o j@sHdZddlZddlmZmZddlmZddlmZddl m Z ddl m Z m Z ddlmZmZdd lmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"dd l#m$Z$m%Z%m&Z&m'Z'dd l(m)Z)m*Z*m+Z,m-Z-m.Z.m/Z/dd lm0Z0m1Z1m2Z2m3Z3dd l4m5Z5gdZ6e7Z8z ddlm9Z9m:Z:Wn e;ydZddZ?dddZ@dddZAdddZBeCfddZDd d!ZEeEZFd"d#ZGd$d%ZHzdd&l#mIZJWn e;yeHZJYnwd'd(ZKdd)d*ZLd+d,Zdd.d/ZMd0d1ZNd2d3ZOd4d5ZPdd6d7ZQdd8d9ZRdd:d;ZSddd?ZUd@dAdBdCZVddDdEZWdFdGZXdHdIZYdJdKZZdLdMZ[dNdOZ\dPdQZ]dRdSZ^dTdUZ_dVdWZ`dXdYZadZd[Zbd\d]Zcdd^d_Zdd`daZeddbdcddZfe5dekrddflmgZhddbdgdhZgefjeg_nefZgdidjZiejekffdkdlZldmdnZmdodpZndqdrZodsdtZpeqeeduZrdvdwZsdxdyZtdzd{Zud|d}Zvd~dZwgdZxe ddZyddZze{j0Z|ddZ}ddZ~ddZddZddZddZddddZddZddddZddZddddZddZddddZe dddGdddZddddZddZdS)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) hexversion)8Stats 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_maxFTcCtt||S)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)niterablerhW/var/www/html/Deteccion_Ine/venv/lib/python3.10/site-packages/more_itertools/recipes.pyr[qs r[cCst|t|S)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)functionstartrhrhrirYsrYcCsFzt|}Wntytt||dYSwt|td||dS)zReturn an iterator over the last *n* items of *iterable*. >>> t = tail(3, 'ABCDEFG') >>> list(t) ['E', 'F', 'G'] maxlenrN)len TypeErroriterrrmax)rfrgsizerhrhrirZs   rZcCs.|dur t|dddStt|||ddS)aXAdvance *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 Nrrm)rnextr)iteratorrfrhrhrir/s r/cCstt||d|S)zReturns the nth item or a default value. >>> l = range(10) >>> nth(l, 3) 3 >>> nth(l, 20, "zebra") 'zebra' N)rtr)rgrfdefaultrhrhrir=s r=cCs,t||}|D] }|D]}dSdSdS)a 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)rgkeyrufirstsecondrhrhrir,s r,cCrd)zcReturn the how many times the predicate is true. >>> quantify([True, False, True]) 2 )sumrj)rgpredrhrhrirGsrGcCst|tdS)aReturns 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 rrgrhrhrir@s r@cCsttt||S)zvReturns the sequence elements *n* times >>> list(ncycles(["a", "b"], 3)) ['a', 'b', 'a', 'b', 'a', 'b'] )r from_iterablertuplergrfrhrhrir< sr<cCsttt||S)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. )rzrjr )Zvec1Zvec2rhrhrir1s r1)sumprodcCs t|S)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})Z list_of_listsrhrhrir4+s r4cGs&|dur t|t|St|t||S)aKCall *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] N)rr)rktimesargsrhrhrirN7srNcCst|S)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_pairwiser|rhrhrirRs rfillcCsXt|g|}|dkrt|d|iSdkr t|ddiSdkr't|S td)aGroup 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 r fillvaluestrictTignorez Expected fill, strict, or ignore)rqrzip ValueError)rgrf incompleter iteratorsrhrhrir5^s  r5cgsDtt|}tt|ddD]}tt||}tt|EdHqdS)aGVisit 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). rN)rjrqrangerorrrt) iterablesrZ num_activerhrhrirOs  rOcsBdurtt|ttfdd}||fS)a 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, ' ']) Nc3s> |r |V|sD]}|rn|ndSqN)popleftappend)queuevalueZ false_queuerur{Z true_queuerhrigens zpartition..gen)boolrqr)r{rgrrhrrirAs rAcs,t|tfddttdDS)a1Yields 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|]}t|VqdSr)r).0rsrhri zpowerset..)rer r}rror|rhrrirEs$rEccsdt}|durt|j|D] }|||VqdS|D]}||}||vr/|||VqdS)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)rgrwseenelementkrhrhrir`s  r`cCs4|dur ttdt|Sttttdt||S)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'] Nrr)rjr$rrt)rgrwrhrhriras racCst|||d}t||dS)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. )rwreverse)rw)sortedra)rgrwrZ sequencedrhrhrir_ s r_ccs<t||dur|V |Vq1swYdS)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)rk exceptionrxrhrhrir7s r7cCstt|||S)a 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' )rtfilter)rgrvr{rhrhrir2:sr2rrcGs ttt||}ttt|S)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)``. )r~rjr()rrpoolsrhrhrirMNsrMcCs*t|}|dur t|n|}tt||S)abReturn 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)``. N)r~ror')rgrpoolrhrhrirLbs rLcs8t|t}ttt||}tfdd|DS)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)``. cg|]}|qSrhrhrirrhri z&random_combination..)r~rorr'r)rgrrfindicesrhrrirJts rJcs@t|ttfddt|D}tfdd|DS)aSReturn 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)``. c3s|]}tVqdSr)r&rrfrhrirsz6random_combination_with_replacement..crrhrhrrrhrirrz7random_combination_with_replacement..)r~rorr)rgrrrh)rfrrirIs rIcCst|}t|}t||}|dkr||7}d|kr |ks#ttg}|r[||||d|d}}}||krP||8}|||||d}}||ks;||d||s't|S)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. rrr)r~ror IndexErrorr)rgrr"rrfcresultrhrhrir>s&  r>cCs t|g|S)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 )rrgrhrhrirFs rFccsbt|ddd}t|}tdg|d|}t|td|dD] }||t||Vq!dS)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 Nrrrmr)r~rorr rr_sumprod)signalZkernelrfwindowxrhrhrir0s# r0cCs(t|\}}tt||t|}||fS)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) predicateitZtruesafterrhrhrir.s r.cCs:t|d\}}}t|dt|dt|dt|||S)zReturn overlapping triplets from *iterable*. >>> list(triplewise('ABCDE')) [('A', 'B', 'C'), ('B', 'C', 'D'), ('C', 'D', 'E')] N)rrtr)rgt1t2t3rhrhrir^s     r^cCs6t||}t|D] \}}tt|||dq t|Sr)r enumeratertrr)rgrfrrrurhrhri_sliding_window_islices rccsBt|}tt||d|d}|D] }||t|VqdS)Nrrm)rqrrrr~)rgrfrurrrhrhri_sliding_window_deques  rcCsR|dkr t||S|dkrt||S|dkrt|S|dkr"t|Std|)aYReturn 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 )rrrrrrrhrhrirV%s  rVcCs4t|}ttttt|dd}ttt||S)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) rerslicerrrorjr!r)rgseqZslicesrhrhrirW>s rWcCs(dg}|D] }tt|d| f}q|S)ukCompute a polynomial's coefficients from its roots. >>> 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)rer0)rootsZpolyrootrhrhrirCLsrCccst|dd}|dur(t|||}t||D]\}}||us"||kr%|VqdS|dur0t|n|}|d}tt |||d|}Vq<1sKwYdS)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)getattrrrrorr)rgrrlstopZ seq_indexrurrrhrhrir8bs    r8ccs|dkrdVd}td|d}t|d|t|ddD])}t|d|||EdHttt|||||||||||<||}qt|d|EdHdS)zeYield the primes less than n. >>> list(sieve(30)) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] rr)rrr)rN) bytearrayr8rbytesror)rfrldataprhrhrirUs . rUrccsd|dkr tdt|}tt||}r0|r"t||kr"td|Vtt||}sdSdS)aBatch 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)rrqr~rro)rgrfrrubatchrhrhri_batcheds ri )r-cCst|||dS)Nr)itertools_batched)rgrfrrhrhrir-sr-cCst|ddiS)a Swap the rows and columns of the input matrix. >>> 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)matrixrhrhrir]s r]cCs,zt|Wn tyYdSwt||S)z.Scalars are bytes, strings, and non-iterables.T)rqrp isinstance)rZ stringlikerhrhri _is_scalars    rcCsRt|} zt|}Wn ty|YSwt|f|}t|r#|St|}q)z.Depth-first iterator over scalars in a tensor.)rqrt StopIterationr rr})Ztensorrurrhrhri_flatten_tensors    rcCsDt|tr tt||S|^}}t|}ttt||}t||S)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 r}rr reversedr)rshapeZ first_dimdimsZ scalar_streamZreshapedrhrhrirHs ! rHcCs&t|d}tttt|t||S)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)ror-rrrr])m1m2rfrhrhrir: s r:cCstd|D]7}d}}d}|dkr4||||}||||}||||}t|||}|dks||kr<|Sqtd)Nrrzprime or under 5)rrr)rfbrydrhrhri_factor_pollardsrccs|dkrdStD]}||s|V||}||rq g}|dkr$|gng}|D]}|dks2t|r8||q(t|}||||f7}q(t|EdHdS)aYield 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_211r6rrr)rfprimeZprimestodoZfactrhrhrir3-s"  r3cCs>t|}|dkrt|dSttt|tt|}t||S)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)rotyperjpowrrrr) coefficientsrrfpowersrhrhrirBNs   rBcCs tt|S)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|rhrhrirXes rXcCs&t|}ttd|}ttt||S)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)rorrrerjr )rrfrrhrhrirDpsrDcCs"tt|D]}|||8}q|S)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)rfrrhrhrir\sr\))i)r)i)I)ltT7)r=)lay)r iS_)l;n>)rrr )lp )rrrrrr)l)riEi$inii=ik)l%!Hn fW) rrrrrrrr%)cCsH|d|Ad}||?}d|>||kr|d@r|dks J||fS)z#Return s, d such that 2**s * d == nrr) bit_length)rfrrrhrhri _shift_to_odds$rcCs|dkr|d@rd|kr|ksJJt|d\}}t|||}|dks.||dkr0dSt|dD]}|||}||dkrGdSq6dS)NrrTF)rrr)rfbaserrr_rhrhri_strong_probable_primes,   rcsdkrdvSd@r dr dr dr dr ds"d StD] \}}|kr.n q$fd d td D}tfd d |DS)aReturn ``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. r>rrrrrrrrrrrrFc3s|] }tddVqdS)rrN)_private_randrangerrrhrirszis_prime..@c3rr)r)rrrrhrirr)_perfect_testsrall)rflimitbasesrhrrir6s!0 r6cCs td|S)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 Nrrrhrhrir9s r9cGstttt||S)uNumber 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 )countsrhrhrir;s*r;ccsv|j}g}g}tt% t|t|||dVt|t|||d|ddVq1s4wYdS)z.Non-windowed running_median() for Python 3.14+TrrN)__next__rrrbr r rcrureadlohirhrhri#_running_median_minheap_and_maxheap5s  r ccs~|j}g}g}tt) t|t|| |d Vt|t||  |d|ddVq1s8wYdS)zDBackport of non-windowed running_median() for Python 3.13 and prior.TrrN)rrrr r rrhrhri_running_median_minheap_onlyEs  r ccst}g}|D]9}||t||t||kr$t||}||=t|}|d}|d@r4||n ||d||dVqdS)z+Yield median of values in a sliding window.rrN)rrrrorr)rurnrorderedrrrfmrhrhri_running_median_windowedUs   ,rrmcCsFt|}|durt|}|dkrtdt||Stst|St|S)aDCumulative 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(). NrWindow size should be positive)rq_indexrr_max_heap_availabler r rgrnrurhrhrirRhs rRccsRt}d}|D]}||||7}t||kr||8}|t|VqdS)Nr)rrror)rurfrZ running_sumrrhrhri_windowed_running_means   rcCs>t|}|durttt|tdS|dkrtdt||S)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`. Nrrr)rqrjr%r rrrrrhrhrirQs  rQccst}t|D]:\}}|r|dd||kr||r4|dd|ks4||r4|dd|kr&|||f|ddVqdSNrrrrrrpopr)rurnZsisr"rrhrhri_windowed_running_minrcC6t|}|durt|tdS|dkrtdt||S)aDSmallest 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. Nfuncrr)rqr minrrrrhrhrirS   rSccst}t|D]:\}}|r|dd||kr||r4|dd|ks4||r4|dd|kr&|||f|ddVqdSrr)rurnZsdsr"rrhrhri_windowed_running_maxrrcCr)aCLargest 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. Nrrr)rqr rrrrrrhrhrirPrrP)frozenslotsc@s6eZdZUeed<eed<eed<eed<eed<dS)r+rsminimumZmedianmaximummeanN)__name__ __module__ __qualname__r__annotations__floatrhrhrhrir+ s  r+c Csdt|d\}}}}tt|durtdn ttd|t|t||dt||dt ||dt ||dS)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. Nrrm) rrjr+rr rrrSrRrPrQ)rgrnt0rrrrhrhrirTs"    rTcCslt|}t|dkrt|dkrdStdttt|}t|} t|ttt||s5t ||Sq#)zReturn a random derangement of elements in the iterable. Equivalent to but much faster than ``choice(list(derangements(iterable)))``. rrrhzNo derangments to choose from) r~rorrerr)anyrjr#r$)rgrpermrlrhrhrirK/s   rK)rr)rN)NF)NN)rN)__doc__randombisectrr collectionsr contextlibr dataclassesr functoolsrr heapqr r itertoolsr r rrrrrrrrrrrrrrrmathrrrroperatorr r!r"rr#r$r%r&r'r(r)sysr*__all__objectZ_markerrbrc ImportErrorrr[rYrZr/r=r,rrGr@r?r<r1rrr4rNr5rOrArEr`rar_r7r2rMrLrJrIr>rFr0r.r^rrrVrWrCr8rUrr-rr]strrrrrHr:rr~rr3rBrXrDr\rrrRandomrr6r9r;r r rrRrrQrrSrrPr+rTrKrhrhrhris    H  ;    (      )(  $    "+  )     ) !   0-% !