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(starmap(operator.mul, zip(vec1, vec2, strict=True)))
.
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, n 
(p0, p1, …, p_n1), … 


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]), … 


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


predicate, seq 
elements of seq where predicate(elem) fails 


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

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


iterable 
(p[0], p[1]), (p[1], p[2]) 


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


predicate, seq 
seq[0], seq[1], until predicate 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 
Examples 
Results 









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, *, initial=None])¶
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
.)Usually, the number of elements output matches the input iterable. However, if the keyword argument initial is provided, the accumulation leads off with the initial value so that the output has one more element than the input iterable.
Roughly equivalent to:
def accumulate(iterable, func=operator.add, *, initial=None): 'Return running totals' # accumulate([1,2,3,4,5]) → 1 3 6 10 15 # accumulate([1,2,3,4,5], initial=100) → 100 101 103 106 110 115 # accumulate([1,2,3,4,5], operator.mul) → 1 2 6 24 120 it = iter(iterable) total = initial if initial is None: 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:>>> 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 10 annual payments of 90 >>> account_update = lambda bal, pmt: round(bal * 1.05) + pmt >>> list(accumulate(repeat(90, 10), account_update, initial=1_000)) [1000, 960, 918, 874, 828, 779, 728, 674, 618, 559, 497]
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.
Changed in version 3.8: Added the optional initial parameter.
 itertools.batched(iterable, n)¶
Batch data from the iterable into tuples of length n. The last batch may be shorter than n.
Loops over the input iterable and accumulates data into tuples up to size n. The input is consumed lazily, just enough to fill a batch. The result is yielded as soon as the batch is full or when the input iterable is exhausted:
>>> flattened_data = ['roses', 'red', 'violets', 'blue', 'sugar', 'sweet'] >>> unflattened = list(batched(flattened_data, 2)) >>> unflattened [('roses', 'red'), ('violets', 'blue'), ('sugar', 'sweet')] >>> for batch in batched('ABCDEFG', 3): ... print(batch) ... ('A', 'B', 'C') ('D', 'E', 'F') ('G',)
Roughly equivalent to:
def batched(iterable, n): # batched('ABCDEFG', 3) → ABC DEF G if n < 1: raise ValueError('n must be at least one') it = iter(iterable) while batch := tuple(islice(it, n)): yield batch
New in version 3.12.
 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.
The combination tuples are emitted in lexicographic ordering according to the order of the input iterable. So, if the input iterable is sorted, the output 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 repeated 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.
The combination tuples are emitted in lexicographic ordering according to the order of the input iterable. So, if the input iterable is sorted, the output 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 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 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): 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 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.If start is
None
, then iteration starts at zero. If step isNone
, then the step defaults to one.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
 itertools.pairwise(iterable)¶
Return successive overlapping pairs taken from the input iterable.
The number of 2tuples in the output iterator will be one fewer than the number of inputs. It will be empty if the input iterable has fewer than two values.
Roughly equivalent to:
def pairwise(iterable): # pairwise('ABCDEFG') → AB BC CD DE EF FG iterator = iter(iterable) a = next(iterator, None) for b in iterator: yield a, b a = b
New in version 3.10.
 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.The permutation tuples are emitted in lexicographic order according to the order of the input iterable. So, if the input iterable is sorted, the output 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 repeated values within a 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)
Before
product()
runs, it completely consumes the input iterables, keeping pools of values in memory to generate the products. Accordingly, it is only useful with finite inputs.
 itertools.repeat(object[, times])¶
Make an iterator that returns object over and over again. Runs indefinitely unless the times argument is specified.
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 (when the data has been “prezipped”).The difference between
map()
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
Note, the element that first fails the predicate condition is consumed from the input iterator and there is no way to access it. This could be an issue if an application wants to further consume the input iterator after takewhile has been run to exhaustion. To work around this problem, consider using moreiterools before_and_after() instead.
 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):
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 a
tee()
has been created, 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. ARuntimeError
may be raised when simultaneously using iterators returned by the sametee()
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 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:
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)
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
.
Itertools Recipes¶
This section shows recipes for creating an extended toolset using the existing itertools as building blocks.
The primary purpose of the itertools recipes is educational. The recipes show
various ways of thinking about individual tools — for example, that
chain.from_iterable
is related to the concept of flattening. The recipes
also give ideas about ways that the tools can be combined — for example, how
starmap()
and repeat()
can work together. The recipes also show patterns
for using itertools with the operator
and collections
modules as
well as with the builtin itertools such as map()
, filter()
,
reversed()
, and enumerate()
.
A secondary purpose of the recipes is to serve as an incubator. The
accumulate()
, compress()
, and pairwise()
itertools started out as
recipes. Currently, the sliding_window()
, iter_index()
, and sieve()
recipes are being tested to see whether they prove their worth.
Substantially all of these recipes and many, many others can be installed from the moreitertools project found on the Python Package Index:
python m pip install moreitertools
Many of the recipes offer the same high performance as the underlying toolset. 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. High speed is retained by preferring “vectorized” building blocks over the use of forloops and generators which incur interpreter overhead.
import collections
import functools
import math
import operator
import random
def take(n, iterable):
"Return first n items of the iterable as a list."
return list(islice(iterable, n))
def prepend(value, iterable):
"Prepend a single value in front of an iterable."
# prepend(1, [2, 3, 4]) → 1 2 3 4
return chain([value], iterable)
def tabulate(function, start=0):
"Return function(0), function(1), ..."
return map(function, count(start))
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 flatten(list_of_lists):
"Flatten one level of nesting."
return chain.from_iterable(list_of_lists)
def ncycles(iterable, n):
"Returns the sequence elements n times."
return chain.from_iterable(repeat(tuple(iterable), n))
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 quantify(iterable, predicate=bool):
"Given a predicate that returns True or False, count the True results."
return sum(map(predicate, iterable))
def first_true(iterable, default=False, predicate=None):
"Returns the first true value or the *default* if there is no true value."
# 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(predicate, iterable), default)
def all_equal(iterable, key=None):
"Returns True if all the elements are equal to each other."
# all_equal('4٤໔４৪', key=int) → True
return len(take(2, groupby(iterable, key))) <= 1
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.casefold) → A B c A D
if key is None:
return map(operator.itemgetter(0), groupby(iterable))
return map(next, map(operator.itemgetter(1), groupby(iterable, key)))
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.casefold) → A B c D
seen = set()
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 sliding_window(iterable, n):
"Collect data into overlapping fixedlength chunks or blocks."
# sliding_window('ABCDEFG', 4) → ABCD BCDE CDEF DEFG
it = iter(iterable)
window = collections.deque(islice(it, n1), maxlen=n)
for x in it:
window.append(x)
yield tuple(window)
def grouper(iterable, n, *, incomplete='fill', fillvalue=None):
"Collect data into nonoverlapping fixedlength chunks or blocks."
# grouper('ABCDEFG', 3, fillvalue='x') → ABC DEF Gxx
# grouper('ABCDEFG', 3, incomplete='strict') → ABC DEF ValueError
# grouper('ABCDEFG', 3, incomplete='ignore') → ABC DEF
iterators = [iter(iterable)] * n
match incomplete:
case 'fill':
return zip_longest(*iterators, fillvalue=fillvalue)
case 'strict':
return zip(*iterators, strict=True)
case 'ignore':
return zip(*iterators)
case _:
raise ValueError('Expected fill, strict, or ignore')
def roundrobin(*iterables):
"Visit input iterables in a cycle until each is exhausted."
# roundrobin('ABC', 'D', 'EF') → A D E B F C
# Algorithm credited to George Sakkis
iterators = map(iter, iterables)
for num_active in range(len(iterables), 0, 1):
iterators = cycle(islice(iterators, num_active))
yield from map(next, iterators)
def partition(predicate, iterable):
"""Partition entries into false entries and true entries.
If *predicate* is slow, consider wrapping it with functools.lru_cache().
"""
# partition(is_odd, range(10)) → 0 2 4 6 8 and 1 3 5 7 9
t1, t2 = tee(iterable)
return filterfalse(predicate, t1), filter(predicate, t2)
def subslices(seq):
"Return all contiguous nonempty subslices of a sequence."
# subslices('ABCD') → A AB ABC ABCD B BC BCD C CD D
slices = starmap(slice, combinations(range(len(seq) + 1), 2))
return map(operator.getitem, repeat(seq), slices)
def iter_index(iterable, value, start=0, stop=None):
"Return indices where a value occurs in a sequence or iterable."
# iter_index('AABCADEAF', 'A') → 0 1 4 7
seq_index = getattr(iterable, 'index', None)
if seq_index is None:
# Path for general iterables
it = islice(iterable, start, stop)
for i, element in enumerate(it, start):
if element is value or element == value:
yield i
else:
# Path for sequences with an index() method
stop = len(iterable) if stop is None else stop
i = start
try:
while True:
yield (i := seq_index(value, i, stop))
i += 1
except ValueError:
pass
def iter_except(func, exception, first=None):
""" Call a function repeatedly until an exception is raised.
Converts a calluntilexception interface to an iterator interface.
"""
# iter_except(d.popitem, KeyError) → nonblocking dictionary iterator
try:
if first is not None:
yield first()
while True:
yield func()
except exception:
pass
The following recipes have a more mathematical flavor:
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 sum_of_squares(iterable):
"Add up the squares of the input values."
# sum_of_squares([10, 20, 30]) → 1400
return math.sumprod(*tee(iterable))
def reshape(matrix, cols):
"Reshape a 2D matrix to have a given number of columns."
# reshape([(0, 1), (2, 3), (4, 5)], 3) → (0, 1, 2), (3, 4, 5)
return batched(chain.from_iterable(matrix), cols)
def transpose(matrix):
"Swap the rows and columns of a 2D matrix."
# transpose([(1, 2, 3), (11, 22, 33)]) → (1, 11) (2, 22) (3, 33)
return zip(*matrix, strict=True)
def matmul(m1, m2):
"Multiply two matrices."
# matmul([(7, 5), (3, 5)], [(2, 5), (7, 9)]) → (49, 80), (41, 60)
n = len(m2[0])
return batched(starmap(math.sumprod, product(m1, transpose(m2))), n)
def convolve(signal, kernel):
"""Discrete linear convolution of two iterables.
Equivalent to polynomial multiplication.
Convolutions are mathematically commutative; however, the inputs are
evaluated differently. The signal is consumed lazily and can be
infinite. The kernel is fully consumed before the calculations begin.
Article: https://betterexplained.com/articles/intuitiveconvolution/
Video: https://www.youtube.com/watch?v=KuXjwB4LzSA
"""
# convolve([1, 1, 20], [1, 3]) → 1 4 17 60
# convolve(data, [0.25, 0.25, 0.25, 0.25]) → Moving average (blur)
# convolve(data, [1/2, 0, 1/2]) → 1st derivative estimate
# convolve(data, [1, 2, 1]) → 2nd derivative estimate
kernel = tuple(kernel)[::1]
n = len(kernel)
padded_signal = chain(repeat(0, n1), signal, repeat(0, n1))
windowed_signal = sliding_window(padded_signal, n)
return map(math.sumprod, repeat(kernel), windowed_signal)
def polynomial_from_roots(roots):
"""Compute a polynomial's coefficients from its roots.
(x  5) (x + 4) (x  3) expands to: x³ 4x² 17x + 60
"""
# polynomial_from_roots([5, 4, 3]) → [1, 4, 17, 60]
factors = zip(repeat(1), map(operator.neg, roots))
return list(functools.reduce(convolve, factors, [1]))
def polynomial_eval(coefficients, x):
"""Evaluate a polynomial at a specific value.
Computes with better numeric stability than Horner's method.
"""
# Evaluate x³ 4x² 17x + 60 at x = 5
# polynomial_eval([1, 4, 17, 60], x=5) → 0
n = len(coefficients)
if not n:
return type(x)(0)
powers = map(pow, repeat(x), reversed(range(n)))
return math.sumprod(coefficients, powers)
def polynomial_derivative(coefficients):
"""Compute the first derivative of a polynomial.
f(x) = x³ 4x² 17x + 60
f'(x) = 3x² 8x 17
"""
# polynomial_derivative([1, 4, 17, 60]) → [3, 8, 17]
n = len(coefficients)
powers = reversed(range(1, n))
return list(map(operator.mul, coefficients, powers))
def sieve(n):
"Primes less than n."
# sieve(30) → 2 3 5 7 11 13 17 19 23 29
if n > 2:
yield 2
start = 3
data = bytearray((0, 1)) * (n // 2)
limit = math.isqrt(n) + 1
for p in iter_index(data, 1, start, limit):
yield from iter_index(data, 1, start, p*p)
data[p*p : n : p+p] = bytes(len(range(p*p, n, p+p)))
start = p*p
yield from iter_index(data, 1, start)
def factor(n):
"Prime factors of n."
# factor(99) → 3 3 11
# factor(1_000_000_000_000_007) → 47 59 360620266859
# factor(1_000_000_000_000_403) → 1000000000000403
for prime in sieve(math.isqrt(n) + 1):
while not n % prime:
yield prime
n //= prime
if n == 1:
return
if n > 1:
yield n
def totient(n):
"Count of natural numbers up to n that are coprime to n."
# https://mathworld.wolfram.com/TotientFunction.html
# totient(12) → 4 because len([1, 5, 7, 11]) == 4
for p in unique_justseen(factor(n)):
n = n // p
return n