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a g�h�� � @ s� d Z ddlZddlmZ ddlmZ ddlmZ ddlm Z m Z ddl m Z m Z mZmZmZmZmZmZmZmZmZmZmZ ddlmZmZm Z m Z dd l m Z m Z m!Z!m"Z" dd lm#Z#m$Z$m%Z% dd l&m'Z' g d �Z(e)� Z*ze+d d� W n e,y� e+Z-Y n0 e e+d d�Z-zddlm.Z/ W n e0�y8 dd� Z/Y n0 dd� Z1d�dd�Z2dd� Z3d�dd�Z4d�dd�Z5d�d d �Z6e7fd d �Z8d d!� Z9e9Z:d"d#� Z;d$d%� Z<d&d'� Z=d�d(d)�Z>d*d+� Z?zdd,l m@ZA W n e0�y� e?Z@Y n0 d-d.� Z@e?j e@_ G d/d0� d0eB�ZCd1d2� ZDd3d4� ZEd�d6d7�ZFd8d9� ZGd:d;� ZHd<d=� ZId�d>d?�ZJd�d@dA�ZKd�dCdD�ZLd�dEdF�ZMd�dGdH�ZNdIdJ�dKdL�ZOd�dMdN�ZPdOdP� ZQdQdR� ZRdSdT� ZSdUdV� ZTdWdX� ZUdYdZ� ZVd[d\� ZWd]d^� ZXd_d`� ZYdadb� ZZdcdd� Z[dedf� Z\d�dgdh�Z]didj� Z^dBd�dkdl�Z_e'dmk�r ddnl m`Za dBd�dodp�Z`n e_Z`e_j e`_ dqdr� Zbdsdt� Zcdudv� Zddwdx� Zeefe^dy��Zgdzd{� Zhd|d}� Zid~d� Zjd�d�� Zkd�d�� Zlg d��Zme d�d�� �Znd�d�� Zoe�p� j#Zqd�d�� Zrd�d�� Zsd�d�� ZtdS )�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)�deque��suppress)�Sized)� lru_cache�partial) � accumulate�chain� combinations�compress�count�cycle�groupby�islice�product�repeat�starmap�tee� zip_longest)�prod�comb�isqrt�gcd)�mul�not_� itemgetter�getitem)� randrange�sample�choice)� hexversion)1� 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�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� rX ��/root/rpmbuild/BUILDROOT/imh-python39-modules-3.9.7-92.el8.x86_64/opt/imh-python/lib/python3.9/site-packages/more_itertools/recipes.py�<lambda>i � rZ c C s 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�iterablerX rX rY rK l s rK 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�startrX rX rY rI | s rI c C s8 t |t�r$t|tdt|�| �d�S tt|| d��S dS )z�Return an iterator over the last *n* items of *iterable*. >>> t = tail(3, 'ABCDEFG') >>> list(t) ['E', 'F', 'G'] r N��maxlen)� isinstancer r �max�len�iterr r] rX rX rY rJ � s rJ c C s, |du rt | dd� ntt| ||�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 rc )r �nextr )�iteratorr^ rX rX rY 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)ri r )r_ r^ �defaultrX rX rY r2 � s r2 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 )r_ �keyrj �first�secondrX rX rY r! � s r! c C s t t|| ��S )zcReturn the how many times the predicate is true. >>> quantify([True, False, True]) 2 )�sumr` )r_ �predrX rX rY r= � s r= 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 �r_ rX rX rY r5 � s r5 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�r_ r^ rX rX rY r1 s r1 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. )ro r` r )Zvec1Zvec2rX rX rY 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 rr )Z listOfListsrX rX rY r) ! s r) c G s& |du rt | 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�argsrX rX rY rC - s rC 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 ri �zip)r_ �a�brX rX rY � _pairwiseH s r| )r6 c C s t | �S rU )�itertools_pairwiserq rX rX rY r6 \ s r6 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__rX rY r� c s �z UnequalIterablesError.__init__)N)�__name__� __module__� __qualname__r� � __classcell__rX rX r� rY r~ b s r~ c c s6 t | dti�D ]"}|D ]}|tu rt� �q|V qd S )N� fillvalue)r �_markerr~ )� iterablesZcombo�valrX rX rY �_zip_equal_generatorm s r� c G sr zRt | d �}t| dd � d�D ](\}}t |�}||kr t|||fd��q t| � W S tyl t| � Y S 0 d S )Nr � )r� )rg � enumerater~ ry � TypeErrorr� )r� Z first_size�i�it�sizerX rX rY � _zip_equalu s r� �fillc C sP t | �g| }|dkr$t|d|i�S |dkr4t|� S |dkrDt|� S td��dS )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� rS �ignorez Expected fill, strict, or ignoreN)rh r r� ry � ValueError)r_ r^ � incompleter� � iteratorsrX rX rY r* � s r* c g sB 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)r` rh �rangerg r r ri )r� r� Z num_activerX rX rY rD � s rD c C sH | du r t } 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 r` r r )rp r_ �t1�t2�p�p1Zp2rX rX rY r7 � s r7 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 s | ]}t � |�V qd S rU )r )�.0�r��srX rY � <genexpr>� r[ zpowerset.<locals>.<genexpr>r� )r\ r rr r� rg rq rX r� rY r; � s r; c c s� t � }|j}g }|j}|du}| D ]X}|r2||�n|}z||vrN||� |V W q" tyx ||vrt||� |V Y q"0 q"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�appendr� ) r_ rl ZseensetZ seenset_addZseenlistZ seenlist_addZuse_key�element�krX rX rY rP � s rP c C s4 |du rt 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� )r` r r ri )r_ rl rX rX rY rQ s rQ Fc 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. )rl �reverse)rl )�sortedrQ )r_ rl r� Z sequencedrX rX rY rO , s rO c c sF t |��* |dur|� V | � V qW d � n1 s80 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 )ru � exceptionrm rX rX rY r, @ s r, 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' )ri �filter)r_ rk rp rX rX rY r' ] 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, **kwarg)``. c S s g | ] }t |��qS rX �rs �r� �poolrX rX rY � <listcomp>� r[ z"random_product.<locals>.<listcomp>c s s | ]}t |�V qd S rU )r r� rX rX rY r� � r[ z!random_product.<locals>.<genexpr>r� )r rw �poolsrX rX rY rB q s rB c C s* t | �}|du rt|�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)rs rg r )r_ r� r� rX rX rY rA � s rA 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 s | ]}� | V qd S rU rX �r� r� �r� rX rY r� � r[ z%random_combination.<locals>.<genexpr>)rs rg r� r r� )r_ r� r^ �indicesrX r� rY r@ � s r@ 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 rU )r r� �r^ rX rY r� � r[ z6random_combination_with_replacement.<locals>.<genexpr>c 3 s | ]}� | V qd S rU rX r� r� rX rY r� � r[ )rs rg r� r� )r_ r� r� rX )r^ r� rY r? � s r? c C s� t | �}t|�}|dk s ||kr$t�d}t||| �}td|d �D ]}||| | | }qD|dk rn||7 }|dk s~||kr�t�g }|r�|| | |d |d }}}||kr�||8 }||| | |d }}q�|�|d| � q�t |�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� )rs rg r� �minr� � IndexErrorr� ) r_ r� �indexr� r^ �cr� r� �resultrX rX rY r3 � s( r3 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 )�valuerj rX rX rY r< � s r< c c s` 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 rc r� )rs rg r r r r� �_sumprod)�signalZkernelr^ �windowrV rX rX rY r% � s # r% c s0 t � �� g �� ��fdd�}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. c 3 s. � D ]$} �| �r| V q�� | � d S qd S rU )r� )�elem�r� � predicateZ transitionrX rY � true_iterator- s z'before_and_after.<locals>.true_iterator)rh r )r� r� r� Zremainder_iteratorrX r� rY 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� Nrx )r_ r� r� Zt3rX rX rY rN = s rN c C s6 t | |�}t|�D ]\}}tt|||�d � qt|� S rU )r r� ri r ry )r_ r^ r� r� rj rX rX rY �_sliding_window_isliceM s r� c c s@ t | �}tt||d �|d�}|D ]}|�|� t|�V q"d S )Nr� rc )rh r r r� rs )r_ r^ rj r� rV rX rX rY �_sliding_window_dequeU s r� c C sV |dkrt | |�S |dkr$t| |�S |dkr4t| �S |dkrDt| �S td|� ���dS )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 N)r� r� r6 ry r� rt rX rX rY rF ^ s rF 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� ) r\ r �slicer r� rg r` r r )r_ �seqZslicesrX rX rY rG w s rG c C s( dg}| D ]}t t|d| f��}q |S )u 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] Supports all numeric types: int, float, complex, Decimal, Fraction. r� )r\ r% )�rootsZpoly�rootrX rX rY r9 � s r9 c c s� t | dd�}|du rLt| ||�}t||�D ] \}}||u sB||kr*|V q*n\|du r\t| �n|}|d }tt��( |||d |� }V qrW d � n1 s�0 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� rg r r� )r_ r� rb �stopZ seq_indexrj r� r� rX rX rY r- � s r- c c s� | dkrdV d}t d�| d }t|d|t| �d d�D ]R}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)� bytearrayr- r �bytesrg r� )r^ rb �datar� rX rX rY rE � s . rE c c sN |dk rt d��t| �}tt||�� }rJ|rBt|�|krBt d��|V qdS )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� rh rs r rg )r_ r^ rS rj �batchrX rX rY �_batched� s r� i� )r" c C s t | ||d�S )NrR )�itertools_batched)r_ r^ rS rX rX rY 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� rX rX rY rM � s rM c C s t t�| �|�S )z�Reshape the 2-D input *matrix* to have a column count given by *cols*. >>> matrix = [(0, 1), (2, 3), (4, 5)] >>> cols = 3 >>> list(reshape(matrix, cols)) [(0, 1, 2), (3, 4, 5)] )r" r rr )�matrix�colsrX rX rY r> s r> 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 )rg r" r r� r rM )�m1�m2r^ rX rX rY r/ s r/ c C s� t d| �D ]h}d }}d}|dkrb|| | | }|| | | }|| | | }t|| | �}q|| kr | S q td��d S )Nr� r� zprime or under 5)r� r r� )r^ r{ rV rW �drX rX rY �_factor_pollard s r� �� c c s� | dk r dS t D ] }| | s|V | | } qqg }| dkr@| gng }|D ]8} | dk s\t| �rh|�| � qHt| �}||| | f7 }qHt|�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_211r+ r� r� r� )r^ �primeZprimes�todoZfactrX rX rY r( . s r( c C s> t | �}|dkr t|�d�S ttt|�tt|���}t| |�S )ad 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 Supports all numeric types: int, float, complex, Decimal, Fraction. r )rg �typer` �powr �reversedr� r� )� coefficientsrV r^ �powersrX rX rY r8 O s r8 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� rX rX rY rH d s rH c C s& t | �}ttd|��}ttt| |��S )uX 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] Supports all numeric types: int, float, complex, Decimal, Fraction. r� )rg r� r� r\ r` r )r� r^ r� rX rX rY r: o 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( )r^ r� rX rX rY rL � s rL ))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)r^ r� r� rX rX rY � _shift_to_odd� s $r� c C s� | dkr&| d@ r&d| kr$| k s*n J �t | d �\}}t||| �}|dksZ|| d kr^dS t|d �D ]"}|| | }|| d krj dS qjdS )Nr� r� TF)r� r� r� )r^ �baser� r� rV �_rX rX rY �_strong_probable_prime� s * r� c s� � dk r� dv S � d@ r@� d r@� d r@� d r@� d r@� d sDd S t D ]\}}� |k rH qtqH� 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� rX rY r� � r[ zis_prime.<locals>.<genexpr>�@ c 3 s | ]}t � |�V qd S rU )r� )r� r� r� rX rY r� � r[ )�_perfect_testsr� �all)r^ �limit�basesrX r� rY r+ � s !0 r+ 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� rX rX rY r. � s r. 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, 1, 1, 2) 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)``. When the multiplicities are all just 1, :func:`multinomial` is a special case of ``math.factorial`` so that ``multinomial(1, 1, 1, 1, 1, 1, 1) == math.factorial(7)``. Reference: https://en.wikipedia.org/wiki/Multinomial_theorem )r r` r r )�countsrX rX rY r0 s *r0 )r )N)N)N)N)r� N)N)N)NF)N)NN)N)r N)u�__doc__�random� collectionsr � contextlibr �collections.abcr � functoolsr r � itertoolsr r r r r r r r r r r r r �mathr r r r �operatorr r r r r r r �sysr �__all__�objectr� ry r� r� rT r� � ImportErrorrK rI rJ r$ r2 r! r� r= r5 r4 r1 r& r) rC r| r6 r} r� r~ r� r� r* rD r7 r; rP rQ rO r, r' rB rA r@ r? r3 r< r% r# rN r� r� rF rG r9 r- rE r� r" r� rM r> r/ r� rs r� r( r8 rH r: rL r� r� r� �Randomr� r+ r. r0 rX rX rX rY �<module> s� < 4 ( ( - *+! ) ! 0
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