޺iSSrSSKrSSKJrJr SSKJr SSKJr SSK J r J r J r SSK JrJr SSKJrJrJrJrJrJrJrJrJrJrJrJrJrJr SS KJ r J!r!J"r"J#r# SS K$J%r%J&r&J'r'J(r(J)r) SS KJ*r*J+r+J,r, SS K-J.r. /S Qr/\0"5r1\2"SS9 \ "\2SS9r3SSKJ5r6 SSK J8r8J9r9 Sr:Sr;S]SjrS^Sjr?S^Sjr@\A4SjrBSrC\CrDSrESrFSrGS^SjrHS rISS!KJJrK S"rJ\IR\Jl"S#S$\L5rMS%rNS&rOS_S'jrPS(rQS)rRS*rSS^S+jrTS^S,jrUS`S-jrVS^S.jrWSaS/jrXS0S1.S2jrYS^S3jrZS4r[S5r\S6r]S7r^S8r_S9r`S:raS;rbS<rcS=rdS>reS?rfSbS@jrgSArhSS.SBjri\.SC:aSSDKJjrk SS.SEjrj\iR\jlO\irjSFrl\m\n44SGjroSHrpSIrqSJrrSKrs\t"\h"SL55ruSMrvSNrwSOrxSPrySQrz/SRQr{\ SS5r|STr}\R"5RTrSUrSVrSWrSXrSYrSZrSS[.S\jrg!\4a \2r3GNf=f!\7a Sr6GNf=f!\7a Sr:GNf=f!\7a \IrJGNOf=f)caImported from the recipes section of the itertools documentation. All functions taken from the recipes section of the itertools library docs [1]_. Some backward-compatible usability improvements have been made. .. [1] http://docs.python.org/library/itertools.html#recipes N) bisect_leftinsort)dequesuppress) lru_cachepartialreduce)heappush heappushpop) accumulatechain combinationscompresscountcyclegroupbyisliceproductrepeatstarmap takewhiletee zip_longest)prodcombisqrtgcd)mulnot_ itemgettergetitemindex) randrangesamplechoice) hexversion)2 all_equalbatchedbefore_and_afterconsumeconvolve dotproduct first_truefactorflattengrouperis_prime iter_except iter_indexloopsmatmul multinomialncyclesnthnth_combinationpadnonepad_nonepairwise partitionpolynomial_evalpolynomial_from_rootspolynomial_derivativepowersetprependquantifyreshape#random_combination_with_replacementrandom_combinationrandom_permutationrandom_product repeatfunc roundrobinrunning_mediansievesliding_window subslicessum_of_squarestabulatetailtaketotient transpose triplewiseuniqueunique_everseenunique_justseenTstrict)sumprodc[X5$N)r-)xys U/var/www/piano.thomer.com/venv/lib/python3.13/site-packages/more_itertools/recipes.pyrbls Jq,) heappush_maxheappushpop_maxFc*[[X55$)zReturn first *n* items of the *iterable* as a list. >>> take(3, range(10)) [0, 1, 2] If there are fewer than *n* items in the iterable, all of them are returned. >>> take(10, range(3)) [0, 1, 2] )listr)niterables rarSrSxs x# $$rcc,[U[U55$)aReturn an iterator over the results of ``func(start)``, ``func(start + 1)``, ``func(start + 2)``... *func* should be a function that accepts one integer argument. If *start* is not specified it defaults to 0. It will be incremented each time the iterator is advanced. >>> square = lambda x: x ** 2 >>> iterator = tabulate(square, -3) >>> take(4, iterator) [9, 4, 1, 0] )mapr)functionstarts rarQrQs xu &&rcc[U5n[U[SX - 5S5$![a [ [ XS95s$f=f)zsReturn an iterator over the last *n* items of *iterable*. >>> t = tail(3, 'ABCDEFG') >>> list(t) ['E', 'F', 'G'] rNmaxlen)lenrmax TypeErroriterr)rhrisizes rarRrRsK88}hAtx 0$77 /E(-../s &AAcLUc [USS9 g[[XU5S5 g)aAdvance *iterable* by *n* steps. If *n* is ``None``, consume it entirely. Efficiently exhausts an iterator without returning values. Defaults to consuming the whole iterator, but an optional second argument may be provided to limit consumption. >>> i = (x for x in range(10)) >>> next(i) 0 >>> consume(i, 3) >>> next(i) 4 >>> consume(i) >>> next(i) Traceback (most recent call last): File "", line 1, in StopIteration If the iterator has fewer items remaining than the provided limit, the whole iterator will be consumed. >>> i = (x for x in range(3)) >>> consume(i, 5) >>> next(i) Traceback (most recent call last): File "", line 1, in StopIteration Nrro)rnextr)iteratorrhs rar+r+s'@ y hq! VH #T*rcc.[[XS5U5$)zmReturns the nth item or a default value. >>> l = range(10) >>> nth(l, 3) 3 >>> nth(l, 20, "zebra") 'zebra' N)rwr)rirhdefaults rar9r9s xD)7 33rcc@[X5nUH nUHn g g g)aw Returns ``True`` if all the elements are equal to each other. >>> all_equal('aaaa') True >>> all_equal('aaab') False A function that accepts a single argument and returns a transformed version of each input item can be specified with *key*: >>> all_equal('AaaA', key=str.casefold) True >>> all_equal([1, 2, 3], key=lambda x: x < 10) True FT)r)rikeyrxfirstseconds rar(r(s-$x%HF rcc*[[X55$)zWReturn the how many times the predicate is true. >>> quantify([True, False, True]) 2 )sumrk)ripreds rarDrDs s4" ##rcc,[U[S55$)zReturns the sequence of elements and then returns ``None`` indefinitely. >>> take(5, pad_none(range(3))) [0, 1, 2, None, None] Useful for emulating the behavior of the built-in :func:`map` function. See also :func:`padded`. N)rrris rar<r<s 6$< ((rccT[R"[[U5U55$)zjReturns the sequence elements *n* times >>> list(ncycles(["a", "b"], 3)) ['a', 'b', 'a', 'b', 'a', 'b'] )r from_iterablertuplerirhs rar8r8s    veHoq9 ::rcc4[[[X55$)zReturns the dot product of the two iterables. >>> dotproduct([10, 15, 12], [0.65, 0.80, 1.25]) 33.5 >>> 10 * 0.65 + 15 * 0.80 + 12 * 1.25 33.5 In Python 3.12 and later, use ``math.sumprod()`` instead. )rrkr)vec1vec2s rar-r-s s3# $$rcc.[R"U5$)zReturn an iterator flattening one level of nesting in a list of lists. >>> list(flatten([[0, 1], [2, 3]])) [0, 1, 2, 3] See also :func:`collapse`, which can flatten multiple levels of nesting. )rr) listOfListss rar0r0+s   { ++rcc\Uc[U[U55$[U[X!55$)a Call *func* with *args* repeatedly, returning an iterable over the results. If *times* is specified, the iterable will terminate after that many repetitions: >>> from operator import add >>> times = 4 >>> args = 3, 5 >>> list(repeatfunc(add, times, *args)) [8, 8, 8, 8] If *times* is ``None`` the iterable will not terminate: >>> from random import randrange >>> times = None >>> args = 1, 11 >>> take(6, repeatfunc(randrange, times, *args)) # doctest:+SKIP [2, 4, 8, 1, 8, 4] )rr)functimesargss rarJrJ7s,, }tVD\** 4, --rccJ[U5up[US5 [X5$)zReturns an iterator of paired items, overlapping, from the original >>> take(4, pairwise(count())) [(0, 1), (1, 2), (2, 3), (3, 4)] On Python 3.10 and above, this is an alias for :func:`itertools.pairwise`. Nrrwzip)riabs ra _pairwiserRs" x=DADM q9rc)r=c[U5$r^)itertools_pairwisers rar=r=fs !(++rcc,^\rSrSrSU4SjjrSrU=r$)UnequalIterablesErrorilcR>SnUbUSR"U6- n[TU] U5 g)Nz Iterables have different lengthsz/: index 0 has length {}; index {} has length {})formatsuper__init__)selfdetailsmsg __class__s rarUnequalIterablesError.__init__ms80   EMM C rcr^)__name__ __module__ __qualname____firstlineno__r__static_attributes__ __classcell__)rs@rarrls rcrc#x# [US[06H#nUHnU[LdM[5e Uv M% g7f)N fillvalue)r_markerr) iterablescombovals ra_zip_equal_generatorrws:i;7;Cg~+-- >> list(grouper('ABCDEF', 3)) [('A', 'B', 'C'), ('D', 'E', 'F')] The keyword arguments *incomplete* and *fillvalue* control what happens for iterables whose length is not a multiple of *n*. When *incomplete* is `'fill'`, the last group will contain instances of *fillvalue*. >>> list(grouper('ABCDEFG', 3, incomplete='fill', fillvalue='x')) [('A', 'B', 'C'), ('D', 'E', 'F'), ('G', 'x', 'x')] When *incomplete* is `'ignore'`, the last group will not be emitted. >>> list(grouper('ABCDEFG', 3, incomplete='ignore', fillvalue='x')) [('A', 'B', 'C'), ('D', 'E', 'F')] When *incomplete* is `'strict'`, a subclass of `ValueError` will be raised. >>> iterator = grouper('ABCDEFG', 3, incomplete='strict') >>> list(iterator) # doctest: +IGNORE_EXCEPTION_DETAIL Traceback (most recent call last): ... UnequalIterablesError fillrr[ignorez Expected fill, strict, or ignore)rtrrr ValueError)rirh incompleter iteratorss rar1r1s^:h 1$IVI;;;X9%%XI;<>> list(roundrobin('ABC', 'D', 'EF')) ['A', 'D', 'E', 'B', 'F', 'C'] This function produces the same output as :func:`interleave_longest`, but may perform better for some inputs (in particular when the number of iterables is small). rN)rkrtrangerqrrrw)rr num_actives rarKrKsLD)$IC NAr2 &78 tY'''3'sAAA AcUc[n[US5up#n[[X55upV[U[[U55[X654$)aw Returns a 2-tuple of iterables derived from the input iterable. The first yields the items that have ``pred(item) == False``. The second yields the items that have ``pred(item) == True``. >>> is_odd = lambda x: x % 2 != 0 >>> iterable = range(10) >>> even_items, odd_items = partition(is_odd, iterable) >>> list(even_items), list(odd_items) ([0, 2, 4, 6, 8], [1, 3, 5, 7, 9]) If *pred* is None, :func:`bool` is used. >>> iterable = [0, 1, False, True, '', ' '] >>> false_items, true_items = partition(None, iterable) >>> list(false_items), list(true_items) ([0, False, ''], [1, True, ' ']) )boolrrkrr )rrit1t2pp1p2s rar>r>sK( |Ha IBA T FB RT2 '")9 ::rcc^[U5m[R"U4Sj[[ T5S-555$)aYields all possible subsets of the iterable. >>> list(powerset([1, 2, 3])) [(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)] :func:`powerset` will operate on iterables that aren't :class:`set` instances, so repeated elements in the input will produce repeated elements in the output. >>> seq = [1, 1, 0] >>> list(powerset(seq)) [(), (1,), (1,), (0,), (1, 1), (1, 0), (1, 0), (1, 1, 0)] For a variant that efficiently yields actual :class:`set` instances, see :func:`powerset_of_sets`. c3<># UHn[TU5v M g7fr^)r).0rss ra powerset..sM;La|Aq11;Lr)rgrrrrq)rirs @rarBrBs2" XA   M5Q!;LM MMrcc## [5nURn/nURnUSLnUH(nU(aU"U5OUnX;aU"U5 Uv M(M* g![a X;aU"U5 Uv MKMNf=f7f)aJ Yield unique elements, preserving order. >>> list(unique_everseen('AAAABBBCCDAABBB')) ['A', 'B', 'C', 'D'] >>> list(unique_everseen('ABBCcAD', str.lower)) ['A', 'B', 'C', 'D'] Sequences with a mix of hashable and unhashable items can be used. The function will be slower (i.e., `O(n^2)`) for unhashable items. Remember that ``list`` objects are unhashable - you can use the *key* parameter to transform the list to a tuple (which is hashable) to avoid a slowdown. >>> iterable = ([1, 2], [2, 3], [1, 2]) >>> list(unique_everseen(iterable)) # Slow [[1, 2], [2, 3]] >>> list(unique_everseen(iterable, key=tuple)) # Faster [[1, 2], [2, 3]] Similarly, you may want to convert unhashable ``set`` objects with ``key=frozenset``. For ``dict`` objects, ``key=lambda x: frozenset(x.items())`` can be used. N)setaddappendrs) rir|seenset seenset_addseenlist seenlist_adduse_keyelementks rarXrXs6eG++KH??LoG#CL A     Q ! s)?A?AA?A<5A?;A<<A?c Uc[[S5[U55$[[[[S5[X555$)zYields elements in order, ignoring serial duplicates >>> list(unique_justseen('AAAABBBCCDAABBB')) ['A', 'B', 'C', 'D', 'A', 'B'] >>> list(unique_justseen('ABBCcAD', str.lower)) ['A', 'B', 'C', 'A', 'D'] rr)rkr!rrw)rir|s rarYrY's< {:a='("344 tSA(>? @@rcc([XUS9n[X1S9$)aYields unique elements in sorted order. >>> list(unique([[1, 2], [3, 4], [1, 2]])) [[1, 2], [3, 4]] *key* and *reverse* are passed to :func:`sorted`. >>> list(unique('ABBcCAD', str.casefold)) ['A', 'B', 'c', 'D'] >>> list(unique('ABBcCAD', str.casefold, reverse=True)) ['D', 'c', 'B', 'A'] The elements in *iterable* need not be hashable, but they must be comparable for sorting to work. )r|reverse)r|)sortedrY)rir|r sequenceds rarWrW6s x':I 9 ..rcc#t# [U5 Ub U"5v U"5v M !,(df  g=f7f)aYields results from a function repeatedly until an exception is raised. Converts a call-until-exception interface to an iterator interface. Like ``iter(func, sentinel)``, but uses an exception instead of a sentinel to end the loop. >>> l = [0, 1, 2] >>> list(iter_except(l.pop, IndexError)) [2, 1, 0] Multiple exceptions can be specified as a stopping condition: >>> l = [1, 2, 3, '...', 4, 5, 6] >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError))) [7, 6, 5] >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError))) [4, 3, 2] >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError))) [] Nr)r exceptionr}s rar3r3Js3, )   'M&L  s 8' 58c,[[X 5U5$)ad 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) == True`` . >>> first_true(range(10)) 1 >>> first_true(range(10), pred=lambda x: x > 5) 6 >>> first_true(range(10), default='missing', pred=lambda x: x > 9) 'missing' )rwfilter)rirzrs rar.r.gs" t& 00rcrrcnUVs/sHn[U5PM snU-n[SU55$s snf)aDraw an item at random from each of the input iterables. >>> random_product('abc', range(4), 'XYZ') # doctest:+SKIP ('c', 3, 'Z') If *repeat* is provided as a keyword argument, that many items will be drawn from each iterable. >>> random_product('abcd', range(4), repeat=2) # doctest:+SKIP ('a', 2, 'd', 3) This equivalent to taking a random selection from ``itertools.product(*args, repeat=repeat)``. c38# UHn[U5v M g7fr^)r&)rpools rar!random_product..s0%$%s)r)rrrpoolss rarIrI{s7 &* *TTU4[T *V 3E 0%0 00 +s2c`[U5nUc [U5OUn[[X!55$)aFReturn a random *r* length permutation of the elements in *iterable*. If *r* is not specified or is ``None``, then *r* defaults to the length of *iterable*. >>> random_permutation(range(5)) # doctest:+SKIP (3, 4, 0, 1, 2) This equivalent to taking a random selection from ``itertools.permutations(iterable, r)``. )rrqr%)rirrs rarHrHs+ ?DYD AA  !!rcc^[U5m[T5n[[[ U5U55n[U4SjU55$)zReturn a random *r* length subsequence of the elements in *iterable*. >>> random_combination(range(5), 3) # doctest:+SKIP (2, 3, 4) This equivalent to taking a random selection from ``itertools.combinations(iterable, r)``. c3.># UH nTUv M g7fr^rrrrs rar%random_combination..*'Qa')rrqrr%r)rirrhindicesrs @rarGrGs= ?D D AVE!Ha()G *'* **rcc^^[U5m[T5m[U4Sj[U555n[U4SjU55$)a;Return a random *r* length subsequence of elements in *iterable*, allowing individual elements to be repeated. >>> random_combination_with_replacement(range(3), 5) # doctest:+SKIP (0, 0, 1, 2, 2) This equivalent to taking a random selection from ``itertools.combinations_with_replacement(iterable, r)``. c3:># UHn[T5v M g7fr^)r$rrrhs rar6random_combination_with_replacement..s48aYq\\8sc3.># UH nTUv M g7fr^rrs rarrrr)rrqrr)rirrrhrs @@rarFrFs< ?D D A45844G *'* **rcc[U5n[U5nUS:dX:a[eSn[XU- 5n[ SUS-5HnXTU- U--U-nM US:aX%- nUS:dX%:a[ e/nU(aNXQ-U-US- US- pnX%:aX%-nXTU- -U-US- pEX%:aMUR USU- 5 U(aMN[U5$)aEquivalent to ``list(combinations(iterable, r))[index]``. The subsequences of *iterable* that are of length *r* can be ordered lexicographically. :func:`nth_combination` computes the subsequence at sort position *index* directly, without computing the previous subsequences. >>> nth_combination(range(5), 3, 5) (0, 3, 4) ``ValueError`` will be raised If *r* is negative or greater than the length of *iterable*. ``IndexError`` will be raised if the given *index* is invalid. rrr)rrqrminr IndexErrorr) rirr#rrhcrrresults rar:r:s ?D D A A15 A A1u A 1a!e_ QOq  qy   uz F %1*a!eQUaj JEA;!#QUqj  d26l# ! =rcc[U/U5$)aYield *value*, followed by the elements in *iterator*. >>> value = '0' >>> iterator = ['1', '2', '3'] >>> list(prepend(value, iterator)) ['0', '1', '2', '3'] To prepend multiple values, see :func:`itertools.chain` or :func:`value_chain`. )r)valuerxs rarCrCs %( ##rcc## [U5SSS2n[U5n[S/US9U-n[U[ SUS- 55H!nUR U5 [ X5v M# g7f)u-Discrete linear convolution of two iterables. Equivalent to polynomial multiplication. For example, multiplying ``(x² -x - 20)`` by ``(x - 3)`` gives ``(x³ -4x² -17x + 60)``. >>> list(convolve([1, -1, -20], [1, -3])) [1, -4, -17, 60] Examples of popular kinds of kernels: * The kernel ``[0.25, 0.25, 0.25, 0.25]`` computes a moving average. For image data, this blurs the image and reduces noise. * The kernel ``[1/2, 0, -1/2]`` estimates the first derivative of a function evaluated at evenly spaced inputs. * The kernel ``[1, -2, 1]`` estimates the second derivative of a function evaluated at evenly spaced inputs. 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. Supports all numeric types: int, float, complex, Decimal, Fraction. References: * Article: https://betterexplained.com/articles/intuitive-convolution/ * Video by 3Blue1Brown: https://www.youtube.com/watch?v=KuXjwB4LzSA Nrrror)rrqrrrr_sumprod)signalkernelrhwindowr_s rar,r,siF6]4R4 F F A A3q !A %F 66!QU+ , av&&-sA*A,c^[U5up#[[X5[U55nX#4$)aA variant of :func:`takewhile` that allows complete access to the remainder of the iterator. >>> it = iter('ABCdEfGhI') >>> all_upper, remainder = before_and_after(str.isupper, it) >>> ''.join(all_upper) 'ABC' >>> ''.join(remainder) # takewhile() would lose the 'd' 'dEfGhI' Note that the first iterator must be fully consumed before the second iterator can generate valid results. )rrrr) predicatertruesafters rar*r*&s,r7LE Yy0#e* =E <rcc[US5upn[US5 [US5 [US5 [XU5$)zReturn overlapping triplets from *iterable*. >>> list(triplewise('ABCDE')) [('A', 'B', 'C'), ('B', 'C', 'D'), ('C', 'D', 'E')] rNr)rirrt3s rarVrV9s;Xq!JBBTNTNTN rr?rcc|[X5n[U5Hup4[[XCU5S5 M [ U6$r^)rrrwrr)rirhrrrxs ra_sliding_window_islicer Is8H I +  VH #T*,  ?rcc## [U5n[[X!S- 5US9nUH!nURU5 [ U5v M# g7f)Nrro)rtrrrr)rirhrxrr_s ra_sliding_window_dequerQsCH~H 6(E*1 5F  aFmsA A cUS:a [X5$US:a [X5$US:Xa [U5$US:Xa [U5$[ SU35e)a=Return a sliding window of width *n* over *iterable*. >>> list(sliding_window(range(6), 4)) [(0, 1, 2, 3), (1, 2, 3, 4), (2, 3, 4, 5)] If *iterable* has fewer than *n* items, then nothing is yielded: >>> list(sliding_window(range(3), 4)) [] For a variant with more features, see :func:`windowed`. rzn should be at least one, not )rr r=rrrs rarNrNZs^ 2v$X11 Q%h22 a!! a8}9!=>>rcc [U5n[[[[ [ U5S-5S55n[ [[U5U5$)zReturn all contiguous non-empty subslices of *iterable*. >>> list(subslices('ABC')) [['A'], ['A', 'B'], ['A', 'B', 'C'], ['B'], ['B', 'C'], ['C']] This is similar to :func:`substrings`, but emits items in a different order. rr) rgrslicerrrqrkr"r)riseqslicess rarOrOss@ x.C ULs3x!|)>> roots = [5, -4, 3] # (x - 5) * (x + 4) * (x - 3) >>> polynomial_from_roots(roots) # x³ - 4 x² - 17 x + 60 [1, -4, -17, 60] Note that polynomial coefficients are specified in descending power order. Supports all numeric types: int, float, complex, Decimal, Fraction. r)rgr,)rootspolyroots rar@r@s1 3DHTAu:./ Krcc## [USS5nUc0[XU5n[XR5HupgXqLdXq:XdMUv M gUc [U5OUnUS- n[ [ 5 U"XS-U5=nv M!,(df  g=f7f)aYield the index of each place in *iterable* that *value* occurs, beginning with index *start* and ending before index *stop*. >>> list(iter_index('AABCADEAF', 'A')) [0, 1, 4, 7] >>> list(iter_index('AABCADEAF', 'A', 1)) # start index is inclusive [1, 4, 7] >>> list(iter_index('AABCADEAF', 'A', 1, 7)) # stop index is not inclusive [1, 4] The behavior for non-scalar *values* matches the built-in Python types. >>> list(iter_index('ABCDABCD', 'AB')) [0, 4] >>> list(iter_index([0, 1, 2, 3, 0, 1, 2, 3], [0, 1])) [] >>> list(iter_index([[0, 1], [2, 3], [0, 1], [2, 3]], [0, 1])) [0, 2] See :func:`locate` for a more general means of finding the indexes associated with particular values. r#Nr)getattrrrrqrr)rirrmstop seq_indexrxrrs rar4r4s2'40I(40#H4JA7#35 !% s8}$ AI j !%eUD99q:" !s4B -B 'A;; B B c #H# US:aSv Sn[S5US--n[USU[U5S-S9HLn[USXU-5ShvN [[ [ X3-XU-555X#U-XU-2'X3-nMN [USU5ShvN gNON7f)zYYield the primes less than n. >>> list(sieve(30)) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] rr)rrr)rN) bytearrayr4rbytesrqr)rhrmdatars rarMrMs 1u E V Q 'D aU1X\ :dAu!e444"'E!%E,B(C"DUQQ ;$5))) 5*s%A B"BA B"B B" B"c## US:a [S5e[U5n[[X155=n(aCU(a[ U5U:wa [S5eUv [[X155=n(aMBgg7f)arBatch data into tuples of length *n*. If the number of items in *iterable* is not divisible by *n*: * The last batch will be shorter if *strict* is ``False``. * :exc:`ValueError` will be raised if *strict* is ``True``. >>> list(batched('ABCDEFG', 3)) [('A', 'B', 'C'), ('D', 'E', 'F'), ('G',)] On Python 3.13 and above, this is an alias for :func:`itertools.batched`. rzn must be at least onezbatched(): incomplete batchN)rrtrrrq)rirhr[rxbatchs ra_batchedr%sp 1u122H~H,- -% - c%jAo:; ; ,- -% - -s A8A><A>i )r)c[XUS9$)NrZ)itertools_batched)rirhr[s rar)r)s V<>> list(transpose([(1, 2, 3), (11, 22, 33)])) [(1, 11), (2, 22), (3, 33)] The caller should ensure that the dimensions of the input are compatible. If the input is empty, no output will be produced. ) _zip_strictrs rarUrUs  rccP[U5 [X5$![a gf=f)z.Scalars are bytes, strings, and non-iterables.T)rtrs isinstance)r stringlikes ra _is_scalarr.s/ U  e (( s  %%c[U5n[U5n[U4U5n[ U5(aU$[R "U5nMC![a Us$f=f)z.Depth-first iterator over scalars in a tensor.)rtrw StopIterationrr.r)tensorrxrs ra_flatten_tensorr2 sgF|H  NE%8, e  O&&x0  O s A AAc[U[5(a [[R"U5U5$Utp#[ U5n[ [[U5U5n[XR5$)aChange the shape of a *matrix*. If *shape* is an integer, the matrix must be two dimensional and the shape is interpreted as the desired number of columns: >>> matrix = [(0, 1), (2, 3), (4, 5)] >>> cols = 3 >>> list(reshape(matrix, cols)) [(0, 1, 2), (3, 4, 5)] If *shape* is a tuple (or other iterable), the input matrix can have any number of dimensions. It will first be flattened and then rebuilt to the desired shape which can also be multidimensional: >>> matrix = [(0, 1), (2, 3), (4, 5)] # Start with a 3 x 2 matrix >>> list(reshape(matrix, (2, 3))) # Make a 2 x 3 matrix [(0, 1, 2), (3, 4, 5)] >>> list(reshape(matrix, (6,))) # Make a vector of length six [0, 1, 2, 3, 4, 5] >>> list(reshape(matrix, (2, 1, 3, 1))) # Make 2 x 1 x 3 x 1 tensor [(((0,), (1,), (2,)),), (((3,), (4,), (5,)),)] Each dimension is assumed to be uniform, either all arrays or all scalars. Flattening stops when the first value in a dimension is a scalar. Scalars are bytes, strings, and non-iterables. The reshape iterator stops when the requested shape is complete or when the input is exhausted, whichever comes first. ) r,intr)rrr2r reversedr)matrixshape first_dimdims scalar_streamreshapeds rarErEsYB%u**62E::I#F+Mgx~}=H ( &&rcc x[US5n[[[[ U[ U555U5$)a Multiply two matrices. >>> list(matmul([(7, 5), (3, 5)], [(2, 5), (7, 9)])) [(49, 80), (41, 60)] The caller should ensure that the dimensions of the input matrices are compatible with each other. Supports all numeric types: int, float, complex, Decimal, Fraction. r)rqr)rrrrU)m1m2rhs rar6r6@s0 BqE A 78WR2%?@! DDrcc[SU5HKnS=p#SnUS:Xa4X"-U-U-nX3-U-U-nX3-U-U-n[X#- U5nUS:XaM4X@:wdMIUs $ [S5e)Nrrzprime or under 5)rrr)rhrr_r`ds ra_factor_pollardrAOs1a[  1faAaAaAAE1 A 1f 6H ' ((rcc#># US:ag[H!nX-(aMUv X-nX-(dMM# /nUS:aU/O/nUH?nUS:d[U5(aURU5 M,[U5nX4X-4- nMA [ U5ShvN gN7f)zYield the prime factors of n. >>> list(factor(360)) [2, 2, 2, 3, 3, 5] Finds small factors with trial division. Larger factors are either verified as prime with ``is_prime`` or split into smaller factors with Pollard's rho algorithm. rNri)_primes_below_211r2rrAr)rhprimeprimestodofacts rar/r/bs 1u#))K KA))# Fa%A3RD  v:! MM! "1%D 19% %D  f~sBBA$BBBc [U5nUS:Xa[U5"S5$[[[ U5[ [ U555n[X5$)aEvaluate a polynomial at a specific value. Computes with better numeric stability than Horner's method. Evaluate ``x^3 - 4 * x^2 - 17 * x + 60`` at ``x = 2.5``: >>> coefficients = [1, -4, -17, 60] >>> x = 2.5 >>> polynomial_eval(coefficients, x) 8.125 Note that polynomial coefficients are specified in descending power order. Supports all numeric types: int, float, complex, Decimal, Fraction. r)rqtyperkpowrr5rr) coefficientsr_rhpowerss rar?r?sI LAAvAwqz fQi%(!3 4F L ))rcc$[[U56$)zReturn the sum of the squares of the input values. >>> sum_of_squares([10, 20, 30]) 1400 Supports all numeric types: int, float, complex, Decimal, Fraction. )rrr*s rarPrPs SW rcct[U5n[[SU55n[[ [ X55$)uCompute the first derivative of a polynomial. Evaluate the derivative of ``x³ - 4 x² - 17 x + 60``: >>> coefficients = [1, -4, -17, 60] >>> derivative_coefficients = polynomial_derivative(coefficients) >>> derivative_coefficients [3, -8, -17] Note that polynomial coefficients are specified in descending power order. Supports all numeric types: int, float, complex, Decimal, Fraction. r)rqr5rrgrkr)rLrhrMs rarArAs0 LA eAqk "F C. //rccJ[[U55H nXU--nM U$)uReturn the count of natural numbers up to *n* that are coprime with *n*. Euler's totient function φ(n) gives the number of totatives. Totative are integers k in the range 1 ≤ k ≤ n such that gcd(n, k) = 1. >>> n = 9 >>> totient(n) 6 >>> totatives = [x for x in range(1, n) if gcd(n, x) == 1] >>> totatives [1, 2, 4, 5, 7, 8] >>> len(totatives) 6 Reference: https://en.wikipedia.org/wiki/Euler%27s_totient_function )rr/)rhrEs rarTrTs&&VAY %Z Hrc))i)r)i)I)ltT7)r=)lay)r iS_)l;n>)rrrS )lp )rrrWrSrXrU)l)riEi$inii=ik)l%!Hn fW) rrrWrSrXrUrVrQ%)c~US- U- R5S- nX- nSU-U-U:XaUS-(aUS:deX4$)z#Return s, d such that 2**s * d == nrr) bit_length)rhrr@s ra _shift_to_oddr`sO a%1  "Q&A A Fa<1 Q161 1 4KrccUS:aUS-(aSUs=::aU:de e[US- 5up#[XU5nUS:XdX@S- :Xag[US- 5HnXD-U-nX@S- :XdM g g)NrrTF)r`rKr)rhbaserr@r__s ra_strong_probable_primerds EAAMM2 2M2 2 Q DA DQAAv!e 1q5\ EAI A: rcc^TS:aTS;$TS-(a2TS-(a(TS-(aTS-(aTS-(a TS-(dg [H upTU:dM O U4S j[S 55n[U4S jU55$) amReturn ``True`` if *n* is prime and ``False`` otherwise. Basic examples: >>> is_prime(37) True >>> is_prime(3 * 13) False >>> is_prime(18_446_744_073_709_551_557) True Find the next prime over one billion: >>> next(filter(is_prime, count(10**9))) 1000000007 Generate random primes up to 200 bits and up to 60 decimal digits: >>> from random import seed, randrange, getrandbits >>> seed(18675309) >>> next(filter(is_prime, map(getrandbits, repeat(200)))) 893303929355758292373272075469392561129886005037663238028407 >>> next(filter(is_prime, map(randrange, repeat(10**60)))) 269638077304026462407872868003560484232362454342414618963649 This function is exact for values of *n* below 10**24. For larger inputs, the probabilistic Miller-Rabin primality test has a less than 1 in 2**128 chance of a false positive. rY>rrrWrSrXrUrrrWrSrXrUFc3B># UHn[STS- 5v M g7f)rrN)_private_randrangers raris_prime..*s Ay!#Aq1u--ys@c3<># UHn[TU5v M g7fr^)rd)rrbrhs rarrh,sA54%a..5r)_perfect_testsrall)rhlimitbasess` rar2r2syB 2v((( Ea!eA!a%AFq2v&  u9 'BuRyA A5A AArcc[SU5$)zReturns an iterable with *n* elements for efficient looping. Like ``range(n)`` but doesn't create integers. >>> i = 0 >>> for _ in loops(5): ... i += 1 >>> i 5 Nr)rhs rar5r5/s $?rccH[[[[U5U55$)ueNumber of distinct arrangements of a multiset. The expression ``multinomial(3, 4, 2)`` has several equivalent interpretations: * In the expansion of ``(a + b + c)⁹``, the coefficient of the ``a³b⁴c²`` term is 1260. * There are 1260 distinct ways to arrange 9 balls consisting of 3 reds, 4 greens, and 2 blues. * There are 1260 unique ways to place 9 distinct objects into three bins with sizes 3, 4, and 2. The :func:`multinomial` function computes the length of :func:`distinct_permutations`. For example, there are 83,160 distinct anagrams of the word "abracadabra": >>> from more_itertools import distinct_permutations, ilen >>> ilen(distinct_permutations('abracadabra')) 83160 This can be computed directly from the letter counts, 5a 2b 2r 1c 1d: >>> from collections import Counter >>> list(Counter('abracadabra').values()) [5, 2, 2, 1, 1] >>> multinomial(5, 2, 2, 1, 1) 83160 A binomial coefficient is a special case of multinomial where there are only two categories. For example, the number of ways to arrange 12 balls with 5 reds and 7 blues is ``multinomial(5, 7)`` or ``math.comb(12, 5)``. Likewise, factorial is a special case of multinomial where the multiplicities are all just 1 so that ``multinomial(1, 1, 1, 1, 1, 1, 1) == math.factorial(7)``. Reference: https://en.wikipedia.org/wiki/Multinomial_theorem )rrkrr )countss rar7r7=sT D*V,f5 66rcc ## URn/n/n[[5 [U[ X1"555 USv [ U[ X!"555 USUS-S- v MM!,(df  g=f7f)z.Non-windowed running_median() for Python 3.14+rrN)__next__rr0rdr r rerxreadlohis ra#_running_median_minheap_and_maxheaprxjsz   D B B -  [TV4 5Q%K RTV4 5a52a5=A% %  ! s BAA11 A?;Bc ## URn/n/n[[5 [U[ X1"55*5 US*v [U[ X!"5*5*5 USUS- S- v MQ!,(df  g=f7f)zDBackport of non-windowed running_median() for Python 3.13 and prior.rrN)rsrr0r r rts ra_running_median_minheap_onlyrzzs   D B B -  R+b$&11 2a5&L R+b46'22 3a52a5=A% %  ! s BAA55 B?Bc# # [5n/nUHxnURU5 [X45 [U5U:a[ X2R 55nX5 [U5nUS-nUS-(aX7OX7S- X7-S- v Mz g7f)z+Yield median of values in a sliding window.rrN)rrrrqrpopleft)rxrprorderedr_rrhms ra_running_median_windowedrsWFG  aw w<& G^^%56A L FEgjA(Cq'HHsB Broc[U5nUb'[U5nUS::a [S5e[X!5$[(d [ U5$[ U5$)aCumulative median of values seen so far or values in a sliding window. Set *maxlen* to a positive integer to specify the maximum size of the sliding window. The default of *None* is equivalent to an unbounded window. For example: >>> list(running_median([5.0, 9.0, 4.0, 12.0, 8.0, 9.0])) [5.0, 7.0, 5.0, 7.0, 8.0, 8.5] >>> list(running_median([5.0, 9.0, 4.0, 12.0, 8.0, 9.0], maxlen=3)) [5.0, 7.0, 5.0, 9.0, 8.0, 9.0] Supports numeric types such as int, float, Decimal, and Fraction, but not complex numbers which are unorderable. On version Python 3.13 and prior, max-heaps are simulated with negative values. The negation causes Decimal inputs to apply context rounding, making the results slightly different than that obtained by statistics.median(). rzWindow size should be positive)rtr#rr_max_heap_availablerzrx)rirprxs rarLrLsV.H~H v Q;=> >'99  +H55 .x 88rc)rr^)rN)NF)NN)rN)__doc__randombisectrr collectionsr contextlibr functoolsrr r heapqr r itertoolsr rrrrrrrrrrrrrmathrrrroperatorrr r!r"r#r$r%r&sysr'__all__objectrrr)rsr\r ImportErrorrdrerrSrQrRr+r9r(rrDr<r;r8r-r0rJrr=rrrrrr1rKr>rBrXrYrWr3r.rIrHrGrFr:rCr,r*rVr rrNrOr@r4rMr%r)r'rUstrr!r.r2rEr6rArrDr/r?rPrArTrkr`rdRandomrgr2r5r7rxrzrrLrrcrars&00' ('::,,3 j (,t#d+K-( 3 % '$ 8 %+P 44!$ ) ; % ,.6  )8 ,!((HJ / %=P($;8N**Z A/(:1("#1("$ + +"'T $('V&  ?2 -,&;R**%*(6',=&&GOG #&u) 1&'R E ) %*%B*.0& 2   &]]_..-B` *7Z & & I&(,"9w)K-,H-  `HsHH HH(H7 HH H%$H%(H43H47II