10.1. itertools
— Functions creating iterators for efficient looping¶
This module implements a number of 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 map()
and count()
to form map(f, count())
.
These tools and their builtin counterparts also work well with the highspeed
functions in the operator
module. For example, the multiplication
operator can be mapped across two vectors to form an efficient dotproduct:
sum(map(operator.mul, vector1, vector2))
.
Infinite iterators:
Iterator 
Arguments 
Results 
Example 

start, [step] 
start, start+step, start+2*step, … 


p 
p0, p1, … plast, p0, p1, … 


elem [,n] 
elem, elem, elem, … endlessly or up to n times 

Iterators terminating on the shortest input sequence:
Iterator 
Arguments 
Results 
Example 

p [,func] 
p0, p0+p1, p0+p1+p2, … 


p, q, … 
p0, p1, … plast, q0, q1, … 


iterable 
p0, p1, … plast, q0, q1, … 


data, selectors 
(d[0] if s[0]), (d[1] if s[1]), … 


pred, seq 
seq[n], seq[n+1], starting when pred fails 


pred, seq 
elements of seq where pred(elem) is false 


iterable[, key] 
subiterators grouped by value of key(v) 

seq, [start,] stop [, step] 
elements from seq[start:stop:step] 


func, seq 
func(*seq[0]), func(*seq[1]), … 


pred, seq 
seq[0], seq[1], until pred fails 


it, n 
it1, it2, … itn splits one iterator into n 

p, q, … 
(p[0], q[0]), (p[1], q[1]), … 

Combinatoric iterators:
Iterator 
Arguments 
Results 

p, q, … [repeat=1] 
cartesian product, equivalent to a nested forloop 

p[, r] 
rlength tuples, all possible orderings, no repeated elements 

p, r 
rlength tuples, in sorted order, no repeated elements 

p, r 
rlength tuples, in sorted order, with repeated elements 












10.1.1. 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.

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
orFraction
.) If the input iterable is empty, the output iterable will also be empty.Roughly equivalent to:
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
There are a number of uses for the func argument. It can be set to
min()
for a running minimum,max()
for a running maximum, oroperator.mul()
for a running product. Amortization tables can be built by accumulating interest and applying payments. Firstorder recurrence relations can be modeled by supplying the initial value in the iterable and using only the accumulated total in func argument:>>> 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']
See
functools.reduce()
for a similar function that returns only the final accumulated value.New in version 3.2.
Changed in version 3.3: Added the optional func parameter.

itertools.
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
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

itertools.
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 = 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[j1] + 1 yield tuple(pool[i] for i in indices)
The code for
combinations()
can be also expressed as a subsequence ofpermutations()
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! / (nr)!
when0 <= r <= n
or zero whenr > n
.

itertools.
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
combinations_with_replacement()
can be also expressed as a subsequence ofproduct()
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+r1)! / r! / (n1)!
whenn > 0
.New in version 3.1.

itertools.
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 zip(data, selectors) if s)
New in version 3.1.

itertools.
count
(start=0, step=1)¶ Make an iterator that returns evenly spaced values starting with number start. Often used as an argument to
map()
to generate consecutive data points. Also, used withzip()
to add sequence numbers. Roughly 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())
.Changed in version 3.1: Added step argument and allowed noninteger arguments.

itertools.
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).

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 startup 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 isNone
, 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 theuniq
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 thegroupby()
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()
is roughly equivalent to: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): 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 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 nonzero, 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 multiline 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 isNone
, 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 fulllength 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 = list(range(n)) cycles = list(range(n, nr, 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
permutations()
can be also expressed as a subsequence ofproduct()
, 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! / (nr)!
when0 <= r <= n
or zero whenr > n
.

itertools.
product
(*iterables, repeat=1)¶ Cartesian product of input iterables.
Roughly equivalent to nested forloops 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 asproduct(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 withzip()
to create an invariant part of 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 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 “prezipped”). The difference betweenmap()
andstarmap()
parallels the distinction betweenfunction(a,b)
andfunction(*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 queue).
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 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.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 oftee()
.

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 filledin with fillvalue. Iteration continues until the longest iterable is exhausted. Roughly equivalent to:
class ZipExhausted(Exception): pass def zip_longest(*args, **kwds): # zip_longest('ABCD', 'xy', fillvalue='') > Ax By C D fillvalue = kwds.get('fillvalue') counter = len(args)  1 def sentinel(): nonlocal counter if not counter: raise ZipExhausted counter = 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
zip_longest()
function should be wrapped with something that limits the number of calls (for exampleislice()
ortakewhile()
). If not specified, fillvalue defaults toNone
.
10.1.2. Itertools 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 forloops and generators 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 nsteps 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 zerolength 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 builtin 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 fixedlength 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 calluntilexception 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) # nonblocking dict iterator
iter_except(d.popleft, IndexError) # nonblocking deque iterator
iter_except(q.get_nowait, Queue.Empty) # loop over a producer Queue
iter_except(s.pop, KeyError) # nonblocking 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, nr)
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, n1, r1
while index >= c:
index = c
c, n = c*(nr)//n, n1
result.append(pool[1n])
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))