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o ;jS� � @ sN d Z ddlZddlmZmZ ddlmZ ddlmZ ddl m Z m Z m Z ddl mZmZ ddlmZmZmZmZmZmZmZmZmZmZmZm Z m Z m Z dd l m Z m!Z!m"Z"m#Z# dd l$m%Z%m&Z&m'Z'm(Z(m)Z) dd lm*Z*m+Z+m,Z, dd l-m.Z. g d �Z/e0� Z1ze2dd� W n e3y� e2Z4Y nw e e2dd�Z4zddl m5Z6 W n e7y� dd� Z6Y nw z ddl m8Z8m9Z9 W n e7y� dZ:Y nw dZ:dd� Z;d�dd�Z<dd� Z=d�dd �Z>d�d d �Z?d�d d �Z@eAfd!d"�ZBd#d$� ZCeCZDd%d&� ZEd'd(� ZFd)d*� ZGd�d+d,�ZHd-d.� ZIzdd/lmJZK W n e7�y eIZJY n w d0d1� ZJeIj eJ_ G d2d3� d3eL�ZMd4d5� ZNd6d7� ZOd�d9d:�ZPd;d<� ZQd=d>� ZRd?d@� ZSd�dAdB�ZTd�dCdD�ZUd�dEdF�ZVd�dGdH�ZWd�dIdJ�ZXdKdL�dMdN�ZYd�dOdP�ZZdQdR� Z[dSdT� Z\dUdV� Z]dWdX� Z^dYdZ� Z_d[d\� Z`d]d^� Zad_d`� Zbdadb� Zcdcdd� Zddedf� Zedgdh� Zfd�didj�Zgdkdl� Zhdd�dmdn�Zie.dok�r�ddplmjZk dd�dqdr�Zjeij ej_ neiZjdsdt� Zlemenffdudv�Zodwdx� Zpdydz� Zqd{d|� Zrd}d~� Zsetehd��Zud�d�� Zvd�d�� Zwd�d�� Zxd�d�� Zyd�d�� Zzg d��Z{e d�d�� �Z|d�d�� Z}e�~� j*Zd�d�� Z�d�d�� Z�d�d�� Z�d�d�� Z�d�d�� Z�d�d�� Z�dd��d�d��Z�dS )�a Imported 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_left�insort)�deque��suppress)� lru_cache�partial�reduce)�heappush� heappushpop)� accumulate�chain� combinations�compress�count�cycle�groupby�islice�product�repeat�starmap� takewhile�tee� zip_longest)�prod�comb�isqrt�gcd)�mul�not_� itemgetter�getitem�index)� randrange�sample�choice)� hexversion)2� all_equal�batched�before_and_after�consume�convolve� dotproduct� first_true�factor�flatten�grouper�is_prime� iter_except� iter_index�loops�matmul� multinomial�ncycles�nth�nth_combination�padnone�pad_none�pairwise� partition�polynomial_eval�polynomial_from_roots�polynomial_derivative�powerset�prepend�quantify�reshape�#random_combination_with_replacement�random_combination�random_permutation�random_product� repeatfunc� roundrobin�running_median�sieve�sliding_window� subslices�sum_of_squares�tabulate�tail�take�totient� transpose� triplewise�unique�unique_everseen�unique_justseenT��strict)�sumprodc C s t | |�S �N)r, )�x�y� r_ �]/opt/saltstack/salt/lib/python3.10/site-packages/setuptools/_vendor/more_itertools/recipes.py�<lambda>l s ra )� heappush_max�heappushpop_maxFc C � t t|| ��S )z�Return 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 )�n�iterabler_ r_ r` rR x s rR c C s t | t|��S )a� Return 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 )�function�startr_ r_ r` rP � s rP c C sF zt |�}W n ty tt|| d�� Y S w t|td|| �d�S )z�Return an iterator over the last *n* items of *iterable*. >>> t = tail(3, 'ABCDEFG') >>> list(t) ['E', 'F', 'G'] ��maxlenr N)�len� TypeError�iterr r �max)rf rg �sizer_ r_ r` rQ � s �rQ c C s. |du r t | dd� dS tt| ||�d� dS )aX Advance *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 "<stdin>", line 1, in <module> 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 "<stdin>", line 1, in <module> StopIteration Nr rk )r �nextr )�iteratorrf r_ r_ r` r* � s r* c C s t t| |d�|�S )z�Returns the nth item or a default value. >>> l = range(10) >>> nth(l, 3) 3 >>> nth(l, 20, "zebra") 'zebra' N)rr r )rg rf �defaultr_ r_ r` r8 � s r8 c C s, t | |�}|D ] }|D ]} dS dS dS )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 )rg �keyrs �first�secondr_ r_ r` r' � s r' c C rd )zcReturn the how many times the predicate is true. >>> quantify([True, False, True]) 2 )�sumrh )rg �predr_ r_ r` rC � s rC c C s t | td��S )a Returns 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 r �rg r_ r_ r` r; s r; c C s t �tt| �|��S )zvReturns the sequence elements *n* times >>> list(ncycles(["a", "b"], 3)) ['a', 'b', 'a', 'b', 'a', 'b'] )r � from_iterabler �tuple�rg rf r_ r_ r` r7 s r7 c C s t tt| |��S )z�Returns 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. )rx rh r )Zvec1Zvec2r_ r_ r` r, s r, c C s t �| �S )z�Return 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 listOfListsr_ r_ r` r/ + s r/ c G s& |du r t | t|��S t | t||��S )aG 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] N)r r )�func�times�argsr_ r_ r` rI 7 s rI c C s t | �\}}t|d� t||�S )z�Returns 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`. N�r rr �zip)rg �a�br_ r_ r` � _pairwiseR s r� )r< c C s t | �S r\ )�itertools_pairwiserz r_ r_ r` r< f s r< c s e Zd Zd� fdd� Z� ZS )�UnequalIterablesErrorNc s* d}|d ur |dj |� 7 }t� �|� d S )Nz Iterables have different lengthsz/: index 0 has length {}; index {} has length {})�format�super�__init__)�self�details�msg�� __class__r_ r` r� m s �z UnequalIterablesError.__init__r\ )�__name__� __module__� __qualname__r� � __classcell__r_ r_ r� r` r� l s r� c c s8 � t | dti�D ]}|D ] }|tu rt� �q |V qd S )N� fillvalue)r �_markerr� )� iterablesZcombo�valr_ r_ r` �_zip_equal_generatorw s ���r� c G sn z)t | d �}t| dd � d�D ]\}}t |�}||kr$t|||fd��qt| � W S ty6 t| � Y S w )Nr � )r� )rm � enumerater� r� rn r� )r� Z first_size�i�itrq r_ r_ r` � _zip_equal s � �r� �fillc C sL t | �g| }|dkrt|d|i�S |dkrt|� S |dkr"t|� S td��)a� Group 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 subclass of `ValueError` will be raised. >>> iterator = grouper('ABCDEFG', 3, incomplete='strict') >>> list(iterator) # doctest: +IGNORE_EXCEPTION_DETAIL Traceback (most recent call last): ... UnequalIterablesError r� r� rZ �ignorez Expected fill, strict, or ignore)ro r r� r� � ValueError)rg rf Z incompleter� � iteratorsr_ r_ r` r0 � s r0 c g sD � t t| �}tt| �dd�D ]}tt||��}t t|�E dH qdS )aG 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). r ���N)rh ro �rangerm r r rr )r� r� Z num_activer_ r_ r` rJ � s � �rJ c C sH | du rt } t|d�\}}}tt| |��\}}t|tt|��t||�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, ' ']) N� )�boolr rh r r )ry rg �t1�t2�pZp1Zp2r_ r_ r` r= � s r= c s, t | �� t�� fdd�tt� �d �D ��S )a1 Yields 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`. c 3 � � | ]}t � |�V qd S r\ )r )�.0�r��sr_ r` � <genexpr>� � � zpowerset.<locals>.<genexpr>r� )re r r{ r� rm rz r_ r� r` rA � s $rA c c s� � t � }|j}g }|j}|du}| D ]+}|r||�n|}z ||vr(||� |V W q ty= ||vr;||� |V Y qw dS )a� 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)�set�add�appendrn ) rg ru ZseensetZ seenset_addZseenlistZ seenlist_addZuse_key�element�kr_ r_ r` rW � s( �� ���rW c C s4 |du r t td�t| ��S t tt td�t| |���S )z�Yields 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'] Nr r� )rh r r rr )rg ru r_ r_ r` rX ' s rX c C s t | ||d�}t||d�S )a� Yields 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. )ru �reverse)ru )�sortedrX )rg ru r� Z sequencedr_ r_ r` rV 6 s rV c c s< � t |�� |dur|� V | � V q1 sw Y dS )a� Yields 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~ � exceptionrv r_ r_ r` r2 J s � ��r2 c C s t t|| �|�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' )rr �filter)rg rt ry r_ r_ r` r- g s r- r� �r c G s$ dd� |D �| }t dd� |D ��S )a� Draw 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)``. c S s g | ]}t |��qS r_ �r| �r� �poolr_ r_ r` � <listcomp>� s z"random_product.<locals>.<listcomp>c s s � | ]}t |�V qd S r\ )r% r� r_ r_ r` r� � � � z!random_product.<locals>.<genexpr>r� )r r� Zpoolsr_ r_ r` rH { s rH c C s* t | �}|du r t|�n|}t t||��S )ab Return 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| rm r$ )rg r� r� r_ r_ r` rG � s rG c s8 t | �� t� �}ttt|�|��}t � fdd�|D ��S )z�Return 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)``. c 3 � � | ]}� | V qd S r\ r_ �r� r� �r� r_ r` r� � r� z%random_combination.<locals>.<genexpr>)r| rm r� r$ r� )rg r� rf �indicesr_ r� r` rF � s rF c s@ t | ��t��� t� fdd�t|�D ��}t �fdd�|D ��S )aS 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)``. c 3 s � | ]}t � �V qd S r\ )r# r� �rf r_ r` r� � r� z6random_combination_with_replacement.<locals>.<genexpr>c 3 r� r\ r_ r� r� r_ r` r� � r� )r| rm r� r� )rg r� r� r_ )rf r� r` rE � s rE c C s� t | �}t|�}|dk s||krt�d}t||| �}td|d �D ] }||| | | }q"|dk r7||7 }|dk s?||krAt�g }|ry|| | |d |d }}}||krn||8 }||| | |d }}||ksY|�|d| � |sEt |�S )a Equivalent 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 r� r� )r| rm r� �minr� � IndexErrorr� ) rg r� r" r� rf �cr� r� �resultr_ r_ r` r9 � s, ��r9 c C s t | g|�S )a Yield *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 )�valuers r_ r_ r` rB � s rB c c sb � t |�ddd� }t|�}tdg|d�| }t| td|d ��D ] }|�|� t||�V q!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 Nr� r rk r� )r| rm r r r r� �_sumprod)�signalZkernelrf �windowr] r_ r_ r` r+ � s �# �r+ c C s( t |�\}}tt| |�t|��}||fS )a� A 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. )r r r r� )� predicater� ZtruesZafterr_ r_ r` r) & s r) c C s: t | d�\}}}t|d� t|d� t|d� t|||�S )z�Return overlapping triplets from *iterable*. >>> list(triplewise('ABCDE')) [('A', 'B', 'C'), ('B', 'C', 'D'), ('C', 'D', 'E')] r� Nr� )rg r� r� Zt3r_ r_ r` rU 9 s rU c C s6 t | |�}t|�D ] \}}tt|||�d � q t|� S r\ )r r� rr r r� )rg rf r� r� rs r_ r_ r` �_sliding_window_isliceI s r� c c sB � t | �}tt||d �|d�}|D ] }|�|� t|�V qd S )Nr� rk )ro r r r� r| )rg rf rs r� r] r_ r_ r` �_sliding_window_dequeQ s � �r� c C sR |dkr t | |�S |dkrt| |�S |dkrt| �S |dkr"t| �S td|� ���)aY 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`. � � r� z n should be at least one, not )r� r� r< r� r� r} r_ r_ r` rM Z s rM c C s4 t | �}ttttt|�d �d��}ttt|�|�S )z�Return 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. r� r� ) re r �slicer r� rm rh r! r )rg �seqZslicesr_ r_ r` rN s s rN c C s( dg}| D ] }t t|d| f��}q|S )uk Compute 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� )re r+ )�rootsZpoly�rootr_ r_ r` r? � s r? c c s� � t | dd�}|du r(t| ||�}t||�D ]\}}||u s"||kr%|V qdS |du r0t| �n|}|d }tt�� |||d |� }V q<1 sKw Y dS )a� Yield 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� )�getattrr r� rm r r� )rg r� rj �stopZ seq_indexrs r� r� r_ r_ r` r3 � s � �� ��r3 c c s� � | dkrdV d}t d�| d }t|d|t| �d d�D ])}t|d||| �E dH ttt|| | || ���||| | || �< || }q t|d|�E dH dS )zeYield the primes less than n. >>> list(sieve(30)) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] r� r� )r r� r� )r� N)� bytearrayr3 r �bytesrm r� )rf rj �datar� r_ r_ r` rL � s � . rL c c sd � |dk r t d��t| �}tt||�� }r0|r"t|�|kr"t d��|V tt||�� }sdS dS )a� Batch 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`. r� zn must be at least onezbatched(): incomplete batchN)r� ro r| r rm )rg rf rZ rs Zbatchr_ r_ r` �_batched� s � �r� i� )r( c C s t | ||d�S )NrY )�itertools_batched)rg rf rZ r_ r_ r` r( � s r( c C s t | � S )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. )� _zip_strict�r� r_ r_ r` rT � s rT c C s, zt | � W n ty Y dS w t| |�S )z.Scalars are bytes, strings, and non-iterables.T)ro rn � isinstance)r� Z stringliker_ r_ r` � _is_scalar s � r� c C sR t | �} zt|�}W n ty | Y S w t|f|�}t|�r#|S t�|�}q)z.Depth-first iterator over scalars in a tensor.)ro rr � StopIterationr r� r{ )Ztensorrs r� r_ r_ r` �_flatten_tensor s � �r� c C sD t |t�r tt�| �|�S |^}}t| �}ttt|�|�}t||�S )a� Change 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 r{ r� r �reversedr )Zmatrix�shapeZ first_dimZdimsZ scalar_streamZreshapedr_ r_ r` rD s ! rD c C s& 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 )rm r( r r� r rT )Zm1Zm2rf r_ r_ r` r5 @ s r5 c C s� t d| �D ]7}d }}d}|dkr4|| | | }|| | | }|| | | }t|| | �}|dks|| kr<| S qtd��)Nr� r� zprime or under 5)r� r r� )rf r� r] r^ �dr_ r_ r` �_factor_pollardO s ��r� �� c c s� � | dk rdS t D ]}| | s|V | | } | | rq g }| dkr$| gng }|D ] } | dk s2t| �r8|�| � q(t| �}||| | f7 }q(t|�E dH dS )a Yield 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. r� Nr� i� )�_primes_below_211r1 r� r� r� )rf �primeZprimesZtodoZfactr_ r_ r` r. b s" � �� r. c C s> t | �}|dkrt|�d�S ttt|�tt|���}t| |�S )a� Evaluate 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 )rm �typerh �powr r� r� r� )� coefficientsr] rf �powersr_ r_ r` r> � s r> c C s t t| �� S )z�Return 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. )r� r r� r_ r_ r` rO � s rO c C s& t | �}ttd|��}ttt| |��S )u� Compute 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� )rm r� r� re rh r )r� rf r� r_ r_ r` r@ � s r@ c C s" t t| ��D ]}| | | 8 } q| S )u� Return 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 )r� r. )rf r� r_ r_ r` rS � s rS ))i� )r� )i�� )� �I )l �tT7 )r� � �= )l �ay)r� � � iS_ )l ;n>�)r� r� � r� � )l � p� )r� r� r� r� r� r� )l )r� iE i�$ in i�� i=� i��k)l �%!H�n �fW ) r� r� r� r� r� r� � � r� � r� �% �) c C sH | d | A � � d }| |? }d|> | | kr |d@ r |dks J �||fS )z#Return s, d such that 2**s * d == nr� r )� bit_length)rf r� r� r_ r_ r` � _shift_to_odd� s $r� c C s� | dkr| d@ rd| kr| k sJ � J �t | d �\}}t||| �}|dks.|| d kr0dS t|d �D ]}|| | }|| d krG dS q6dS )Nr� r� TF)r� r� r� )rf �baser� r� r] �_r_ r_ r` �_strong_probable_prime� s , �r� c s� � dk r� dv S � d@ r � d r � d r � d r � d r � d s"d S t D ] \}}� |k r. n q$� fd d �td �D �}t� fd d �|D ��S )a� Return ``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� > r� r� r� r� r� r� r� r� r� r� r� r� Fc 3 s � | ] }t d � d �V qdS )r� r� N)�_private_randranger� r� r_ r` r� * s � zis_prime.<locals>.<genexpr>�@ c 3 r� r\ )r� )r� r� r� r_ r` r� , r� )�_perfect_testsr� �all)rf �limit�basesr_ r� r` r1 � s !0 �r1 c C s t d| �S )z�Returns 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� r� r_ r_ r` r4 / s r4 c G s t ttt| �| ��S )u� Number 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 )r rh r r )�countsr_ r_ r` r6 = s *r6 c c sv � | j }g }g }tt��% t|t||� �� |d V t|t||� �� |d |d d V q1 s4w Y dS )z.Non-windowed running_median() for Python 3.14+Tr r� N)�__next__r r� rb r r rc �rs �read�lo�hir_ r_ r` �#_running_median_minheap_and_maxheapj s � ��r c c s~ � | j }g }g }tt��) t|t||� � � |d V t|t||� � � |d |d d V q1 s8w Y dS )zDBackport of non-windowed running_median() for Python 3.13 and prior.Tr r� N)r r r� r r r r_ r_ r` � _running_median_minheap_onlyz s � ��r c c s� � t � }g }| D ]9}|�|� t||� t|�|kr$t||�� �}||= t|�}|d }|d@ r4|| n ||d || d V qdS )z+Yield median of values in a sliding window.r� r� N)r r� r rm r �popleft)rs rl r� Zorderedr] r� rf �mr_ r_ r` �_running_median_windowed� s � ,�r rk c C sF t | �}|durt|�}|dkrtd��t||�S ts t|�S t|�S )aD Cumulative median of values seen so far or values in a sliding window. Set *maxlen* to a positive integer to specify the maximum size of the sliding window. The default of *None* is equivalent to an unbounded window. For example: >>> list(running_median([5.0, 9.0, 4.0, 12.0, 8.0, 9.0])) [5.0, 7.0, 5.0, 7.0, 8.0, 8.5] >>> list(running_median([5.0, 9.0, 4.0, 12.0, 8.0, 9.0], maxlen=3)) [5.0, 7.0, 5.0, 9.0, 8.0, 9.0] Supports numeric types such as int, float, Decimal, and Fraction, but not complex numbers which are unorderable. On version Python 3.13 and prior, max-heaps are simulated with negative values. The negation causes Decimal inputs to apply context rounding, making the results slightly different than that obtained by statistics.median(). Nr z Window size should be positive)ro r" r� r �_max_heap_availabler r )rg rl rs r_ r_ r` rK � s rK )r r\ )r� N)NF)NN)r N)��__doc__�random�bisectr r � collectionsr � contextlibr � functoolsr r r �heapqr r � itertoolsr r r r r r r r r r r r r r �mathr r r r �operatorr r r r! r" r# r$ r% �sysr& �__all__�objectr� r� rn r� r[ r� � ImportErrorrb rc r rR rP rQ r* r8 r' r� rC r; r: r7 r, r/ rI r� r< r� r� r� r� r� r0 rJ r= rA rW rX rV r2 r- rH rG rF rE r9 rB r+ r) rU r� r� rM rN r? r3 rL r� r( r� rT �strr� r� r� rD r5 r� r| r� r. r> rO r@ rS r r� r� �Randomr r1 r4 r6 r r r rK r_ r_ r_ r` �<module> s� @ 5 � � � ( � ( - *+ ) ) ! 0-
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