+ iTRt^RIt^RIHtHt^RIHt^RIHt^RI H t ^RI H t H t ^RIHtHt^RIHtHtHtHtHtHtHtHtHtHtHtHtHtH t H!t!H"t"^R I#H$t$H%t%H&t&H't'^R I(H)t)H*t*H+t,H-t-H.t.H/t/^R IH0t0H1t1H2t2H3t3^R I4H5t5.R NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'NR(NR)NR*NR+NR,NR-NR.NR/NR0NR1NR2NR3NR4NR5NR6NR7NR8NR9NR:NR;NRNR?NR@NRANRBNRCNRDNt6]7!4t8^REIH9t9H:t:RFt;RHt=RRIlt>RJt?RRKlt@RRLltARRMltB]C3RNltDROtE]EtFRPtGRQtH^RRI#HItJRStKRRTltLRUtRRVltMRWtNRXtORYtPRRZltQRR[ltRRR\ltSRR]ltTRR^ltUR_^/R`ltVRRaltWRbtXRctYRdtZRet[Rft\Rgt]Rht^Rit_Rjt`RktaRltbRmtcRRnltdRoteRpRG/Rqltf]5Rr8d ^RsIHgthRpRG/Rtltg]fP]gnM]ftgRuti]j]k33RvltlRwtmRxtnRytoRztp]q!]e!^44trR{tsR|ttR}tuR~tvRtw.ROtx] R4tyRtz]P!4P`t|Rt}Rt~RtRtRtRtRR/RltRtRR/RltRtRR/RltRtRR/Rlt] !RFRFR7!RR 44tRR/RltRtR# ]<dRGt;ELi;i ]<d]HtJELmi;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) dataclass) lru_cachereduce)heappush heappushpop) accumulatechain combinationscompresscountcycle filterfalsegroupbyislicepairwiseproductrepeatstarmap takewhiletee zip_longest)prodcombisqrtgcd)mulgetitemindexis_ itemgettertruediv) randrangesamplechoiceshuffle) hexversionStats all_equalbatchedbefore_and_afterconsumeconvolve dotproduct first_truefactorflattengrouperis_prime iter_except iter_indexloopsmatmul multinomialncyclesnthnth_combinationpadnonepad_noner partitionpolynomial_evalpolynomial_from_rootspolynomial_derivativepowersetprependquantifyreshape#random_combination_with_replacementrandom_combinationrandom_derangementrandom_permutationrandom_product repeatfunc roundrobin running_max running_meanrunning_median running_minrunning_statisticssievesliding_window subslicessum_of_squarestabulatetailtaketotient transpose triplewiseuniqueunique_everseenunique_justseen) heappush_maxheappushpop_maxTFc*\\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&&6lib/python3.14/site-packages/more_itertools/recipes.pyr[r[qs x# $$c,\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&&rhrYrYs xu &&ric\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)rfrgsizes&& rhrZrZsK88}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 Nro)rnextr)iteratorrfs&&rhr/r/s'@ y hq! VH #T*ric.\\WR4V4#)zmReturns the nth item or a default value. >>> l = range(10) >>> nth(l, 3) 3 >>> nth(l, 20, "zebra") 'zebra' N)rwr)rgrfdefaults&&&rhr=r=s xD)7 33ricF\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)rgkeyrxfirstseconds&& rhr,r,s-$x%HF ric*\\W44#)zWReturn the how many times the predicate is true. >>> quantify([True, False, True]) 2 )sumrk)rgpreds&&rhrGrGs s4" ##ric,\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 rrgs&rhr@r@s 6$< ((ricT\P!\\V4V44#)zjReturns the sequence elements *n* times >>> list(ncycles(["a", "b"], 3)) ['a', 'b', 'a', 'b', 'a', 'b'] )r from_iterablertuplergrfs&&rhr<r< s    veHoq9 ::ric4\\\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. )rrkr )vec1vec2s&&rhr1r1s s3# $$ri)sumprodc.\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) list_of_listss&rhr4r4+s   } --ric^Vf\V\V44#\V\W!44#)aCall *function* 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)rltimesargss&&*rhrNrN7s,, }x.. 8VD0 11ric\V4#)z Wrapper for :func:`itertools.pairwise`. .. warning:: This function is deprecated as of version 11.0.0. It will be removed in a future major release. )itertools_pairwisers&rhrrRs h ''ric\V4.V,pT;R8Xd \VRV/#;R8Xd \VRR/#R8Xd \V!#\R4h)ajGroup elements from *iterable* into fixed-length groups of length *n*. >>> 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 `ValueError` will be raised. >>> iterator = grouper('ABCDEFG', 3, incomplete='strict') >>> list(iterator) # doctest: +IGNORE_EXCEPTION_DETAIL Traceback (most recent call last): ... ValueError fill fillvaluestrictTignorez Expected fill, strict, or ignore)rtrzip ValueError)rgrf incompleter iteratorss&&&& rhr5r5^sZ:h 1$I   ?Y? ?  /$/ /  ? " ?@ @ric'"\\V4p\\V4^R4F/p\ \ W44p\\ V4RjxL K1 R#L 5i)a/Visit input iterables in a cycle until each is exhausted. >>> 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)rkrtrangerqrrrw) iterablesr num_actives* rhrOrOsLD)$IC NAr2 &78 tY'''3'sAA A A caaaaSf\o\V4o\4o\4oVVVV3RlpV!S4V!S43#)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, ' ']) c3<"V'dVP4xKSF%pS!V4'dSMSPV4KF R#5i)TN)popleftappend)queuevalue false_queuerxr true_queues& rhgenpartition..gensBmmo%!#E{{ CCEJ"s AAA)boolrtr)rrgrrrxrsf& @@@rhrArAsF( |H~H'KJ { S_ ,,rica\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#5iN)r).0rss& rh powerset..sM;La|Aq11;L)rer rrrq)rgrs&@rhrErEs2" XA   M5Q!;LM MMric#"\4pVf5\VPV4FpVPV4VxK R#VF(pV!V4pWB9gKVPV4VxK* R#5i)aYield unique elements, preserving order. Remember all elements ever seen. >>> list(unique_everseen('AAAABBBCCDAABBB')) ['A', 'B', 'C', 'D'] >>> list(unique_everseen('ABBCcAD', str.casefold)) ['A', 'B', 'C', 'D'] Raises ``TypeError`` for unhashable items. Some unhashable objects can be converted to hashable objects using the *key* parameter: * For ``list`` objects, try ``key=tuple``. * For ``set`` objects, try ``key=frozenset``. * For ``dict`` objects, try ``key=lambda x: frozenset(x.items())`` or in Python 3.15 and later, set ``key=frozendict``. Alternatively, consider the ``unique()`` itertool recipe. It sorts the data and then uses equality to eliminate duplicates. Hashability is not required. N)setr __contains__add)rgr|seenelementks&& rhr`r`sf. 5D {"4#4#4h?G HHW M@ GG A}   s AA5A5c 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'] )rkr$rrw)rgr|s&&rhraras< {:a='("344 tSA(>? @@ric4\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|)sortedra)rgr|r sequenceds&&& rhr_r_ s x':I 9 ..ric#"\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(function, 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)rl exceptionr}s&&&rhr7r7s5, )    'M*    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' )rwfilter)rgrzrs&&&rhr2r2:s" t& 00rirct\\\V44V,p\\\V44#)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)``. )rrkr()rrpoolss$* rhrMrMNs, #eY' (6 1E VU# $$ricb\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)``. )rrqr')rgrpools&& rhrLrLbs+ ?DYD AA  !!ric\V4p\V4p\\\ V4V44p\VUu.uF qRV,NK up4#uupi)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)``. )rrqrr'r)rgrrrfindicesis&& rhrJrJtsL ?D D AVE!Ha()G 7+7aq''7+ ,,+sAca\V4p\V4o\V3Rl\V444p\VUu.uF qBV,NK up4#uupi)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&rrrfs& rhr6random_combination_with_replacement..s48aYq\\8s)rrqrr)rgrrrrrfs&& @rhrIrIsL ?D D A45844G 7+7aq''7+ ,,+sAc\V4p\V4p\WA4pV^8d W%, p^Tu;8:dV8g\h\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. ``IndexError`` will be raised if the given *index* is invalid. r)rrqr IndexErrorr)rgrr"rrfcresults&&& rhr>r>s ?D D A Q A qy  >>  F %1*a!eQUaj JEA;!#QUq d26l# =ric\V.V4#)aYield *value*, followed by the elements in *iterable*. >>> value = '0' >>> iterable = ['1', '2', '3'] >>> list(prepend(value, iterable)) ['0', '1', '2', '3'] To prepend multiple values, see :func:`itertools.chain` or :func:`value_chain`. )r )rrgs&&rhrFrFs %( ##ric#"\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 Nror)rrqrr rr_sumprod)signalkernelrfwindowxs&& rhr0r0siF6]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) predicateittruesafters&& rhr.r.s,r7LE Yy0#e* =E <ric\V^4wrp\VR4\VR4\VR4\WV4#)zReturn overlapping triplets from *iterable*. >>> list(triplewise('ABCDE')) [('A', 'B', 'C'), ('B', 'C', 'D'), ('C', 'D', 'E')] N)rrwr)rgt1t2t3s& rhr^r^s;Xq!JBBTNTNTN rr?ric~\W4p\V4Fwr4\\WCV4R4K \ V!#r)r enumeraterwrr)rgrfrrrxs&& rh_sliding_window_islicers8H I +  VH #T*,  ?ric#"\V4p\\W!^, 4VR7pVF!pVPV4\ V4xK# R#5i)roN)rtrrrr)rgrfrxrrs&& rh_sliding_window_dequersCH~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 )rrrrrrs&&rhrVrV%s^ 2v$X11 Q%h22 a!! a8}9!=>>ric \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. ) rerslicerrrqrkr!r)rgseqslicess& rhrWrW>s@ 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. )rer0)rootspolyroots& rhrCrCLs1 3DHTAu:./ Kric#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)getattrrrrqrr)rgrrmstop seq_indexrxrrs&&&& rhr8r8bs2'40I(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)r) bytearrayr8rbytesrqr)rfrmdataps& rhrUrUs 1u E V Q 'D aU1X\ :dAu!e444"'E!%E,B(C"DUQQ ;$5))) 5*s%A C "C#AC C C  C rc#"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)rrtrrrq)rgrfrrxbatchs&&$ rh_batchedrs[ 1u122H~H,- -% - c%jAo:; ;  .s AA'#A'i )r-c\WVR7#))r)itertools_batched)rgrfrs&&$rhr-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. rT)r)matrixs&rhr]r]s  $t $$ricT\V4\Y4# \dR#i;i)z.Scalars are bytes, strings, and non-iterables.T)rtrs isinstance)r stringlikes&&rh _is_scalarrs/ U  e (( s  ''c\V4p\V4p\T3T4p\ T4'dT#\P !T4pKE \dTu#i;i)z.Depth-first iterator over scalars in a tensor.)rtrw StopIterationr rr)tensorrxrs& rh_flatten_tensorr 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. ) rintr-r rr r reversedr)rshape first_dimdims scalar_streamreshapeds&& rhrHrHsYB%u**62E::I#F+Mgx~}=H ( &&ric \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. )rqr-rrrr])m1m2rfs&& rhr:r: s0 BqE A 78WR2%?@! DDric\^V4Fop^;r#^pV^8XdWW",V,V,pW3,V,V,pW3,V,V,p\W#, V4pK]W@8wgKmVu# \R4h)rzprime or under 5)rrr)rfbryds& rh_factor_pollardrsy1a[  1faAaAaAAE1 A 6H ' ((ric#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_211r6rrr)rfprimeprimestodofacts& rhr3r3-s 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. )rqtyperkpowrrrr) coefficientsrrfpowerss&& rhrBrBNsI LAAvAwqz fQi%(!3 4F L ))ric&\\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. )rrrs&rhrXrXes S] ##rict\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. )rqrrrerkr )r%rfr&s& rhrDrDps0 LA eAqk "F C. //ricZ\\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 )rr3)rfrs& rhr\r\s&&VAY %Z HricV^, V, P4^, pW, p^V,V,V8XdV^,'dV^8gQhW3#)z#Return s, d such that 2**s * d == n) bit_length)rfrrs& rh _shift_to_oddr,sQ a%1  "Q&A A Fa<1 Q161 1 4Kric6V^8d"V^,'d^Tu;8:d V8gQhQh\V^, 4wr#\WV4pV^8XgW@^, 8XdR#\V^, 4F"pWD,V,pW@^, 8XgK!R# R#)TF)r,r$r)rfbaserrr_s&& rh_strong_probable_primer1s EAAMM2 2M2 2 Q DA DQAAv!e 1q5\ EAI A: ricaS^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)r.N)_private_randrangers& rhris_prime..s Ay!#Aq1u--ys #c3<<"TFp\SV4xK R#5ir)r1)rr/rfs& rhrr5sA54%a..5rT>r. )_perfect_testsrall)rflimitbasessf rhr6r6sB 2v((( EEa!eeA!a%%AFFq2vv&  u9 'BuRyA 3A5A33A3A3A5A AAric\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)rfs&rhr9r9s $?ricH\\\\V4V44#)ueNumber of distinct arrangements of a multiset. The expression ``multinomial(3, 4, 2)`` has several equivalent interpretations: * In the expansion of ``(a + b + c)⁹``, the coefficient of the ``a³b⁴c²`` term is 1260. * There are 1260 distinct ways to arrange 9 balls consisting of 3 reds, 4 greens, and 2 blues. * There are 1260 unique ways to place 9 distinct objects into three bins with sizes 3, 4, and 2. The :func:`multinomial` function computes the length of :func:`distinct_permutations`. For example, there are 83,160 distinct anagrams of the word "abracadabra": >>> from more_itertools import distinct_permutations, ilen >>> ilen(distinct_permutations('abracadabra')) 83160 This can be computed directly from the letter counts, 5a 2b 2r 1c 1d: >>> from collections import Counter >>> list(Counter('abracadabra').values()) [5, 2, 2, 1, 1] >>> multinomial(5, 2, 2, 1, 1) 83160 A binomial coefficient is a special case of multinomial where there are only two categories. For example, the number of ways to arrange 12 balls with 5 reds and 7 blues is ``multinomial(5, 7)`` or ``math.comb(12, 5)``. Likewise, factorial is a special case of multinomial where the multiplicities are all just 1 so that ``multinomial(1, 1, 1, 1, 1, 1, 1) == math.factorial(7)``. Reference: https://en.wikipedia.org/wiki/Multinomial_theorem )rrkrr )countss*rhr;r;sT D*V,f5 66ric #F"VPp.p.p\\4;_uu_4\V\ W1!444V^,x\ V\ W!!444V^,V^,,^, xKb +'giR#;i5i)z.Non-windowed running_median() for Python 3.14+N)__next__rr rbr r rcrxreadlohis& rh#_running_median_minheap_and_maxheaprI5s{   D B B -  [TV4 5Q%K RTV4 5a52a5=A% % ! s(B!A#B  B  B!c #N"VPp.p.p\\4;_uu_4\V\ W1!44)4V^,)x\V\ W!!4)4)4V^,V^,, ^, xKf +'giR#;i5i)zDBackport of non-windowed running_median() for Python 3.13 and prior.N)rDrr r r rEs& rh_running_median_minheap_onlyrKEs   D B B -  R+b$&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)rrrrqrr)rxrprorderedrrrfms&& rh_running_median_windowedrOUsWFG  aw w<& G^^%56A L FEEgjA(Cq'HHsB/B1rpc\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(). Window size should be positive)rt_indexrrO_max_heap_availablerKrIrgrprxs&$ rhrRrRhsV.H~H  Q;=> >'99  +H55 .x 88ric#"\4p^pVFVpVPV4W4, p\V4V8dW2P4,pV\V4, xKX R#5irN)rrrqr)rxrfr running_sumrs&& rh_windowed_running_meanrXsX WFK e v;? >>+ +KCK'' sA+A-c\V4pVf$\\\V4\ ^44#V^8:d \ R4h\ W!4#)aCumulative mean of values seen so far or values in a sliding window. Set *maxlen* to a positive integer to specify the maximum size of the sliding window. The default of *None* is equivalent to an unbounded window. For example: >>> list(running_mean([40, 30, 50, 46, 39, 44])) [40.0, 35.0, 40.0, 41.5, 41.0, 41.5] >>> list(running_mean([40, 30, 50, 46, 39, 44], maxlen=3)) [40.0, 35.0, 40.0, 42.0, 45.0, 43.0] Supports numeric types such as int, float, complex, Decimal, and Fraction. No extra effort is made to reduce round-off errors for float inputs. So the results may be slightly different from `statistics.mean`. rQ)rtrkr%r rrrXrTs&$ rhrQrQsH,H~H ~7Jx0%(;; {9:: !( 33ric#V"\4p\V4Fwr4V'd,V^,^,W1, 8XdVP4V'd(VR,^,V8gVP4K/VP W434V^,^,xK R#5irNrrrrpopr)rxrpsisr"rs&& rh_windowed_running_minr_p 'C!(+  3q6!9. KKM#b'!*u, GGI E>"!fQi , AB)AB)c|\V4pVf\V\R7#V^8:d \R4h\ W!4#)aSmallest 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_min([4, 3, 7, 0, 8, 1, 6, 2, 9, 5])) [4, 3, 3, 0, 0, 0, 0, 0, 0, 0] >>> list(running_min([4, 3, 7, 0, 8, 1, 6, 2, 9, 5], maxlen=3)) [4, 3, 3, 0, 0, 0, 1, 1, 2, 2] Supports numeric types such as int, float, Decimal, and Fraction, but not complex numbers which are unorderable. funcrQ)rtr minrr_rTs&$ rhrSrS=&H~H ~(-- {9::  22ric#V"\4p\V4Fwr4V'd,V^,^,W1, 8XdVP4V'd(VR,^,V8gVP4K/VP W434V^,^,xK R#5ir[r\)rxrpsdsr"rs&& rh_windowed_running_maxrir`rac|\V4pVf\V\R7#V^8:d \R4h\ W!4#)aLargest 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_max([4, 3, 7, 0, 8, 1, 6, 2, 9, 5])) [4, 4, 7, 7, 8, 8, 8, 8, 9, 9] >>> list(running_max([4, 3, 7, 0, 8, 1, 6, 2, 9, 5], maxlen=3)) [4, 4, 7, 7, 8, 8, 8, 6, 9, 9] Supports numeric types such as int, float, Decimal, and Fraction, but not complex numbers which are unorderable. rcrQ)rtr rrrrirTs&$ rhrPrPrfri)frozenslotsc,a]tRtRtoV3RltRtVtR#)r+i cV<V^8dQh/S[;R&S[;R&S[;R&S[;R&S[;R&#)r.ruminimummedianmaximummean)r float)format __classdict__s"rh __annotate__Stats.__annotate__ s? IN M  N  K riN)__name__ __module__ __qualname____firstlineno____annotate_func____static_attributes____classdictcell__)rus@rhr+r+ sric \V^4wr#rE\\Vf \^4M\ \ ^V4\ V44\W!R7\W1R7\WAR7\WQR74#)aStatistics for 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. Yields instances of a ``Stats`` dataclass with fields for the dataset *size*, *minimum* value, *median* value, *maximum* value, and the arithmetic *mean*. Supports numeric types such as int, float, Decimal, and Fraction, but not complex numbers which are unorderable. ro) rrkr+rr rrrSrRrPrQ)rgrpt0rrrs&$ rhrTrTsc1%NBB  NaeAv.>v(OB&r)B&R'  ric:\V4p\V4^8d\V4^8XdR#\R4h\\ \V444p\V4p\ V4\ \\W244'dK-\V!!V4#)zReturn a random derangement of elements in the iterable. Equivalent to but much faster than ``choice(list(derangements(iterable)))``. zNo derangments to choose fromrx) rrqrrerr)anyrkr#r$)rgrpermrms& rhrKrK/s{ /C 3x!| s8q=I899 c#h D $KE  3sE())t$S) )ri)rr)rN)NF)NNrV))i)r.)i)I)ltT7)r.r9=)lay)r.r;iS_)l;n>)r.r7r8r9r:)lp )r.r7r8r9r:r;)l)r.iEi$inii=ik)l%!Hn fW) r.r7r8r9r:r;rr%))__doc__randombisectrr collectionsr contextlibr dataclassesr functoolsrr heapqr r itertoolsr r rrrrrrrrrrrrrrrmathrrrroperatorr r!r"rRr#r$r%r&r'r(r)sysr*__all__object_markerrbrcrS ImportErrorr[rYrZr/r=r,rrGr@r?r<r1rrr4rNr5rOrArEr`rar_r7r2rMrLrJrIr>rFr0r.r^rrrVrWrCr8rUrr-rr]strrrr rHr:rrrr3rBrXrDr\r<r,r1Randomr4r6r9r;rIrKrOrRrXrQr_rSrirPr+rTrKrxrirhrs6&!''$('LL559  9 9 9  9   9   9 9 9  9 9 9 9 9 9  9   !9 "#9 $%9 & '9 ()9 *+9 ,-9 ./9 019 239 459 679 899 :;9 <=9 >?9 @*A9 BC9 DE9 FG9 HI9 JK9 LM9 NO9 PQ9 RS9 TU9 VW9 X Y9 Z[9 \]9 ^_9 `a9 b c9 d e9 fg9 hi9 jk9 l m9 no9 pq9 v (3 % '$ 8 %+P 44!$ ) ; %( .26 (&AR($%-PN*!H A/(:1(%a%("$ - -"D $('V&  ?2 -,&;R**E(6=u=&&GOG %#&u) 1&'R E ) %*%B*.$0& 2   &]]_..-B` *7Z & & I&"9t"9J(4T4B3D3<3D3< $d#$46*I.  xHs$=J 3J JJ J'&J'