| |
| :mod:`itertools` --- Functions creating iterators for efficient looping |
| ======================================================================= |
| |
| .. module:: itertools |
| :synopsis: Functions creating iterators for efficient looping. |
| .. moduleauthor:: Raymond Hettinger <python@rcn.com> |
| .. sectionauthor:: Raymond Hettinger <python@rcn.com> |
| |
| |
| .. testsetup:: |
| |
| from itertools import * |
| |
| |
| This module implements a number of :term:`iterator` building blocks inspired by |
| constructs from the Haskell and SML programming languages. Each has been recast |
| in a form suitable for Python. |
| |
| The module standardizes a core set of fast, memory efficient tools that are |
| useful by themselves or in combination. Standardization helps avoid the |
| readability and reliability problems which arise when many different individuals |
| create their own slightly varying implementations, each with their own quirks |
| and naming conventions. |
| |
| The tools are designed to combine readily with one another. This makes it easy |
| to construct more specialized tools succinctly and efficiently in pure Python. |
| |
| For instance, SML provides a tabulation tool: ``tabulate(f)`` which produces a |
| sequence ``f(0), f(1), ...``. But, this effect can be achieved in Python |
| by combining :func:`map` and :func:`count` to form ``map(f, count())``. |
| |
| Likewise, the functional tools are designed to work well with the high-speed |
| functions provided by the :mod:`operator` module. |
| |
| Whether cast in pure python form or compiled code, tools that use iterators are |
| more memory efficient (and often faster) than their list based counterparts. Adopting |
| the principles of just-in-time manufacturing, they create data when and where |
| needed instead of consuming memory with the computer equivalent of "inventory". |
| |
| |
| .. seealso:: |
| |
| The Standard ML Basis Library, `The Standard ML Basis Library |
| <http://www.standardml.org/Basis/>`_. |
| |
| Haskell, A Purely Functional Language, `Definition of Haskell and the Standard |
| Libraries <http://www.haskell.org/definition/>`_. |
| |
| |
| .. _itertools-functions: |
| |
| Itertool functions |
| ------------------ |
| |
| The following module functions all construct and return iterators. Some provide |
| streams of infinite length, so they should only be accessed by functions or |
| loops that truncate the stream. |
| |
| |
| .. function:: chain(*iterables) |
| |
| Make an iterator that returns elements from the first iterable until it is |
| exhausted, then proceeds to the next iterable, until all of the iterables are |
| exhausted. Used for treating consecutive sequences as a single sequence. |
| Equivalent to:: |
| |
| def chain(*iterables): |
| # chain('ABC', 'DEF') --> A B C D E F |
| for it in iterables: |
| for element in it: |
| yield element |
| |
| |
| .. function:: itertools.chain.from_iterable(iterable) |
| |
| Alternate constructor for :func:`chain`. Gets chained inputs from a |
| single iterable argument that is evaluated lazily. Equivalent to:: |
| |
| @classmethod |
| 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 |
| |
| |
| .. function:: combinations(iterable, r) |
| |
| Return *r* length subsequences of elements from the input *iterable*. |
| |
| Combinations are emitted in lexicographic sort order. So, if the |
| input *iterable* is sorted, the combination 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 combination. |
| |
| Equivalent to:: |
| |
| 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 1: |
| 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) |
| |
| The code for :func:`combinations` can be also expressed as a subsequence |
| of :func:`permutations` after filtering entries where the elements are not |
| in sorted order (according to their position in the input pool):: |
| |
| 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) |
| |
| The number of items returned is ``n! / r! / (n-r)!`` when ``0 <= r <= n`` |
| or zero when ``r > n``. |
| |
| .. function:: combinations_with_replacement(iterable, r) |
| |
| Return *r* length subsequences of elements from the input *iterable* |
| allowing individual elements to be repeated more than once. |
| |
| Combinations are emitted in lexicographic sort order. So, if the |
| input *iterable* is sorted, the combination 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, the generated combinations |
| will also be unique. |
| |
| Equivalent to:: |
| |
| 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 1: |
| 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) |
| |
| The code for :func:`combinations_with_replacement` can be also expressed as |
| a subsequence of :func:`product` after filtering entries where the elements |
| are not in sorted order (according to their position in the input pool):: |
| |
| 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) |
| |
| The number of items returned is ``(n+r-1)! / r! / (n-1)!`` when ``n > 0``. |
| |
| .. versionadded:: 3.1 |
| |
| .. function:: compress(data, selectors) |
| |
| Make an iterator that filters elements from *data* returning only those that |
| have a corresponding element in *selectors* that evaluates to ``True``. |
| Stops when either the *data* or *selectors* iterables have been exhausted. |
| Equivalent to:: |
| |
| 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) |
| |
| .. versionadded:: 3.1 |
| |
| |
| .. function:: count(start=0, step=1) |
| |
| Make an iterator that returns evenly spaced values starting with *n*. Often |
| used as an argument to :func:`map` to generate consecutive data points. |
| Also, used with :func:`zip` to add sequence numbers. Equivalent to:: |
| |
| def count(start=0, step=1): |
| # count(10) --> 10 11 12 13 14 ... |
| # count(2.5, 0.5) -> 3.5 3.0 4.5 ... |
| n = start |
| while True: |
| yield n |
| n += step |
| |
| .. versionchanged:: 3.1 |
| added *step* argument and allowed non-integer arguments. |
| |
| .. function:: cycle(iterable) |
| |
| Make an iterator returning elements from the iterable and saving a copy of each. |
| When the iterable is exhausted, return elements from the saved copy. Repeats |
| indefinitely. Equivalent to:: |
| |
| 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). |
| |
| |
| .. function:: 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. 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 |
| |
| .. function:: 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. 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 |
| |
| |
| .. function:: groupby(iterable[, key]) |
| |
| 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 :func:`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 :func:`groupby`. Because the source is shared, when the :func:`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) |
| |
| :func:`groupby` is equivalent to:: |
| |
| class groupby(object): |
| # [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): |
| 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)) |
| def _grouper(self, tgtkey): |
| while self.currkey == tgtkey: |
| yield self.currvalue |
| self.currvalue = next(self.it) # Exit on StopIteration |
| self.currkey = self.keyfunc(self.currvalue) |
| |
| |
| .. function:: 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, :func:`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). 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) |
| it = range(s.start or 0, s.stop or sys.maxsize, s.step or 1) |
| nexti = next(it) |
| for i, element in enumerate(iterable): |
| if i == nexti: |
| yield element |
| nexti = next(it) |
| |
| If *start* is ``None``, then iteration starts at zero. If *step* is ``None``, |
| then the step defaults to one. |
| |
| |
| .. function:: permutations(iterable[, r]) |
| |
| 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. |
| |
| Equivalent to:: |
| |
| 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 = 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 |
| |
| The code for :func:`permutations` can be also expressed as a subsequence of |
| :func:`product`, filtered to exclude entries with repeated elements (those |
| from the same position in the input pool):: |
| |
| 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) |
| |
| The number of items returned is ``n! / (n-r)!`` when ``0 <= r <= n`` |
| or zero when ``r > n``. |
| |
| .. function:: product(*iterables[, repeat]) |
| |
| Cartesian product of input iterables. |
| |
| Equivalent to nested for-loops in a generator expression. For example, |
| ``product(A, B)`` returns the same as ``((x,y) for x in A for y in B)``. |
| |
| The nested loops cycle like an odometer with the rightmost element advancing |
| on every iteration. This pattern creates a lexicographic ordering so that if |
| the input's iterables are sorted, the product tuples are emitted in sorted |
| order. |
| |
| 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 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 = map(tuple, 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) |
| |
| |
| .. function:: 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 :func:`map` for |
| invariant parameters to the called function. Also used with :func:`zip` to |
| create an invariant part of a tuple record. Equivalent to:: |
| |
| 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 |
| |
| |
| .. function:: starmap(function, iterable) |
| |
| Make an iterator that computes the function using arguments obtained from |
| the iterable. Used instead of :func:`map` when argument parameters are already |
| grouped in tuples from a single iterable (the data has been "pre-zipped"). The |
| difference between :func:`map` and :func:`starmap` parallels the distinction |
| between ``function(a,b)`` and ``function(*c)``. Equivalent to:: |
| |
| def starmap(function, iterable): |
| # starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000 |
| for args in iterable: |
| yield function(*args) |
| |
| |
| .. function:: takewhile(predicate, iterable) |
| |
| Make an iterator that returns elements from the iterable as long as the |
| predicate is true. 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 |
| |
| |
| .. function:: tee(iterable[, n=2]) |
| |
| Return *n* independent iterators from a single iterable. The case where ``n==2`` |
| is equivalent to:: |
| |
| def tee(iterable): |
| def gen(next, data={}): |
| for i in count(): |
| if i in data: |
| yield data.pop(i) |
| else: |
| data[i] = next() |
| yield data[i] |
| it = iter(iterable) |
| return (gen(it.__next__), gen(it.__next__)) |
| |
| Note, once :func:`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. |
| |
| Note, this member of the toolkit may require significant auxiliary storage |
| (depending on how much temporary data needs to be stored). In general, if one |
| iterator is going to use most or all of the data before the other iterator, it |
| is faster to use :func:`list` instead of :func:`tee`. |
| |
| |
| .. function:: zip_longest(*iterables[, fillvalue]) |
| |
| 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. Equivalent to:: |
| |
| def zip_longest(*args, fillvalue=None): |
| # zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D- |
| def sentinel(counter = ([fillvalue]*(len(args)-1)).pop): |
| yield counter() # yields the fillvalue, or raises IndexError |
| fillers = repeat(fillvalue) |
| iters = [chain(it, sentinel(), fillers) for it in args] |
| try: |
| for tup in zip(*iters): |
| yield tup |
| except IndexError: |
| pass |
| |
| If one of the iterables is potentially infinite, then the :func:`zip_longest` |
| function should be wrapped with something that limits the number of calls |
| (for example :func:`islice` or :func:`takewhile`). If not specified, |
| *fillvalue* defaults to ``None``. |
| |
| |
| .. _itertools-example: |
| |
| Examples |
| -------- |
| |
| The following examples show common uses for each tool and demonstrate ways they |
| can be combined. |
| |
| .. doctest:: |
| |
| >>> # Show a dictionary sorted and grouped by value |
| >>> from operator import itemgetter |
| >>> d = dict(a=1, b=2, c=1, d=2, e=1, f=2, g=3) |
| >>> di = sorted(d.items(), key=itemgetter(1)) |
| >>> for k, g in groupby(di, key=itemgetter(1)): |
| ... print(k, map(itemgetter(0), g)) |
| ... |
| 1 ['a', 'c', 'e'] |
| 2 ['b', 'd', 'f'] |
| 3 ['g'] |
| |
| >>> # Find runs of consecutive numbers using groupby. The key to the solution |
| >>> # is differencing with a range so that consecutive numbers all appear in |
| >>> # same group. |
| >>> data = [ 1, 4,5,6, 10, 15,16,17,18, 22, 25,26,27,28] |
| >>> for k, g in groupby(enumerate(data), lambda t:t[0]-t[1]): |
| ... print(map(operator.itemgetter(1), g)) |
| ... |
| [1] |
| [4, 5, 6] |
| [10] |
| [15, 16, 17, 18] |
| [22] |
| [25, 26, 27, 28] |
| |
| |
| |
| .. _itertools-recipes: |
| |
| Recipes |
| ------- |
| |
| This section shows recipes for creating an extended toolset using the existing |
| itertools as building blocks. |
| |
| 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 :term:`generator`\s |
| which incur interpreter overhead. |
| |
| .. testcode:: |
| |
| def take(n, iterable): |
| "Return first n items of the iterable as a list" |
| return list(islice(iterable, n)) |
| |
| def enumerate(iterable, start=0): |
| return zip(count(start), iterable) |
| |
| def tabulate(function, start=0): |
| "Return function(0), function(1), ..." |
| return map(function, count(start)) |
| |
| def nth(iterable, n): |
| "Returns the nth item or None" |
| return next(islice(iterable, n, None), None) |
| |
| 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(iterable, n)) |
| |
| def dotproduct(vec1, vec2): |
| return sum(map(operator.mul, vec1, vec2)) |
| |
| def flatten(listOfLists): |
| return list(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) |
| for elem in b: |
| break |
| return zip(a, b) |
| |
| def grouper(n, iterable, fillvalue=None): |
| "grouper(3, 'ABCDEFG', '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 |
| pending = len(iterables) |
| nexts = cycle(iter(it).__next__ for it in iterables) |
| while pending: |
| try: |
| for next in nexts: |
| yield next() |
| except StopIteration: |
| pending -= 1 |
| nexts = cycle(islice(nexts, pending)) |
| |
| 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 iterable: |
| if element not in seen: |
| 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, imap(itemgetter(1), groupby(iterable, key))) |