: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 *
.. versionadded:: 2.3
This module implements a number of :term:`iterator` building blocks inspired
by constructs from APL, Haskell, and SML. 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. Together, they form an "iterator
algebra" making it possible to construct 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), ...``. The same effect can be achieved in Python
by combining :func:`imap` and :func:`count` to form ``imap(f, count())``.
These tools and their built-in counterparts also work well with the high-speed
functions in the :mod:`operator` module. For example, the multiplication
operator can be mapped across two vectors to form an efficient dot-product:
``sum(imap(operator.mul, vector1, vector2))``.
**Infinite Iterators:**
================== ================= ================================================= =========================================
Iterator Arguments Results Example
================== ================= ================================================= =========================================
:func:`count` start, [step] start, start+step, start+2*step, ... ``count(10) --> 10 11 12 13 14 ...``
:func:`cycle` p p0, p1, ... plast, p0, p1, ... ``cycle('ABCD') --> A B C D A B C D ...``
:func:`repeat` elem [,n] elem, elem, elem, ... endlessly or up to n times ``repeat(10, 3) --> 10 10 10``
================== ================= ================================================= =========================================
**Iterators terminating on the shortest input sequence:**
==================== ============================ ================================================= =============================================================
Iterator Arguments Results Example
==================== ============================ ================================================= =============================================================
:func:`chain` p, q, ... p0, p1, ... plast, q0, q1, ... ``chain('ABC', 'DEF') --> A B C D E F``
:func:`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``
:func:`dropwhile` pred, seq seq[n], seq[n+1], starting when pred fails ``dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1``
:func:`groupby` iterable[, keyfunc] sub-iterators grouped by value of keyfunc(v)
:func:`ifilter` pred, seq elements of seq where pred(elem) is true ``ifilter(lambda x: x%2, range(10)) --> 1 3 5 7 9``
:func:`ifilterfalse` pred, seq elements of seq where pred(elem) is false ``ifilterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8``
:func:`islice` seq, [start,] stop [, step] elements from seq[start:stop:step] ``islice('ABCDEFG', 2, None) --> C D E F G``
:func:`imap` func, p, q, ... func(p0, q0), func(p1, q1), ... ``imap(pow, (2,3,10), (5,2,3)) --> 32 9 1000``
:func:`starmap` func, seq func(\*seq[0]), func(\*seq[1]), ... ``starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000``
:func:`tee` it, n it1, it2, ... itn splits one iterator into n
:func:`takewhile` pred, seq seq[0], seq[1], until pred fails ``takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4``
:func:`izip` p, q, ... (p[0], q[0]), (p[1], q[1]), ... ``izip('ABCD', 'xy') --> Ax By``
:func:`izip_longest` p, q, ... (p[0], q[0]), (p[1], q[1]), ... ``izip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-``
==================== ============================ ================================================= =============================================================
**Combinatoric generators:**
============================================== ==================== =============================================================
Iterator Arguments Results
============================================== ==================== =============================================================
:func:`product` p, q, ... [repeat=1] cartesian product, equivalent to a nested for-loop
:func:`permutations` p[, r] r-length tuples, all possible orderings, no repeated elements
:func:`combinations` p, r r-length tuples, in sorted order, no repeated elements
:func:`combinations_with_replacement` p, r r-length tuples, in sorted order, with repeated elements
``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``
============================================== ==================== =============================================================
.. _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.
Roughly equivalent to::
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)
Alternate constructor for :func:`chain`. Gets chained inputs from a
single iterable argument that is evaluated lazily. Roughly equivalent to::
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
.. versionadded:: 2.6
.. 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.
Roughly 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 = 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)
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``.
.. versionadded:: 2.6
.. 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.
Roughly 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 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)
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:: 2.7
.. 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 has been exhausted.
Roughly equivalent to::
def compress(data, selectors):
# compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F
return (d for d, s in izip(data, selectors) if s)
.. versionadded:: 2.7
.. function:: count(start=0, step=1)
Make an iterator that returns evenly spaced values starting with *n*. Often
used as an argument to :func:`imap` to generate consecutive data points.
Also, used with :func:`izip` to add sequence numbers. Equivalent to::
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
When counting with floating point numbers, better accuracy can sometimes be
achieved by substituting multiplicative code such as: ``(start + step * i
for i in count())``.
.. versionchanged:: 2.7
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. Roughly 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. 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
.. 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 roughly 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)
.. versionadded:: 2.4
.. function:: ifilter(predicate, iterable)
Make an iterator that filters elements from iterable returning only those for
which the predicate is ``True``. If *predicate* is ``None``, return the items
that are true. Roughly equivalent to::
def ifilter(predicate, iterable):
# ifilter(lambda x: x%2, range(10)) --> 1 3 5 7 9
if predicate is None:
predicate = bool
for x in iterable:
if predicate(x):
yield x
.. function:: ifilterfalse(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 ifilterfalse(predicate, iterable):
# ifilterfalse(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:: imap(function, *iterables)
Make an iterator that computes the function using arguments from each of the
iterables. If *function* is set to ``None``, then :func:`imap` returns the
arguments as a tuple. Like :func:`map` but stops when the shortest iterable is
exhausted instead of filling in ``None`` for shorter iterables. The reason for
the difference is that infinite iterator arguments are typically an error for
:func:`map` (because the output is fully evaluated) but represent a common and
useful way of supplying arguments to :func:`imap`. Roughly equivalent to::
def imap(function, *iterables):
# imap(pow, (2,3,10), (5,2,3)) --> 32 9 1000
iterables = map(iter, iterables)
while True:
args = [next(it) for it in iterables]
if function is None:
yield tuple(args)
else:
yield function(*args)
.. function:: islice(iterable, stop)
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). 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.maxint, s.step or 1
it = iter(xrange(start, stop, step)))
try:
nexti = next(it)
except StopIteration:
# Consume *iterable* up to the *start* position.
for i, element in izip(xrange(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 izip(xrange(i + 1, stop), iterable):
pass
If *start* is ``None``, then iteration starts at zero. If *step* is ``None``,
then the step defaults to one.
.. versionchanged:: 2.5
accept ``None`` values for default *start* and *step*.
.. function:: izip(*iterables)
Make an iterator that aggregates elements from each of the iterables. Like
:func:`zip` except that it returns an iterator instead of a list. Used for
lock-step iteration over several iterables at a time. Roughly equivalent to::
def izip(*iterables):
# izip('ABCD', 'xy') --> Ax By
iterators = map(iter, iterables)
while iterators:
yield tuple(map(next, iterators))
.. versionchanged:: 2.4
When no iterables are specified, returns a zero length iterator instead of
raising a :exc:`TypeError` exception.
The left-to-right evaluation order of the iterables is guaranteed. This
makes possible an idiom for clustering a data series into n-length groups
using ``izip(*[iter(s)]*n)``.
:func:`izip` should only be used with unequal length inputs when you don't
care about trailing, unmatched values from the longer iterables. If those
values are important, use :func:`izip_longest` instead.
.. function:: izip_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. Roughly equivalent to::
class ZipExhausted(Exception):
pass
def izip_longest(*args, **kwds):
# izip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-
fillvalue = kwds.get('fillvalue')
counter = [len(args) - 1]
def sentinel():
if not counter[0]:
raise ZipExhausted
counter[0] -= 1
yield fillvalue
fillers = repeat(fillvalue)
iterators = [chain(it, sentinel(), fillers) for it in args]
try:
while iterators:
yield tuple(map(next, iterators))
except ZipExhausted:
pass
If one of the iterables is potentially infinite, then the
:func:`izip_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``.
.. versionadded:: 2.6
.. 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.
Roughly 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 = 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``.
.. versionadded:: 2.6
.. function:: product(*iterables[, repeat])
Cartesian product of input iterables.
Roughly 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 roughly equivalent to the following code, except that the
actual implementation does not build up intermediate results in memory::
def product(*args, **kwds):
# 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) * kwds.get('repeat', 1)
result = [[]]
for pool in pools:
result = [x+[y] for x in result for y in pool]
for prod in result:
yield tuple(prod)
.. versionadded:: 2.6
.. 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:`imap` for
invariant function parameters. Also used with :func:`izip` to create constant
fields in a tuple record. Roughly 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 xrange(times):
yield object
A common use for *repeat* is to supply a stream of constant values to *imap*
or *zip*::
>>> list(imap(pow, xrange(10), repeat(2)))
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
.. function:: starmap(function, iterable)
Make an iterator that computes the function using arguments obtained from
the iterable. Used instead of :func:`imap` when argument parameters are already
grouped in tuples from a single iterable (the data has been "pre-zipped"). The
difference between :func:`imap` and :func:`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)
.. versionchanged:: 2.6
Previously, :func:`starmap` required the function arguments to be tuples.
Now, any iterable is allowed.
.. function:: 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
.. function:: tee(iterable[, n=2])
Return *n* independent iterators from a single iterable. Roughly equivalent to::
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
newval = next(it) # fetch a new value and
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 :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.
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
:func:`list` instead of :func:`tee`.
.. versionadded:: 2.4
.. _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 tabulate(function, start=0):
"Return function(0), function(1), ..."
return imap(function, count(start))
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(imap(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(imap(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 izip(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 izip_longest(fillvalue=fillvalue, *args)
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 ifilterfalse(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 imap(next, imap(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 __builtin__.iter(func, sentinel) but uses an exception instead
of a sentinel to end the loop.
Examples:
bsddbiter = iter_except(db.next, bsddb.error, db.first)
heapiter = iter_except(functools.partial(heappop, h), IndexError)
dictiter = iter_except(d.popitem, KeyError)
dequeiter = iter_except(d.popleft, IndexError)
queueiter = iter_except(q.get_nowait, Queue.Empty)
setiter = iter_except(s.pop, KeyError)
"""
try:
if first is not None:
yield first()
while 1:
yield func()
except exception:
pass
def random_product(*args, **kwds):
"Random selection from itertools.product(*args, **kwds)"
pools = map(tuple, args) * kwds.get('repeat', 1)
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(xrange(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 xrange(r))
return tuple(pool[i] for i in indices)
def tee_lookahead(t, i):
"""Inspect the i-th upcomping value from a tee object
while leaving the tee object at its current position.
Raise an IndexError if the underlying iterator doesn't
have enough values.
"""
for value in islice(t.__copy__(), i, None):
return value
raise IndexError(i)
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, imap=imap, mul=operator.mul):
return sum(imap(mul, vec1, vec2))