+ CiShRt^RIt^RIHtHt^RIHt^RIHt^RI H t H t H t ^RI HtHt^RIHtHtHtHtHtHtHtHtHtHtHtHtHtHt^RIH t H!t!H"t"H#t#^R I$H%t%H&t&H't'H(t(H)t)^R IH*t*H+t+H,t,^R I-H.t..R NR NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'NR(NR)NR*NR+NR,NR-NR.NR/NR0NR1NR2NR3NR4NR5NR6NR7NR8NR9NR:NR;NRR?7] !]2R>R?7t3^R@IH5t6^RBI H8t8H9t9R>t:RDt;RREltRRHlt?RRIlt@]A3RJltBRKtC]CtDRLtERMtFRNtGRROltHRPtI^RQIHJtKRRtJ]IP]Jn!RSRT]L4tMRUtNRVtORRWltPRXtQRYtRRZtSRR[ltTRR\ltURR]ltVRR^ltWRR_ltXR`^/RaltYRRbltZRct[Rdt\Ret]Rft^Rgt_Rht`RitaRjtbRktcRltdRmteRntfRRoltgRpthRqRC/Rrlti].Rs8d ^RtIHjtkRqRC/Rultj]iP]jnM]itjRvtl]m]n33RwltoRxtpRytqRztrR{ts]t!]h!^44tuR|tvR}twR~txRtyRtz.ROt{] R4t|Rt}]P!4PTtRtRtRtRtRtRtRR/RltR# ]4d]2t3ELi;i ]7dRAt6ELi;i ]7dRCt:ELi;i ]7d]ItJELUi;i)aImported 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 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\W4#N)r,)xys&&8/usr/lib/python3/dist-packages/more_itertools/recipes.pyrals Jq,) heappush_maxheappushpop_maxFc*\\W44#)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&&r`rRrRxs x# $$rbc,\V\V44#)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&&r`rPrPs xu &&rbc\V4p\V\^W , 4R4# \d\ \ YR74u#i;i)zsReturn an iterator over the last *n* items of *iterable*. >>> t = tail(3, 'ABCDEFG') >>> list(t) ['E', 'F', 'G'] Nmaxlen)lenrmax TypeErroriterr)rgrhsizes&& r`rQrQsK88}hAtx 0$77 /E(-../s * A  A cXVf\V^R7R#\\WV4R4R#)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 Nrn)rnextr)iteratorrgs&&r`r*r*s'@ y hq! VH #T*rbc.\\WR4V4#)zmReturns the nth item or a default value. >>> l = range(10) >>> nth(l, 3) 3 >>> nth(l, 20, "zebra") 'zebra' N)rvr)rhrgdefaults&&&r`r8r8s xD)7 33rbcF\W4pVFpVFpR# R# R#)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)rhkeyrwfirstseconds&& r`r'r's-$x%HF rbc*\\W44#)zWReturn the how many times the predicate is true. >>> quantify([True, False, True]) 2 )sumrj)rhpreds&&r`rCrCs s4" ##rbc,\V\R44#)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)r rrhs&r`r;r;s 6$< ((rbcT\P!\\V4V44#)zjReturns the sequence elements *n* times >>> list(ncycles(["a", "b"], 3)) ['a', 'b', 'a', 'b', 'a', 'b'] )r from_iterablertuplerhrgs&&r`r7r7s    veHoq9 ::rbc4\\\W44#)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. )rrjr)vec1vec2s&&r`r,r,s s3# $$rbc.\P!V4#)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. )r r) listOfListss&r`r/r/+s   { ++rbc^Vf\V\V44#\V\W!44#)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&&*r`rIrI7s,, }tVD\** 4, --rbcJ\V4wr\VR4\W4#)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`. Nrrvzip)rhabs& r` _pairwiserRs" x=DADM q9rb)r<c\V4#r])itertools_pairwisers&r`r<r<fs !(++rbc6aa]tRtRtoRV3RlltRtVtV;t#)UnequalIterablesErrorilc`<RpVeVRP!V!, p\SV` V4R#)z Iterables have different lengthsNz/: index 0 has length {}; index {} has length {})formatsuper__init__)selfdetailsmsg __class__s&& r`rUnequalIterablesError.__init__ms80   EMM C rbr])__name__ __module__ __qualname____firstlineno__r__static_attributes____classdictcell__ __classcell__)r __classdict__s@@r`rrlsrbrc#|"\VR\/F$pVFpV\JgK\4h VxK& R#5i) fillvalueN)r_markerr) iterablescombovals& r`_zip_equal_generatorrws:i;7;Cg~+-- >> list(grouper('ABCDEF', 3)) [('A', 'B', 'C'), ('D', 'E', 'F')] The keyword arguments *incomplete* and *fillvalue* control what happens for iterables whose length is not a multiple of *n*. When *incomplete* is `'fill'`, the last group will contain instances of *fillvalue*. >>> list(grouper('ABCDEFG', 3, incomplete='fill', fillvalue='x')) [('A', 'B', 'C'), ('D', 'E', 'F'), ('G', 'x', 'x')] When *incomplete* is `'ignore'`, the last group will not be emitted. >>> list(grouper('ABCDEFG', 3, incomplete='ignore', fillvalue='x')) [('A', 'B', 'C'), ('D', 'E', 'F')] When *incomplete* is `'strict'`, a subclass of `ValueError` will be raised. >>> iterator = grouper('ABCDEFG', 3, incomplete='strict') >>> list(iterator) # doctest: +IGNORE_EXCEPTION_DETAIL Traceback (most recent call last): ... UnequalIterablesError fillrrZignorez Expected fill, strict, or ignore)rsrrr ValueError)rhrg incompleter iteratorss&&&& r`r0r0s^:h 1$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). N)rjrsrangerprrrv)rr num_actives* r`rJrJsLD)$IC NAr2 &78 tY'''3'sAA A A cVf\p\V^4wr#p\\W44wrV\V\\V44\W643#)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, ' ']) )boolrrjrr)rrht1t2pp1p2s&& r`r=r=sK( |Ha IBA T FB RT2 '")9 ::rbca\V4o\P!V3Rl\\ S4^,444#)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<<"TFp\SV4xK R#5ir])r).0rss& r` powerset..sM;La|Aq11;L)rfr rrrp)rhrs&@r`rArAs2" XA   M5Q!;LM MMrbc# "\4pVPp.pVPpVRJpVF*pV'd V!V4MTpW9dV!V4VxK*K, R# \dY9dT!T4TxKPKSi;i5i)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)setaddappendrr) rhr{seenset seenset_addseenlist seenlist_adduse_keyelementks && r`rWrWs6eG++KH??LoG#CL A     Q ! s*ABABB:BBBc Vf\\^4\V44#\\\\^4\W444#)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'] )rjr rrv)rhr{s&&r`rXrX's< {:a='("344 tSA(>? @@rbc4\WVR7p\W1R7#)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{)sortedrX)rhr{r sequenceds&&& r`rVrV6s x':I 9 ..rbc#"\V4;_uu_4Ve V!4xV!4xK +'giR#;i5i)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&&&r`r2r2Js4, )    'M&L   sA0 A Ac,\\W 4V4#)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' )rvfilter)rhryrs&&&r`r-r-gs" t& 00rbrcVUu.uFp\V4NK upV,p\;QJd.RV4FNK 5#!RV44#uupi)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"TFp\V4xK R#5ir])r%)rpools& r`r!random_product..s0%$%s)r)rrrpoolss$* r`rHrH{sH &* *TTU4[T *V 3E 50%05050%0 00 +sAcb\V4pVf \V4MTp\\W!44#)aFReturn a random *r* length permutation of the elements in *iterable*. If *r* is not specified or is ``None``, then *r* defaults to the length of *iterable*. >>> random_permutation(range(5)) # doctest:+SKIP (3, 4, 0, 1, 2) This equivalent to taking a random selection from ``itertools.permutations(iterable, r)``. )rrpr$)rhrrs&& r`rGrGs+ ?DYD AA  !!rbca\V4o\S4p\\\ V4V44p\;QJd.V3RlV4FNK 5#!V3RlV44#)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)``. c36<"TFpSV,xK R#5ir]rrrrs& r`r%random_combination..*'Qa')rrprr$r)rhrrgindicesrs&& @r`rFrFsN ?D D AVE!Ha()G 5*'*5*5*'* **rbcaa\V4o\S4o\V3Rl\V444p\;QJd.V3RlV4FNK 5#!V3RlV44#)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:<"TFp\S4xK R#5ir])r#rrrgs& r`r6random_combination_with_replacement..s48aYq\\8sc36<"TFpSV,xK R#5ir]rrs& r`rrrr)rrprr)rhrrrgrs&& @@r`rErEsM ?D D A45844G 5*'*5*5*'* **rbc6\V4p\V4pV^8gW8d\h^p\WV, 4p\ ^V^,4F pWTV, V,,V,pK" V^8d W%, pV^8gW%8d\ h.pV'dpWQ,V,V^, V^, rpW%8d)W%,pWTV, ,V,V^, rEK.VP VRV, ,4Kw\V4#)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. r)rrprminr IndexErrorr) rhrr"rrgcrrresults &&& r`r9r9s ?D D A A15 A A1u A 1a!e_ QOq  qy   uz F %1*a!eQUaj JEA;!#QUq d26l# =rbc\V.V4#)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 )valuerws&&r`rBrBs %( ##rbc#"\V4RRR1,p\V4p\^.VR7V,p\V\ ^V^, 44F!pVP V4\ W4xK# R#5i)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 Nrnr)rrprr rr_sumprod)signalkernelrgwindowr^s&& r`r+r+siF6]4R4 F F A A3q !A %F 66!QU+ , av&&-sA:A<c^\V4wr#\\W4\V44pW#3#)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&& r`r)r)&s,r7LE Yy0#e* =E <rbc\V^4wrp\VR4\VR4\VR4\WV4#)zReturn overlapping triplets from *iterable*. >>> list(triplewise('ABCDE')) [('A', 'B', 'C'), ('B', 'C', 'D'), ('C', 'D', 'E')] Nr)rhrrt3s& r`rUrU9s;Xq!JBBTNTNTN rr?rbc~\W4p\V4Fwr4\\WCV4R4K \ V!#r])rrrvrr)rhrgrrrws&& r`_sliding_window_islicer Is8H I +  VH #T*,  ?rbc#"\V4p\\W!^, 4VR7pVF!pVPV4\ V4xK# R#5i)rrnN)rsrrrr)rhrgrwrr^s&& r`_sliding_window_dequerQsCH~H 6(E*1 5F  aFmsAAcV^8d \W4#V^8d \W4#V^8Xd \V4#V^8Xd \V4#\ RV 24h)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`. zn should be at least one, not )rr r<rrrs&&r`rMrMZs^ 2v$X11 Q%h22 a!! a8}9!=>>rbc \V4p\\\\ \ V4^,4^44p\ \\V4V4#)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. ) rfrslicerrrprjr!r)rhseqslicess& r`rNrNss@ 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. )rfr+)rootspolyroots& r`r?r?s1 3DHTAu:./ Krbc#L"\VRR4pVf4\WV4p\WR4FwrgWqJg Wq8XgKVxK R#Vf \V4MTpV^, p\ \ 4;_uu_4V!W^,V4;pxK +'giR#;i5i)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"N)getattrrrrprr)rhrrlstop seq_indexrwrrs&&&& r`r3r3s2'40I(40#H4JA7#35 !% s8}$ AI j ! !%eUD99q:" ! !s6B$;B$8B B!  B$c #"V^8d^x^p\R4V^,,p\V^V\V4^,R7Fdp\V^WV,4RjxL \\ \ W3,WV,444W#V,WV,1&W3,pKf \V^V4RjxL R#LdL5i)zYYield the primes less than n. >>> list(sieve(30)) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] )rN)rr) bytearrayr3rbytesrpr)rgrldatars& r`rLrLs 1u E V Q 'D aU1X\ :dAu!e444"'E!%E,B(C"DUQQ ;$5))) 5*s%A C "C#AC C C  C rZc#"V^8d \R4h\V4p\\W144;p'd*V'd\ V4V8wd \R4hVxKER#5i)arBatch data into tuples of length *n*. If the number of items in *iterable* is not divisible by *n*: * The last batch will be shorter if *strict* is ``False``. * :exc:`ValueError` will be raised if *strict* is ``True``. >>> list(batched('ABCDEFG', 3)) [('A', 'B', 'C'), ('D', 'E', 'F'), ('G',)] On Python 3.13 and above, this is an alias for :func:`itertools.batched`. zn must be at least onezbatched(): incomplete batchN)rrsrrrp)rhrgrZrwbatchs&&$ r`_batchedr#s[ 1u122H~H,- -% - c%jAo:; ;  .s AA'#A'i )r(c\WVR7#)rY)itertools_batched)rhrgrZs&&$r`r(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&r`rTrTs  rbcT\V4\Y4# \dR#i;i)z.Scalars are bytes, strings, and non-iterables.T)rsrr isinstance)r stringlikes&&r` _is_scalarr,s/ U  e (( s  ''c\V4p\V4p\T3T4p\ T4'dT#\P !T4pKE \dTu#i;i)z.Depth-first iterator over scalars in a tensor.)rsrv StopIterationr r,r)tensorrwrs& r`_flatten_tensorr0 sbF|H  NE%8, e  O&&x0  O s A A! A!c\V\4'd!\\P!V4V4#Vvr#\ V4p\ \\V4V4p\WR4#)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(r rr0r reversedr)matrixshape first_dimdims scalar_streamreshapeds&& r`rDrDsYB%u**62E::I#F+Mgx~}=H ( &&rbc \V^,4p\\\\ V\ V444V4#)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. )rpr(rrrrT)m1m2rgs&& r`r5r5@s0 BqE A 78WR2%?@! DDrbc\^V4Fop^;r#^pV^8XdWW",V,V,pW3,V,V,pW3,V,V,p\W#, V4pK]W@8wgKmVu# \R4h)rzprime or under 5)rrr)rgrr^r_ds& r`_factor_pollardr?Osy1a[  1faAaAaAAE1 A 6H ' ((rbc#V"V^8dR#\FpW,'dKVxW,pK .pV^8dV.M.pVFIpVR8g\V4'dVPV4K.\V4pW4W,3, pKK \ V4RjxL R#L5i)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. Ni)_primes_below_211r1rr?r)rgprimeprimestodofacts& r`r.r.bs 1u#))K KA# Fa%A3RD  v:! MM! "1%D 19% %D  f~sB)A;B) B'!B)c \V4pV^8Xd\V4!^4#\\\ V4\ \ V444p\W4#)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. )rptyperjpowrr3rr) coefficientsr^rgpowerss&& r`r>r>sI LAAvAwqz fQi%(!3 4F L ))rbc&\\V4!#)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&r`rOrOs SW rbct\V4p\\^V44p\\ \ W44#)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. )rpr3rrfrjr)rIrgrJs& r`r@r@s0 LA eAqk "F C. //rbcZ\\V44FpWV,,pK V#)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.)rgrBs& r`rSrSs&&VAY %Z HrbcV^, V, P4^, pW, p^V,V,V8XdV^,'dV^8gQhW3#)z#Return s, d such that 2**s * d == n) bit_length)rgrr>s& r` _shift_to_oddrPsQ a%1  "Q&A A Fa<1 Q161 1 4Krbc6V^8d"V^,'d^Tu;8:d V8gQhQh\V^, 4wr#\WV4pV^8XgW@^, 8XdR#\V^, 4F"pWD,V,pW@^, 8XgK!R# R#)TF)rPrHr)rgbaserr>r^_s&& r`_strong_probable_primerUs EAAMM2 2M2 2 Q DA DQAAv!e 1q5\ EAI A: rbcaS^8dSR9#S^,'dLS^,'d=S^,'d.S^,'dS^ ,'dS^ ,'gR#\FwrSV8gKM V3Rl\^@44p\;QJdV3RlV4F 'dK R# R#!V3RlV44#)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. Fc3J<"TFp\^S^, 4xK R#5i)rRN)_private_randrangers& r`ris_prime..*s Ay!#Aq1u--ys #c3<<"TFp\SV4xK R#5ir])rU)rrSrgs& r`rrY,sA54%a..5rT>rR )_perfect_testsrall)rglimitbasessf r`r1r1sB 2v((( EEa!eeA!a%%AFFq2vv&  u9 'BuRyA 3A5A33A3A3A5A AArbc\RV4#)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 N)r)rgs&r`r4r4/s $?rbcH\\\\V4V44#)ueNumber of distinct arrangements of a multiset. The expression ``multinomial(3, 4, 2)`` has several equivalent interpretations: * In the expansion of ``(a + b + c)⁹``, the coefficient of the ``a³b⁴c²`` term is 1260. * There are 1260 distinct ways to arrange 9 balls consisting of 3 reds, 4 greens, and 2 blues. * There are 1260 unique ways to place 9 distinct objects into three bins with sizes 3, 4, and 2. The :func:`multinomial` function computes the length of :func:`distinct_permutations`. For example, there are 83,160 distinct anagrams of the word "abracadabra": >>> from more_itertools import distinct_permutations, ilen >>> ilen(distinct_permutations('abracadabra')) 83160 This can be computed directly from the letter counts, 5a 2b 2r 1c 1d: >>> from collections import Counter >>> list(Counter('abracadabra').values()) [5, 2, 2, 1, 1] >>> multinomial(5, 2, 2, 1, 1) 83160 A binomial coefficient is a special case of multinomial where there are only two categories. For example, the number of ways to arrange 12 balls with 5 reds and 7 blues is ``multinomial(5, 7)`` or ``math.comb(12, 5)``. Likewise, factorial is a special case of multinomial where the multiplicities are all just 1 so that ``multinomial(1, 1, 1, 1, 1, 1, 1) == math.factorial(7)``. Reference: https://en.wikipedia.org/wiki/Multinomial_theorem )rrjrr )countss*r`r6r6=sT D*V,f5 66rbc #F"VPp.p.p\\4;_uu_4\V\ W1!444V^,x\ V\ W!!444V^,V^,,^, xKb +'giR#;i5i)z.Non-windowed running_median() for Python 3.14+N)__next__rr.rcr r rdrwreadlohis& r`#_running_median_minheap_and_maxheaprmjs{   D B B -  [TV4 5Q%K RTV4 5a52a5=A% % ! s(B!A#B  B  B!c #N"VPp.p.p\\4;_uu_4\V\ W1!44)4V^,)x\V\ W!!4)4)4V^,V^,, ^, xKf +'giR#;i5i)zDBackport of non-windowed running_median() for Python 3.13 and prior.N)rhrr.r r ris& r`_running_median_minheap_onlyrozs   D B B -  R+b$&11 2a5&L R+b46'22 3a52a5=A% % ! s(B%A'B B"  B%c#f"\4p.pVFpVPV4\W44\V4V8d\ W2P 44pW5\V4pV^,pV^,'d W7,M"W7^, ,W7,,^, xK R#5i)z+Yield median of values in a sliding window.N)rrrrprpopleft)rwrororderedr^rrgms&& r`_running_median_windowedrtsWFG  aw w<& G^^%56A L FEEgjA(Cq'HHsB/B1roc\V4pVe)\V4pV^8:d \R4h\W!4#\'g \ V4#\ V4#)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(). zWindow size should be positive)rsr"rrt_max_heap_availablerorm)rhrorws&$ r`rKrKsV.H~H v Q;=> >'99  +H55 .x 88rb)rr])rN)NF)NN)rN))i)rR)i)I)ltT7)rRr]=)lay)rRr_iS_)l;n>)rRr[r\r]r^)lp )rRr[r\r]r^r_)l)rRiEi$inii=ik)l%!Hn fW) rRr[r\r]r^r_rzrw%))__doc__randombisectrr collectionsr contextlibr functoolsrrr heapqr r itertoolsr r rrrrrrrrrrrrmathrrrroperatorrrr r!r"r#r$r%sysr&__all__objectrrr'rrr[r ImportErrorrcrdrvrRrPrQr*r8r'rrCr;r:r7r,r/rIrr<rrrrrr0rJr=rArWrXrVr2r-rHrGrFrEr9rBr+r)rUr rrMrNr?r3rLr#r(r%rTstrrr,r0rDr5r?rrAr.r>rOr@rSr`rPrURandomrXr1r4r6rmrortrKrrbr`rs&00' ('::,,3 3  3 3  3   3   3 3  3 3 3 3 3 3  3  3  !3 "#3 $ %3 &'3 ()3 *+3 ,-3 ./3 013 233 453 673 893 :;3 <=3 >*?3 @A3 BC3 DE3 FG3 HI3 JK3 L M3 NO3 PQ3 RS3 TU3 V W3 X Y3 Z[3 \]3 ^_3 ` a3 bc3 de3 j (,t#d+K-( 3 % '$ 8 %+P 44!$ ) ; % ,.6  )8 ,!((HJ / %=P($;8N**Z A/(:1(11("$ + +"'T $('V&  ?2 -,&;R**E(6=u=&&GOG #&u) 1&'R E ) %*%B*.0& 2   &]]_..-B` *7Z & & I&"9t"9w)K-,H-  `HsH% I39JJJ$3 J?J JJ J! 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