # running maximum
      [3, 4, 6, 6, 6, 9, 9, 9, 9, 9]

      # Amortize a 5% loan of 1000 with 4 annual payments of 90
      >>> cashflows = [1000, -90, -90, -90, -90]
      >>> list(accumulate(cashflows, lambda bal, pmt: bal*1.05 + pmt))
      [1000, 960.0, 918.0, 873.9000000000001, 827.5950000000001]

      # Chaotic recurrence relation https://en.wikipedia.org/wiki/Logistic_map
      >>> logistic_map = lambda x, _:  r * x * (1 - x)
      >>> r = 3.8
      >>> x0 = 0.4
      >>> inputs = repeat(x0, 36)     # only the initial value is used
      >>> [format(x, '.2f') for x in accumulate(inputs, logistic_map)]
      ['0.40', '0.91', '0.30', '0.81', '0.60', '0.92', '0.29', '0.79', '0.63',
       '0.88', '0.39', '0.90', '0.33', '0.84', '0.52', '0.95', '0.18', '0.57',
       '0.93', '0.25', '0.71', '0.79', '0.63', '0.88', '0.39', '0.91', '0.32',
       '0.83', '0.54', '0.95', '0.20', '0.60', '0.91', '0.30', '0.80', '0.60']

   Veja "functools.reduce()" para uma função similar que devolve
   apenas o valor acumulado final.

   Novo na versão 3.2.

   Alterado na versão 3.3: Adicionado o parâmetro opcional *func*.

itertools.chain(*iterables)

   Cria um iterador que devolve elementos do primeiro iterável até o
   esgotamento, então continua com o próximo iterável, até que todos
   os iteráveis sejam esgotados. Usando para tratar sequências
   consecutivas como uma única sequencia. aproximadamente equivalente
   a:

      def chain(*iterables):
          # chain('ABC', 'DEF') --> A B C D E F
          for it in iterables:
              for element in it:
                  yield element

classmethod chain.from_iterable(iterable)

   Construtor alternativo para "chain()".  Obtém entradas encadeadas a
   partir de um único argumento iterável que avaliado preguiçosamente.
   Aproximadamente equivalente a:

      def from_iterable(iterables):
          # chain.from_iterable(['ABC', 'DEF']) --> A B C D E F
          for it in iterables:
              for element in it:
                  yield element

itertools.combinations(iterable, r)

   Devolve subsequências de elementos com comprimento *r* a partir da
   entrada *iterável*

   Combinations are emitted in lexicographic sort order.  So, if the
   input *iterable* is sorted, the combination tuples will be produced
   in sorted order.

   Os elementos são tratados como únicos baseado em suas posições, não
   em seus valores. Portanto se os elementos de entrada são únicos,
   não haverá repetição de valores nas sucessivas combinações.

   Aproximadamente equivalente a:

      def combinations(iterable, r):
          # combinations('ABCD', 2) --> AB AC AD BC BD CD
          # combinations(range(4), 3) --> 012 013 023 123
          pool = tuple(iterable)
          n = len(pool)
          if r > n:
              return
          indices = list(range(r))
          yield tuple(pool[i] for i in indices)
          while True:
              for i in reversed(range(r)):
                  if indices[i] != i + n - r:
                      break
              else:
                  return
              indices[i] += 1
              for j in range(i+1, r):
                  indices[j] = indices[j-1] + 1
              yield tuple(pool[i] for i in indices)

   O código  para "combinations()" também pode ser expresso como uma
   subsequência de "permutations()" depois de filtradas as entradas
   onde os elementos não estão ordenandos (de acordo com a sua posição
   na entrada):

      def combinations(iterable, r):
          pool = tuple(iterable)
          n = len(pool)
          for indices in permutations(range(n), r):
              if sorted(indices) == list(indices):
                  yield tuple(pool[i] for i in indices)

   O número de itens devolvidos é "n! / r! / (n-r)!" quando "0 <= r <=
   n" ou zero quando "r > n".

itertools.combinations_with_replacement(iterable, r)

   Devolve subsequências de comprimento *r* de elementos do *iterável*
   de entrada permitindo que elementos individuais sejam repetidos
   mais de uma vez.

   Combinations are emitted in lexicographic sort order.  So, if the
   input *iterable* is sorted, the combination tuples will be produced
   in sorted order.

   Os elementos são tratados como únicos baseado em suas posições, não
   em seus valores. Portanto se os elementos de entrada forem únicos,
   não haverá repetição de valores nas combinações geradas.

   Aproximadamente equivalente a:

      def combinations_with_replacement(iterable, r):
          # combinations_with_replacement('ABC', 2) --> AA AB AC BB BC CC
          pool = tuple(iterable)
          n = len(pool)
          if not n and r:
              return
          indices = [0] * r
          yield tuple(pool[i] for i in indices)
          while True:
              for i in reversed(range(r)):
                  if indices[i] != n - 1:
                      break
              else:
                  return
              indices[i:] = [indices[i] + 1] * (r - i)
              yield tuple(pool[i] for i in indices)

   O código  para "combinations_with_replacement()" também pode ser
   expresso como uma subsequência de "product()" depois de filtradas
   as entradas onde os elementos não estão ordenados (de acordo com a
   sua posição na entrada):

      def combinations_with_replacement(iterable, r):
          pool = tuple(iterable)
          n = len(pool)
          for indices in product(range(n), repeat=r):
              if sorted(indices) == list(indices):
                  yield tuple(pool[i] for i in indices)

   O número de itens devolvidos é "(n+r-1)! / r! / (n-1)!" quando "n >
   0".

   Novo na versão 3.1.

itertools.compress(data, selectors)

   Crie um iterador que filtra elementos de *data* devolvendo apenas
   aqueles que tem um elemento correspondente em *selectors* que seja
   avaliado "True". Interrompe quando os iteráveis *data* ou
   *selectors* tiveram sido esgotados. Aproximadamente equivalente a:

      def compress(data, selectors):
          # compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F
          return (d for d, s in zip(data, selectors) if s)

   Novo na versão 3.1.

itertools.count(start=0, step=1)

   Crie um iterador que devolve valores igualmente espaçados começando
   pelo número *start*. Frequentemente usado com um argumento da
   função "map()" para gerar pontos de dados consecutivos. Também
   usado com "zip()" para adicionar números sequenciais.
   Aproximadamente equivalente a:

      def count(start=0, step=1):
          # count(10) --> 10 11 12 13 14 ...
          # count(2.5, 0.5) -> 2.5 3.0 3.5 ...
          n = start
          while True:
              yield n
              n += step

   Quando é feita uma contagem usando números de ponto flutuante, é
   possível ter melhor precisão substituindo código multiplicativo
   como  "(start + step * i for i in count())".

   Alterado na versão 3.1: Adicionou argumento *step* e permitiu
   argumentos não-inteiros.

itertools.cycle(iterable)

   Crie um iterador que devolve elementos do iterável assim como salva
   uma cópia de cada um. Quando o iterável é esgotado, devolve
   elementos da cópia salva. Repete indefinidamente. Aproximadamente
   equivalente a:

      def cycle(iterable):
          # cycle('ABCD') --> A B C D A B C D A B C D ...
          saved = []
          for element in iterable:
              yield element
              saved.append(element)
          while saved:
              for element in saved:
                    yield element

   Note, this member of the toolkit may require significant auxiliary
   storage (depending on the length of the iterable).

itertools.dropwhile(predicate, iterable)

   Make an iterator that drops elements from the iterable as long as
   the predicate is true; afterwards, returns every element.  Note,
   the iterator does not produce *any* output until the predicate
   first becomes false, so it may have a lengthy start-up time.
   Roughly equivalent to:

      def dropwhile(predicate, iterable):
          # dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1
          iterable = iter(iterable)
          for x in iterable:
              if not predicate(x):
                  yield x
                  break
          for x in iterable:
              yield x

itertools.filterfalse(predicate, iterable)

   Make an iterator that filters elements from iterable returning only
   those for which the predicate is "False". If *predicate* is "None",
   return the items that are false. Roughly equivalent to:

      def filterfalse(predicate, iterable):
          # filterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8
          if predicate is None:
              predicate = bool
          for x in iterable:
              if not predicate(x):
                  yield x

itertools.groupby(iterable, key=None)

   Make an iterator that returns consecutive keys and groups from the
   *iterable*. The *key* is a function computing a key value for each
   element.  If not specified or is "None", *key* defaults to an
   identity function and returns the element unchanged.  Generally,
   the iterable needs to already be sorted on the same key function.

   The operation of "groupby()" is similar to the "uniq" filter in
   Unix.  It generates a break or new group every time the value of
   the key function changes (which is why it is usually necessary to
   have sorted the data using the same key function).  That behavior
   differs from SQL's GROUP BY which aggregates common elements
   regardless of their input order.

   The returned group is itself an iterator that shares the underlying
   iterable with "groupby()".  Because the source is shared, when the
   "groupby()" object is advanced, the previous group is no longer
   visible.  So, if that data is needed later, it should be stored as
   a list:

      groups = []
      uniquekeys = []
      data = sorted(data, key=keyfunc)
      for k, g in groupby(data, keyfunc):
          groups.append(list(g))      # Store group iterator as a list
          uniquekeys.append(k)

   "groupby()" é aproximadamente equivalente a:

      class groupby:
          # [k for k, g in groupby('AAAABBBCCDAABBB')] --> A B C D A B
          # [list(g) for k, g in groupby('AAAABBBCCD')] --> AAAA BBB CC D
          def __init__(self, iterable, key=None):
              if key is None:
                  key = lambda x: x
              self.keyfunc = key
              self.it = iter(iterable)
              self.tgtkey = self.currkey = self.currvalue = object()
          def __iter__(self):
              return self
          def __next__(self):
              self.id = object()
              while self.currkey == self.tgtkey:
                  self.currvalue = next(self.it)    # Exit on StopIteration
                  self.currkey = self.keyfunc(self.currvalue)
              self.tgtkey = self.currkey
              return (self.currkey, self._grouper(self.tgtkey, self.id))
          def _grouper(self, tgtkey, id):
              while self.id is id and self.currkey == tgtkey:
                  yield self.currvalue
                  try:
                      self.currvalue = next(self.it)
                  except StopIteration:
                      return
                  self.currkey = self.keyfunc(self.currvalue)

itertools.islice(iterable, stop)
itertools.islice(iterable, start, stop[, step])

   Make an iterator that returns selected elements from the iterable.
   If *start* is non-zero, then elements from the iterable are skipped
   until start is reached. Afterward, elements are returned
   consecutively unless *step* is set higher than one which results in
   items being skipped.  If *stop* is "None", then iteration continues
   until the iterator is exhausted, if at all; otherwise, it stops at
   the specified position.  Unlike regular slicing, "islice()" does
   not support negative values for *start*, *stop*, or *step*.  Can be
   used to extract related fields from data where the internal
   structure has been flattened (for example, a multi-line report may
   list a name field on every third line).  Roughly equivalent to:

      def islice(iterable, *args):
          # islice('ABCDEFG', 2) --> A B
          # islice('ABCDEFG', 2, 4) --> C D
          # islice('ABCDEFG', 2, None) --> C D E F G
          # islice('ABCDEFG', 0, None, 2) --> A C E G
          s = slice(*args)
          start, stop, step = s.start or 0, s.stop or sys.maxsize, s.step or 1
          it = iter(range(start, stop, step))
          try:
              nexti = next(it)
          except StopIteration:
              # Consume *iterable* up to the *start* position.
              for i, element in zip(range(start), iterable):
                  pass
              return
          try:
              for i, element in enumerate(iterable):
                  if i == nexti:
                      yield element
                      nexti = next(it)
          except StopIteration:
              # Consume to *stop*.
              for i, element in zip(range(i + 1, stop), iterable):
                  pass

   If *start* is "None", then iteration starts at zero. If *step* is
   "None", then the step defaults to one.

itertools.permutations(iterable, r=None)

   Return successive *r* length permutations of elements in the
   *iterable*.

   If *r* is not specified or is "None", then *r* defaults to the
   length of the *iterable* and all possible full-length permutations
   are generated.

   Permutations are emitted in lexicographic sort order.  So, if the
   input *iterable* is sorted, the permutation tuples will be produced
   in sorted order.

   Elements are treated as unique based on their position, not on
   their value.  So if the input elements are unique, there will be no
   repeat values in each permutation.

   Aproximadamente equivalente a:

      def permutations(iterable, r=None):
          # permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC
          # permutations(range(3)) --> 012 021 102 120 201 210
          pool = tuple(iterable)
          n = len(pool)
          r = n if r is None else r
          if r > n:
              return
          indices = list(range(n))
          cycles = list(range(n, n-r, -1))
          yield tuple(pool[i] for i in indices[:r])
          while n:
              for i in reversed(range(r)):
                  cycles[i] -= 1
                  if cycles[i] == 0:
                      indices[i:] = indices[i+1:] + indices[i:i+1]
                      cycles[i] = n - i
                  else:
                      j = cycles[i]
                      indices[i], indices[-j] = indices[-j], indices[i]
                      yield tuple(pool[i] for i in indices[:r])
                      break
              else:
                  return

   O código  para "permutations()" também pode ser expresso como uma
   subsequência de "product()" depois de filtradas as entradas com
   elementos repetidos (os de mesma posição no conjunto de entrada):

      def permutations(iterable, r=None):
          pool = tuple(iterable)
          n = len(pool)
          r = n if r is None else r
          for indices in product(range(n), repeat=r):
              if len(set(indices)) == r:
                  yield tuple(pool[i] for i in indices)

   O número de itens retornado é "n! / (n-r)!" quando "0 <= r <= n" ou
   zero quando "r > n".

itertools.product(*iterables, repeat=1)

   Produto cartesiano de iteráveis de entrada

   Aproximadamente equivalente a laços for aninhados em uma expressão
   geradora. Por exemplo, "product(A, B)" devolve o mesmo que "((x,y)
   for x in A for y in B)".

   Os laços aninhados circulam como um hodômetro com o elemento mais à
   direita avançando a cada iteração. Este padrão cria uma ordenação
   lexicográfica de maneira que se os iteráveis de entrada estiverem
   ordenados, as tuplas produzidas são emitidas de maneira ordenada.

   To compute the product of an iterable with itself, specify the
   number of repetitions with the optional *repeat* keyword argument.
   For example, "product(A, repeat=4)" means the same as "product(A,
   A, A, A)".

   This function is roughly equivalent to the following code, except
   that the actual implementation does not build up intermediate
   results in memory:

      def product(*args, repeat=1):
          # product('ABCD', 'xy') --> Ax Ay Bx By Cx Cy Dx Dy
          # product(range(2), repeat=3) --> 000 001 010 011 100 101 110 111
          pools = [tuple(pool) for pool in args] * repeat
          result = [[]]
          for pool in pools:
              result = [x+[y] for x in result for y in pool]
          for prod in result:
              yield tuple(prod)

itertools.repeat(object[, times])

   Make an iterator that returns *object* over and over again. Runs
   indefinitely unless the *times* argument is specified. Used as
   argument to "map()" for invariant parameters to the called
   function.  Also used with "zip()" to create an invariant part of a
   tuple record.

   Aproximadamente equivalente a:

      def repeat(object, times=None):
          # repeat(10, 3) --> 10 10 10
          if times is None:
              while True:
                  yield object
          else:
              for i in range(times):
                  yield object

   A common use for *repeat* is to supply a stream of constant values
   to *map* or *zip*:

      >>> list(map(pow, range(10), repeat(2)))
      [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

itertools.starmap(function, iterable)

   Make an iterator that computes the function using arguments
   obtained from the iterable.  Used instead of "map()" when argument
   parameters are already grouped in tuples from a single iterable
   (the data has been "pre-zipped").  The difference between "map()"
   and "starmap()" parallels the distinction between "function(a,b)"
   and "function(*c)". Roughly equivalent to:

      def starmap(function, iterable):
          # starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000
          for args in iterable:
              yield function(*args)

itertools.takewhile(predicate, iterable)

   Make an iterator that returns elements from the iterable as long as
   the predicate is true.  Roughly equivalent to:

      def takewhile(predicate, iterable):
          # takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4
          for x in iterable:
              if predicate(x):
                  yield x
              else:
                  break

itertools.tee(iterable, n=2)

   Return *n* independent iterators from a single iterable.

   The following Python code helps explain what *tee* does (although
   the actual implementation is more complex and uses only a single
   underlying FIFO (first-in, first-out) queue).

   Aproximadamente equivalente a:

      def tee(iterable, n=2):
          it = iter(iterable)
          deques = [collections.deque() for i in range(n)]
          def gen(mydeque):
              while True:
                  if not mydeque:             # when the local deque is empty
                      try:
                          newval = next(it)   # fetch a new value and
                      except StopIteration:
                          return
                      for d in deques:        # load it to all the deques
                          d.append(newval)
                  yield mydeque.popleft()
          return tuple(gen(d) for d in deques)

   Once "tee()" has made a split, the original *iterable* should not
   be used anywhere else; otherwise, the *iterable* could get advanced
   without the tee objects being informed.

   "tee" iterators are not threadsafe. A "RuntimeError" may be raised
   when using simultaneously iterators returned by the same "tee()"
   call, even if the original *iterable* is threadsafe.

   This itertool may require significant auxiliary storage (depending
   on how much temporary data needs to be stored). In general, if one
   iterator uses most or all of the data before another iterator
   starts, it is faster to use "list()" instead of "tee()".

itertools.zip_longest(*iterables, fillvalue=None)

   Make an iterator that aggregates elements from each of the
   iterables. If the iterables are of uneven length, missing values
   are filled-in with *fillvalue*. Iteration continues until the
   longest iterable is exhausted.  Roughly equivalent to:

      def zip_longest(*args, fillvalue=None):
          # zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-
          iterators = [iter(it) for it in args]
          num_active = len(iterators)
          if not num_active:
              return
          while True:
              values = []
              for i, it in enumerate(iterators):
                  try:
                      value = next(it)
                  except StopIteration:
                      num_active -= 1
                      if not num_active:
                          return
                      iterators[i] = repeat(fillvalue)
                      value = fillvalue
                  values.append(value)
              yield tuple(values)

   Se um dos iteráveis é potencialmente infinito, então a função
   "zip_longest()" deve ser embrulhada por algo que limite o número de
   chamadas (por exemplo "islice()" ou "takewhile()"). Se não
   especificado, *fillvalue*  tem o valor padrão "None".


Receitas com itertools
======================

Esta seção mostra receitas para criação de um ferramental ampliado
usando as ferramentas existentes de itertools como elementos
construtivos.

The extended tools offer the same high performance as the underlying
toolset. The superior memory performance is kept by processing
elements one at a time rather than bringing the whole iterable into
memory all at once. Code volume is kept small by linking the tools
together in a functional style which helps eliminate temporary
variables.  High speed is retained by preferring "vectorized" building
blocks over the use of for-loops and *generator*s which incur
interpreter overhead.

   def take(n, iterable):
       "Return first n items of the iterable as a list"
       return list(islice(iterable, n))

   def prepend(value, iterator):
       "Prepend a single value in front of an iterator"
       # prepend(1, [2, 3, 4]) -> 1 2 3 4
       return chain([value], iterator)

   def tabulate(function, start=0):
       "Return function(0), function(1), ..."
       return map(function, count(start))

   def tail(n, iterable):
       "Return an iterator over the last n items"
       # tail(3, 'ABCDEFG') --> E F G
       return iter(collections.deque(iterable, maxlen=n))

   def consume(iterator, n=None):
       "Advance the iterator n-steps ahead. If n is None, consume entirely."
       # Use functions that consume iterators at C speed.
       if n is None:
           # feed the entire iterator into a zero-length deque
           collections.deque(iterator, maxlen=0)
       else:
           # advance to the empty slice starting at position n
           next(islice(iterator, n, n), None)

   def nth(iterable, n, default=None):
       "Returns the nth item or a default value"
       return next(islice(iterable, n, None), default)

   def all_equal(iterable):
       "Returns True if all the elements are equal to each other"
       g = groupby(iterable)
       return next(g, True) and not next(g, False)

   def quantify(iterable, pred=bool):
       "Count how many times the predicate is true"
       return sum(map(pred, iterable))

   def padnone(iterable):
       """Returns the sequence elements and then returns None indefinitely.

       Useful for emulating the behavior of the built-in map() function.
       """
       return chain(iterable, repeat(None))

   def ncycles(iterable, n):
       "Returns the sequence elements n times"
       return chain.from_iterable(repeat(tuple(iterable), n))

   def dotproduct(vec1, vec2):
       return sum(map(operator.mul, vec1, vec2))

   def flatten(listOfLists):
       "Flatten one level of nesting"
       return chain.from_iterable(listOfLists)

   def repeatfunc(func, times=None, *args):
       """Repeat calls to func with specified arguments.

       Example:  repeatfunc(random.random)
       """
       if times is None:
           return starmap(func, repeat(args))
       return starmap(func, repeat(args, times))

   def pairwise(iterable):
       "s -> (s0,s1), (s1,s2), (s2, s3), ..."
       a, b = tee(iterable)
       next(b, None)
       return zip(a, b)

   def grouper(iterable, n, fillvalue=None):
       "Collect data into fixed-length chunks or blocks"
       # grouper('ABCDEFG', 3, 'x') --> ABC DEF Gxx"
       args = [iter(iterable)] * n
       return zip_longest(*args, fillvalue=fillvalue)

   def roundrobin(*iterables):
       "roundrobin('ABC', 'D', 'EF') --> A D E B F C"
       # Recipe credited to George Sakkis
       num_active = len(iterables)
       nexts = cycle(iter(it).__next__ for it in iterables)
       while num_active:
           try:
               for next in nexts:
                   yield next()
           except StopIteration:
               # Remove the iterator we just exhausted from the cycle.
               num_active -= 1
               nexts = cycle(islice(nexts, num_active))

   def partition(pred, iterable):
       'Use a predicate to partition entries into false entries and true entries'
       # partition(is_odd, range(10)) --> 0 2 4 6 8   and  1 3 5 7 9
       t1, t2 = tee(iterable)
       return filterfalse(pred, t1), filter(pred, t2)

   def powerset(iterable):
       "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
       s = list(iterable)
       return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))

   def unique_everseen(iterable, key=None):
       "List unique elements, preserving order. Remember all elements ever seen."
       # unique_everseen('AAAABBBCCDAABBB') --> A B C D
       # unique_everseen('ABBCcAD', str.lower) --> A B C D
       seen = set()
       seen_add = seen.add
       if key is None:
           for element in filterfalse(seen.__contains__, iterable):
               seen_add(element)
               yield element
       else:
           for element in iterable:
               k = key(element)
               if k not in seen:
                   seen_add(k)
                   yield element

   def unique_justseen(iterable, key=None):
       "List unique elements, preserving order. Remember only the element just seen."
       # unique_justseen('AAAABBBCCDAABBB') --> A B C D A B
       # unique_justseen('ABBCcAD', str.lower) --> A B C A D
       return map(next, map(itemgetter(1), groupby(iterable, key)))

   def iter_except(func, exception, first=None):
       """ Call a function repeatedly until an exception is raised.

       Converts a call-until-exception interface to an iterator interface.
       Like builtins.iter(func, sentinel) but uses an exception instead
       of a sentinel to end the loop.

       Examples:
           iter_except(functools.partial(heappop, h), IndexError)   # priority queue iterator
           iter_except(d.popitem, KeyError)                         # non-blocking dict iterator
           iter_except(d.popleft, IndexError)                       # non-blocking deque iterator
           iter_except(q.get_nowait, Queue.Empty)                   # loop over a producer Queue
           iter_except(s.pop, KeyError)                             # non-blocking set iterator

       """
       try:
           if first is not None:
               yield first()            # For database APIs needing an initial cast to db.first()
           while True:
               yield func()
       except exception:
           pass

   def first_true(iterable, default=False, pred=None):
       """Returns the first true value in the iterable.

       If no true value is found, returns *default*

       If *pred* is not None, returns the first item
       for which pred(item) is true.

       """
       # first_true([a,b,c], x) --> a or b or c or x
       # first_true([a,b], x, f) --> a if f(a) else b if f(b) else x
       return next(filter(pred, iterable), default)

   def random_product(*args, repeat=1):
       "Random selection from itertools.product(*args, **kwds)"
       pools = [tuple(pool) for pool in args] * repeat
       return tuple(random.choice(pool) for pool in pools)

   def random_permutation(iterable, r=None):
       "Random selection from itertools.permutations(iterable, r)"
       pool = tuple(iterable)
       r = len(pool) if r is None else r
       return tuple(random.sample(pool, r))

   def random_combination(iterable, r):
       "Random selection from itertools.combinations(iterable, r)"
       pool = tuple(iterable)
       n = len(pool)
       indices = sorted(random.sample(range(n), r))
       return tuple(pool[i] for i in indices)

   def random_combination_with_replacement(iterable, r):
       "Random selection from itertools.combinations_with_replacement(iterable, r)"
       pool = tuple(iterable)
       n = len(pool)
       indices = sorted(random.randrange(n) for i in range(r))
       return tuple(pool[i] for i in indices)

   def nth_combination(iterable, r, index):
       'Equivalent to list(combinations(iterable, r))[index]'
       pool = tuple(iterable)
       n = len(pool)
       if r < 0 or r > n:
           raise ValueError
       c = 1
       k = min(r, n-r)
       for i in range(1, k+1):
           c = c * (n - k + i) // i
       if index < 0:
           index += c
       if index < 0 or index >= c:
           raise IndexError
       result = []
       while r:
           c, n, r = c*r//n, n-1, r-1
           while index >= c:
               index -= c
               c, n = c*(n-r)//n, n-1
           result.append(pool[-1-n])
       return tuple(result)

Note, many of the above recipes can be optimized by replacing global
lookups with local variables defined as default values.  For example,
the *dotproduct* recipe can be written as:

   def dotproduct(vec1, vec2, sum=sum, map=map, mul=operator.mul):
       return sum(map(mul, vec1, vec2))
