itertools
--- Functions creating iterators for efficient looping¶
Ce module implémente de nombreuses briques d'itérateurs inspirées par des éléments de APL, Haskell et SML. Toutes ont été retravaillées dans un format adapté à Python.
Ce module standardise un ensemble de base d'outils rapides et efficaces en mémoire qui peuvent être utilisés individuellement ou en les combinant. Ensemble, ils forment une « algèbre d'itérateurs » rendant possible la construction rapide et efficace d'outils spécialisés en Python.
Par exemple, SML fournit un outil de tabulation tabulate(f)
qui produit une séquence f(0), f(1), ...
. Le même résultat peut être obtenu en Python en combinant map()
et count()
pour former map(f, count())
.
Ces outils et leurs équivalents natifs fonctionnent également bien avec les fonctions optimisées du module operator
. Par exemple, l'opérateur de multiplication peut être appliqué à deux vecteurs pour créer un produit scalaire efficace : sum(map(operator.mul, vecteur1, vecteur2))
.
Itérateurs infinis :
Itérateur |
Arguments |
Résultats |
Exemple |
---|---|---|---|
[start[, step]] |
start, start+step, start+2*step, ... |
|
|
p |
p0, p1, ... plast, p0, p1, ... |
|
|
elem [,n] |
elem, elem, elem, ... à l'infini ou jusqu'à n fois |
|
Itérateurs se terminant par la séquence d'entrée la plus courte :
Itérateur |
Arguments |
Résultats |
Exemple |
---|---|---|---|
p [,func] |
p0, p0+p1, p0+p1+p2, ... |
|
|
p, n |
(p0, p1, ..., p_n-1), ... |
|
|
p, q, ... |
p0, p1, ... plast, q0, q1, ... |
|
|
itérable |
p0, p1, ... plast, q0, q1, ... |
|
|
data, selectors |
(d[0] if s[0]), (d[1] if s[1]), ... |
|
|
predicate, seq |
seq[n], seq[n+1], starting when predicate fails |
|
|
predicate, seq |
elements of seq where predicate(elem) fails |
|
|
iterable[, key] |
sous-itérateurs groupés par la valeur de key(v) |
||
seq, [start,] stop [, step] |
éléments de |
|
|
itérable |
(p[0], p[1]), (p[1], p[2]) |
|
|
func, seq |
func(*seq[0]), func(*seq[1]), ... |
|
|
predicate, seq |
seq[0], seq[1], until predicate fails |
|
|
it, n |
it1, it2, ... itn sépare un itérateur en n |
||
p, q, ... |
(p[0], q[0]), (p[1], q[1]), ... |
|
Itérateurs combinatoires :
Itérateur |
Arguments |
Résultats |
---|---|---|
p, q, ... [repeat=1] |
produit cartésien, équivalent à une boucle for imbriquée |
|
p[, r] |
n-uplets de longueur r, tous les ré-arrangements possibles, sans répétition d'éléments |
|
p, r |
n-uplets de longueur r, ordonnés, sans répétition d'éléments |
|
p, r |
n-uplets de longueur r, ordonnés, avec répétition d'éléments |
Exemples |
Résultats |
---|---|
|
|
|
|
|
|
|
|
Itertool Functions¶
Toutes les fonctions du module qui suivent construisent et renvoient des itérateurs. Certaines produisent des flux de longueur infinie ; celles-ci ne doivent donc être contrôlées que par des fonctions ou boucles qui interrompent le flux.
- itertools.accumulate(iterable[, function, *, initial=None])¶
Make an iterator that returns accumulated sums or accumulated results from other binary functions.
The function defaults to addition. The function should accept two arguments, an accumulated total and a value from the iterable.
If an initial value is provided, the accumulation will start with that value and the output will have one more element than the input iterable.
À peu près équivalent à :
def accumulate(iterable, function=operator.add, *, initial=None): 'Return running totals' # accumulate([1,2,3,4,5]) → 1 3 6 10 15 # accumulate([1,2,3,4,5], initial=100) → 100 101 103 106 110 115 # accumulate([1,2,3,4,5], operator.mul) → 1 2 6 24 120 iterator = iter(iterable) total = initial if initial is None: try: total = next(iterator) except StopIteration: return yield total for element in iterator: total = function(total, element) yield total
The function argument can be set to
min()
for a running minimum,max()
for a running maximum, oroperator.mul()
for a running product. Amortization tables can be built by accumulating interest and applying payments:>>> data = [3, 4, 6, 2, 1, 9, 0, 7, 5, 8] >>> list(accumulate(data, max)) # running maximum [3, 4, 6, 6, 6, 9, 9, 9, 9, 9] >>> list(accumulate(data, operator.mul)) # running product [3, 12, 72, 144, 144, 1296, 0, 0, 0, 0] # Amortize a 5% loan of 1000 with 10 annual payments of 90 >>> update = lambda balance, payment: round(balance * 1.05) - payment >>> list(accumulate(repeat(90, 10), update, initial=1_000)) [1000, 960, 918, 874, 828, 779, 728, 674, 618, 559, 497]
Voir
functools.reduce()
pour une fonction similaire qui ne renvoie que la valeur accumulée finale.Ajouté dans la version 3.2.
Modifié dans la version 3.3: Added the optional function parameter.
Modifié dans la version 3.8: Ajout du paramètre optionnel initial.
- itertools.batched(iterable, n)¶
Batch data from the iterable into tuples of length n. The last batch may be shorter than n.
Loops over the input iterable and accumulates data into tuples up to size n. The input is consumed lazily, just enough to fill a batch. The result is yielded as soon as the batch is full or when the input iterable is exhausted:
>>> flattened_data = ['roses', 'red', 'violets', 'blue', 'sugar', 'sweet'] >>> unflattened = list(batched(flattened_data, 2)) >>> unflattened [('roses', 'red'), ('violets', 'blue'), ('sugar', 'sweet')]
À peu près équivalent à :
def batched(iterable, n): # batched('ABCDEFG', 3) → ABC DEF G if n < 1: raise ValueError('n must be at least one') iterator = iter(iterable) while batch := tuple(islice(iterator, n)): yield batch
Ajouté dans la version 3.12.
- itertools.chain(*iterables)¶
Crée un itérateur qui renvoie les éléments du premier itérable jusqu'à son épuisement, puis continue avec l'itérable suivant jusqu'à ce que tous les itérables soient épuisés. Utilisée pour traiter des séquences consécutives comme une seule séquence. À peu près équivalent à :
def chain(*iterables): # chain('ABC', 'DEF') → A B C D E F for iterable in iterables: yield from iterable
- classmethod chain.from_iterable(iterable)¶
Constructeur alternatif pour
chain()
. Récupère des entrées chaînées depuis un unique itérable passé en argument, qui est évalué de manière paresseuse. À peu près équivalent à :def from_iterable(iterables): # chain.from_iterable(['ABC', 'DEF']) → A B C D E F for iterable in iterables: yield from iterable
- itertools.combinations(iterable, r)¶
Renvoie les combinaisons de longueur r de iterable.
The output is a subsequence of
product()
keeping only entries that are subsequences of the iterable. The length of the output is given bymath.comb()
which computesn! / r! / (n - r)!
when0 ≤ r ≤ n
or zero whenr > n
.The combination tuples are emitted in lexicographic order according to the order of the input iterable. If the input iterable is sorted, the output tuples will be produced in sorted order.
Elements are treated as unique based on their position, not on their value. If the input elements are unique, there will be no repeated values within each combination.
À peu près équivalent à :
def combinations(iterable, r): # combinations('ABCD', 2) → AB AC AD BC BD CD # combinations(range(4), 3) → 012 013 023 123 pool = tuple(iterable) n = len(pool) if r > n: return indices = list(range(r)) yield tuple(pool[i] for i in indices) while True: for i in reversed(range(r)): if indices[i] != i + n - r: break else: return indices[i] += 1 for j in range(i+1, r): indices[j] = indices[j-1] + 1 yield tuple(pool[i] for i in indices)
- itertools.combinations_with_replacement(iterable, r)¶
Renvoyer les sous-séquences de longueur r des éléments de l'itérable iterable d'entrée, permettant aux éléments individuels d'être répétés plus d'une fois.
The output is a subsequence of
product()
that keeps only entries that are subsequences (with possible repeated elements) of the iterable. The number of subsequence returned is(n + r - 1)! / r! / (n - 1)!
whenn > 0
.The combination tuples are emitted in lexicographic order according to the order of the input iterable. if the input iterable is sorted, the output tuples will be produced in sorted order.
Elements are treated as unique based on their position, not on their value. If the input elements are unique, the generated combinations will also be unique.
À peu près équivalent à :
def combinations_with_replacement(iterable, r): # combinations_with_replacement('ABC', 2) → AA AB AC BB BC CC pool = tuple(iterable) n = len(pool) if not n and r: return indices = [0] * r yield tuple(pool[i] for i in indices) while True: for i in reversed(range(r)): if indices[i] != n - 1: break else: return indices[i:] = [indices[i] + 1] * (r - i) yield tuple(pool[i] for i in indices)
Ajouté dans la version 3.1.
- itertools.compress(data, selectors)¶
Make an iterator that returns elements from data where the corresponding element in selectors is true. Stops when either the data or selectors iterables have been exhausted. Roughly equivalent to:
def compress(data, selectors): # compress('ABCDEF', [1,0,1,0,1,1]) → A C E F return (datum for datum, selector in zip(data, selectors) if selector)
Ajouté dans la version 3.1.
- itertools.count(start=0, step=1)¶
Make an iterator that returns evenly spaced values beginning with start. Can be used with
map()
to generate consecutive data points or withzip()
to add sequence numbers. Roughly equivalent to:def count(start=0, step=1): # count(10) → 10 11 12 13 14 ... # count(2.5, 0.5) → 2.5 3.0 3.5 ... n = start while True: yield n n += step
When counting with floating-point numbers, better accuracy can sometimes be achieved by substituting multiplicative code such as:
(start + step * i for i in count())
.Modifié dans la version 3.1: Ajout de l'argument step et ajout du support pour les arguments non-entiers.
- itertools.cycle(iterable)¶
Make an iterator returning elements from the iterable and saving a copy of each. When the iterable is exhausted, return elements from the saved copy. Repeats indefinitely. Roughly equivalent to:
def cycle(iterable): # cycle('ABCD') → A B C D A B C D A B C D ... saved = [] for element in iterable: yield element saved.append(element) while saved: for element in saved: yield element
This itertool may require significant auxiliary storage (depending on the length of the iterable).
- itertools.dropwhile(predicate, iterable)¶
Make an iterator that drops elements from the iterable while the predicate is true and afterwards returns every element. Roughly equivalent to:
def dropwhile(predicate, iterable): # dropwhile(lambda x: x<5, [1,4,6,3,8]) → 6 3 8 iterator = iter(iterable) for x in iterator: if not predicate(x): yield x break for x in iterator: yield x
Note this does not produce any output until the predicate first becomes false, so this itertool may have a lengthy start-up time.
- itertools.filterfalse(predicate, iterable)¶
Make an iterator that filters elements from the iterable returning only those for which the predicate returns a false value. If predicate is
None
, returns the items that are false. Roughly equivalent to:def filterfalse(predicate, iterable): # filterfalse(lambda x: x<5, [1,4,6,3,8]) → 6 8 if predicate is None: predicate = bool for x in iterable: if not predicate(x): yield x
- itertools.groupby(iterable, key=None)¶
Crée un itérateur qui renvoie les clés et les groupes de l'itérable iterable. La clé key est une fonction qui génère une clé pour chaque élément. Si key n'est pas spécifiée ou est
None
, elle vaut par défaut une fonction d'identité qui renvoie l'élément sans le modifier. Généralement, l'itérable a besoin d'avoir ses éléments déjà classés selon cette même fonction de clé.L'opération de
groupby()
est similaire au filtreuniq
dans Unix. Elle génère un nouveau groupe à chaque fois que la valeur de la fonction key change (ce pourquoi il est souvent nécessaire d'avoir trié les données selon la même fonction de clé). Ce comportement est différent de celui de GROUP BY de SQL qui agrège les éléments sans prendre compte de leur ordre d'entrée.Le groupe renvoyé est lui-même un itérateur qui partage l'itérable sous-jacent avec
groupby()
. Puisque que la source est partagée, quand l'objetgroupby()
est avancé, le groupe précédent n'est plus visible. Ainsi, si cette donnée doit être utilisée plus tard, elle doit être stockée comme une liste :groups = [] uniquekeys = [] data = sorted(data, key=keyfunc) for k, g in groupby(data, keyfunc): groups.append(list(g)) # Store group iterator as a list uniquekeys.append(k)
groupby()
est à peu près équivalente à :def groupby(iterable, key=None): # [k for k, g in groupby('AAAABBBCCDAABBB')] → A B C D A B # [list(g) for k, g in groupby('AAAABBBCCD')] → AAAA BBB CC D keyfunc = (lambda x: x) if key is None else key iterator = iter(iterable) exhausted = False def _grouper(target_key): nonlocal curr_value, curr_key, exhausted yield curr_value for curr_value in iterator: curr_key = keyfunc(curr_value) if curr_key != target_key: return yield curr_value exhausted = True try: curr_value = next(iterator) except StopIteration: return curr_key = keyfunc(curr_value) while not exhausted: target_key = curr_key curr_group = _grouper(target_key) yield curr_key, curr_group if curr_key == target_key: for _ in curr_group: pass
- itertools.islice(iterable, stop)¶
- itertools.islice(iterable, start, stop[, step])
Make an iterator that returns selected elements from the iterable. Works like sequence slicing but does not support negative values for start, stop, or step.
If start is zero or
None
, iteration starts at zero. Otherwise, elements from the iterable are skipped until start is reached.If stop is
None
, iteration continues until the iterator is exhausted, if at all. Otherwise, it stops at the specified position.If step is
None
, the step defaults to one. Elements are returned consecutively unless step is set higher than one which results in items being skipped.À peu près équivalent à :
def islice(iterable, *args): # islice('ABCDEFG', 2) → A B # islice('ABCDEFG', 2, 4) → C D # islice('ABCDEFG', 2, None) → C D E F G # islice('ABCDEFG', 0, None, 2) → A C E G s = slice(*args) start = 0 if s.start is None else s.start stop = s.stop step = 1 if s.step is None else s.step if start < 0 or (stop is not None and stop < 0) or step <= 0: raise ValueError indices = count() if stop is None else range(max(start, stop)) next_i = start for i, element in zip(indices, iterable): if i == next_i: yield element next_i += step
- itertools.pairwise(iterable)¶
Renvoie des paires successives d'éléments consécutifs de iterable.
En toute logique, il y a une paire de moins que d'éléments dans l'itérable. Aucune paire n'est renvoyée si l'itérable a zéro ou une valeur.
À peu près équivalent à :
def pairwise(iterable): # pairwise('ABCDEFG') → AB BC CD DE EF FG iterator = iter(iterable) a = next(iterator, None) for b in iterator: yield a, b a = b
Ajouté dans la version 3.10.
- itertools.permutations(iterable, r=None)¶
Return successive r length permutations of elements from the iterable.
Si r n'est pas spécifié ou vaut
None
, alors r a pour valeur la longueur de iterable et toutes les permutations de longueur r possibles sont générées.The output is a subsequence of
product()
where entries with repeated elements have been filtered out. The length of the output is given bymath.perm()
which computesn! / (n - r)!
when0 ≤ r ≤ n
or zero whenr > n
.The permutation tuples are emitted in lexicographic order according to the order of the input iterable. If the input iterable is sorted, the output tuples will be produced in sorted order.
Elements are treated as unique based on their position, not on their value. If the input elements are unique, there will be no repeated values within a permutation.
À peu près équivalent à :
def permutations(iterable, r=None): # permutations('ABCD', 2) → AB AC AD BA BC BD CA CB CD DA DB DC # permutations(range(3)) → 012 021 102 120 201 210 pool = tuple(iterable) n = len(pool) r = n if r is None else r if r > n: return indices = list(range(n)) cycles = list(range(n, n-r, -1)) yield tuple(pool[i] for i in indices[:r]) while n: for i in reversed(range(r)): cycles[i] -= 1 if cycles[i] == 0: indices[i:] = indices[i+1:] + indices[i:i+1] cycles[i] = n - i else: j = cycles[i] indices[i], indices[-j] = indices[-j], indices[i] yield tuple(pool[i] for i in indices[:r]) break else: return
- itertools.product(*iterables, repeat=1)¶
Produit cartésien des itérables d'entrée.
À peu près équivalent à des boucles for imbriquées dans une expression de générateur. Par exemple
product(A, B)
renvoie la même chose que((x, y) for x in A for y in B)
.Les boucles imbriquées tournent comme un compteur kilométrique avec l'élément le plus à droite avançant à chaque itération. Ce motif défini un ordre lexicographique afin que, si les éléments des itérables en l'entrée sont ordonnés, les n-uplets produits le sont aussi.
Pour générer le produit d'un itérable avec lui-même, spécifiez le nombre de répétitions avec le paramètre nommé optionnel repeat. Par exemple,
product(A, repeat=4)
est équivalent àproduct(A, A, A, A)
.Cette fonction est à peu près équivalente au code suivant, à la différence près que la vraie implémentation ne crée pas de résultats intermédiaires en mémoire :
def product(*iterables, repeat=1): # product('ABCD', 'xy') → Ax Ay Bx By Cx Cy Dx Dy # product(range(2), repeat=3) → 000 001 010 011 100 101 110 111 pools = [tuple(pool) for pool in iterables] * repeat result = [[]] for pool in pools: result = [x+[y] for x in result for y in pool] for prod in result: yield tuple(prod)
product()
commence par consommer totalement les itérables qui lui sont passés et les conserve en mémoire pour générer les produits. Par conséquent, cette fonction ne sert que sur des itérables finis.
- itertools.repeat(object[, times])¶
Crée un itérateur qui renvoie object à l'infini. S'exécute indéfiniment sauf si l'argument times est spécifié.
À peu près équivalent à :
def repeat(object, times=None): # repeat(10, 3) → 10 10 10 if times is None: while True: yield object else: for i in range(times): yield object
Une utilisation courante de repeat est de fournir un flux constant de valeurs à map ou zip :
>>> list(map(pow, range(10), repeat(2))) [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
- itertools.starmap(function, iterable)¶
Make an iterator that computes the function using arguments obtained from the iterable. Used instead of
map()
when argument parameters have already been "pre-zipped" into tuples.The difference between
map()
andstarmap()
parallels the distinction betweenfunction(a,b)
andfunction(*c)
. Roughly equivalent to:def starmap(function, iterable): # starmap(pow, [(2,5), (3,2), (10,3)]) → 32 9 1000 for args in iterable: yield function(*args)
- itertools.takewhile(predicate, iterable)¶
Make an iterator that returns elements from the iterable as long as the predicate is true. Roughly equivalent to:
def takewhile(predicate, iterable): # takewhile(lambda x: x<5, [1,4,6,3,8]) → 1 4 for x in iterable: if not predicate(x): break yield x
Note, the element that first fails the predicate condition is consumed from the input iterator and there is no way to access it. This could be an issue if an application wants to further consume the input iterator after takewhile has been run to exhaustion. To work around this problem, consider using more-iterools before_and_after() instead.
- itertools.tee(iterable, n=2)¶
Renvoie n itérateurs indépendants depuis un unique itérable.
À peu près équivalent à :
def tee(iterable, n=2): iterator = iter(iterable) shared_link = [None, None] return tuple(_tee(iterator, shared_link) for _ in range(n)) def _tee(iterator, link): try: while True: if link[1] is None: link[0] = next(iterator) link[1] = [None, None] value, link = link yield value except StopIteration: return
Une fois qu’un
tee()
a été créé, l’original de iterable ne doit être utilisé nulle part ailleurs ; sinon iterable pourrait être avancé sans que les objets tee n’en soient informés.tee
iterators are not threadsafe. ARuntimeError
may be raised when simultaneously using iterators returned by the sametee()
call, even if the original iterable is threadsafe.Cet outil peut avoir besoin d'un stockage auxiliaire important (en fonction de la taille des données temporaires nécessaires). En général, si un itérateur utilise la majorité ou toute la donnée avant qu'un autre itérateur ne commence, il est plus rapide d'utiliser
list()
à la place detee()
.
- itertools.zip_longest(*iterables, fillvalue=None)¶
Make an iterator that aggregates elements from each of the iterables.
If the iterables are of uneven length, missing values are filled-in with fillvalue. If not specified, fillvalue defaults to
None
.Iteration continues until the longest iterable is exhausted.
À peu près équivalent à :
def zip_longest(*iterables, fillvalue=None): # zip_longest('ABCD', 'xy', fillvalue='-') → Ax By C- D- iterators = list(map(iter, iterables)) num_active = len(iterators) if not num_active: return while True: values = [] for i, iterator in enumerate(iterators): try: value = next(iterator) except StopIteration: num_active -= 1 if not num_active: return iterators[i] = repeat(fillvalue) value = fillvalue values.append(value) yield tuple(values)
If one of the iterables is potentially infinite, then the
zip_longest()
function should be wrapped with something that limits the number of calls (for exampleislice()
ortakewhile()
).
Recettes itertools¶
Cette section présente des recettes pour créer une vaste boîte à outils en se servant des itertools existants comme des briques.
The primary purpose of the itertools recipes is educational. The recipes show
various ways of thinking about individual tools — for example, that
chain.from_iterable
is related to the concept of flattening. The recipes
also give ideas about ways that the tools can be combined — for example, how
starmap()
and repeat()
can work together. The recipes also show patterns
for using itertools with the operator
and collections
modules as
well as with the built-in itertools such as map()
, filter()
,
reversed()
, and enumerate()
.
A secondary purpose of the recipes is to serve as an incubator. The
accumulate()
, compress()
, and pairwise()
itertools started out as
recipes. Currently, the sliding_window()
, iter_index()
, and sieve()
recipes are being tested to see whether they prove their worth.
Substantially all of these recipes and many, many others can be installed from the more-itertools project found on the Python Package Index:
python -m pip install more-itertools
Many of the recipes offer the same high performance as the underlying toolset. Superior memory performance is kept by processing elements one at a time rather than bringing the whole iterable into memory all at once. Code volume is kept small by linking the tools together in a functional style. High speed is retained by preferring "vectorized" building blocks over the use of for-loops and generators which incur interpreter overhead.
import collections
import contextlib
import functools
import math
import operator
import random
def take(n, iterable):
"Return first n items of the iterable as a list."
return list(islice(iterable, n))
def prepend(value, iterable):
"Prepend a single value in front of an iterable."
# prepend(1, [2, 3, 4]) → 1 2 3 4
return chain([value], iterable)
def tabulate(function, start=0):
"Return function(0), function(1), ..."
return map(function, count(start))
def repeatfunc(func, times=None, *args):
"Repeat calls to func with specified arguments."
if times is None:
return starmap(func, repeat(args))
return starmap(func, repeat(args, times))
def flatten(list_of_lists):
"Flatten one level of nesting."
return chain.from_iterable(list_of_lists)
def ncycles(iterable, n):
"Returns the sequence elements n times."
return chain.from_iterable(repeat(tuple(iterable), n))
def tail(n, iterable):
"Return an iterator over the last n items."
# tail(3, 'ABCDEFG') → E F G
return iter(collections.deque(iterable, maxlen=n))
def consume(iterator, n=None):
"Advance the iterator n-steps ahead. If n is None, consume entirely."
# Use functions that consume iterators at C speed.
if n is None:
collections.deque(iterator, maxlen=0)
else:
next(islice(iterator, n, n), None)
def nth(iterable, n, default=None):
"Returns the nth item or a default value."
return next(islice(iterable, n, None), default)
def quantify(iterable, predicate=bool):
"Given a predicate that returns True or False, count the True results."
return sum(map(predicate, iterable))
def first_true(iterable, default=False, predicate=None):
"Returns the first true value or the *default* if there is no true value."
# first_true([a,b,c], x) → a or b or c or x
# first_true([a,b], x, f) → a if f(a) else b if f(b) else x
return next(filter(predicate, iterable), default)
def all_equal(iterable, key=None):
"Returns True if all the elements are equal to each other."
# all_equal('4٤௪౪໔', key=int) → True
return len(take(2, groupby(iterable, key))) <= 1
def unique_justseen(iterable, key=None):
"Yield unique elements, preserving order. Remember only the element just seen."
# unique_justseen('AAAABBBCCDAABBB') → A B C D A B
# unique_justseen('ABBcCAD', str.casefold) → A B c A D
if key is None:
return map(operator.itemgetter(0), groupby(iterable))
return map(next, map(operator.itemgetter(1), groupby(iterable, key)))
def unique_everseen(iterable, key=None):
"Yield unique elements, preserving order. Remember all elements ever seen."
# unique_everseen('AAAABBBCCDAABBB') → A B C D
# unique_everseen('ABBcCAD', str.casefold) → A B c D
seen = set()
if key is None:
for element in filterfalse(seen.__contains__, iterable):
seen.add(element)
yield element
else:
for element in iterable:
k = key(element)
if k not in seen:
seen.add(k)
yield element
def unique(iterable, key=None, reverse=False):
"Yield unique elements in sorted order. Supports unhashable inputs."
# unique([[1, 2], [3, 4], [1, 2]]) → [1, 2] [3, 4]
return unique_justseen(sorted(iterable, key=key, reverse=reverse), key=key)
def sliding_window(iterable, n):
"Collect data into overlapping fixed-length chunks or blocks."
# sliding_window('ABCDEFG', 4) → ABCD BCDE CDEF DEFG
iterator = iter(iterable)
window = collections.deque(islice(iterator, n - 1), maxlen=n)
for x in iterator:
window.append(x)
yield tuple(window)
def grouper(iterable, n, *, incomplete='fill', fillvalue=None):
"Collect data into non-overlapping fixed-length chunks or blocks."
# grouper('ABCDEFG', 3, fillvalue='x') → ABC DEF Gxx
# grouper('ABCDEFG', 3, incomplete='strict') → ABC DEF ValueError
# grouper('ABCDEFG', 3, incomplete='ignore') → ABC DEF
iterators = [iter(iterable)] * n
match incomplete:
case 'fill':
return zip_longest(*iterators, fillvalue=fillvalue)
case 'strict':
return zip(*iterators, strict=True)
case 'ignore':
return zip(*iterators)
case _:
raise ValueError('Expected fill, strict, or ignore')
def roundrobin(*iterables):
"Visit input iterables in a cycle until each is exhausted."
# roundrobin('ABC', 'D', 'EF') → A D E B F C
# Algorithm credited to George Sakkis
iterators = map(iter, iterables)
for num_active in range(len(iterables), 0, -1):
iterators = cycle(islice(iterators, num_active))
yield from map(next, iterators)
def partition(predicate, iterable):
"""Partition entries into false entries and true entries.
If *predicate* is slow, consider wrapping it with functools.lru_cache().
"""
# partition(is_odd, range(10)) → 0 2 4 6 8 and 1 3 5 7 9
t1, t2 = tee(iterable)
return filterfalse(predicate, t1), filter(predicate, t2)
def subslices(seq):
"Return all contiguous non-empty subslices of a sequence."
# subslices('ABCD') → A AB ABC ABCD B BC BCD C CD D
slices = starmap(slice, combinations(range(len(seq) + 1), 2))
return map(operator.getitem, repeat(seq), slices)
def iter_index(iterable, value, start=0, stop=None):
"Return indices where a value occurs in a sequence or iterable."
# iter_index('AABCADEAF', 'A') → 0 1 4 7
seq_index = getattr(iterable, 'index', None)
if seq_index is None:
iterator = islice(iterable, start, stop)
for i, element in enumerate(iterator, start):
if element is value or element == value:
yield i
else:
stop = len(iterable) if stop is None else stop
i = start
with contextlib.suppress(ValueError):
while True:
yield (i := seq_index(value, i, stop))
i += 1
def iter_except(func, exception, first=None):
"Convert a call-until-exception interface to an iterator interface."
# iter_except(d.popitem, KeyError) → non-blocking dictionary iterator
with contextlib.suppress(exception):
if first is not None:
yield first()
while True:
yield func()
The following recipes have a more mathematical flavor:
def powerset(iterable):
"powerset([1,2,3]) → () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
s = list(iterable)
return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
def sum_of_squares(iterable):
"Add up the squares of the input values."
# sum_of_squares([10, 20, 30]) → 1400
return math.sumprod(*tee(iterable))
def reshape(matrix, cols):
"Reshape a 2-D matrix to have a given number of columns."
# reshape([(0, 1), (2, 3), (4, 5)], 3) → (0, 1, 2), (3, 4, 5)
return batched(chain.from_iterable(matrix), cols)
def transpose(matrix):
"Swap the rows and columns of a 2-D matrix."
# transpose([(1, 2, 3), (11, 22, 33)]) → (1, 11) (2, 22) (3, 33)
return zip(*matrix, strict=True)
def matmul(m1, m2):
"Multiply two matrices."
# matmul([(7, 5), (3, 5)], [(2, 5), (7, 9)]) → (49, 80), (41, 60)
n = len(m2[0])
return batched(starmap(math.sumprod, product(m1, transpose(m2))), n)
def convolve(signal, kernel):
"""Discrete linear convolution of two iterables.
Equivalent to polynomial multiplication.
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.
Article: https://betterexplained.com/articles/intuitive-convolution/
Video: https://www.youtube.com/watch?v=KuXjwB4LzSA
"""
# convolve([1, -1, -20], [1, -3]) → 1 -4 -17 60
# convolve(data, [0.25, 0.25, 0.25, 0.25]) → Moving average (blur)
# convolve(data, [1/2, 0, -1/2]) → 1st derivative estimate
# convolve(data, [1, -2, 1]) → 2nd derivative estimate
kernel = tuple(kernel)[::-1]
n = len(kernel)
padded_signal = chain(repeat(0, n-1), signal, repeat(0, n-1))
windowed_signal = sliding_window(padded_signal, n)
return map(math.sumprod, repeat(kernel), windowed_signal)
def polynomial_from_roots(roots):
"""Compute a polynomial's coefficients from its roots.
(x - 5) (x + 4) (x - 3) expands to: x³ -4x² -17x + 60
"""
# polynomial_from_roots([5, -4, 3]) → [1, -4, -17, 60]
factors = zip(repeat(1), map(operator.neg, roots))
return list(functools.reduce(convolve, factors, [1]))
def polynomial_eval(coefficients, x):
"""Evaluate a polynomial at a specific value.
Computes with better numeric stability than Horner's method.
"""
# Evaluate x³ -4x² -17x + 60 at x = 5
# polynomial_eval([1, -4, -17, 60], x=5) → 0
n = len(coefficients)
if not n:
return type(x)(0)
powers = map(pow, repeat(x), reversed(range(n)))
return math.sumprod(coefficients, powers)
def polynomial_derivative(coefficients):
"""Compute the first derivative of a polynomial.
f(x) = x³ -4x² -17x + 60
f'(x) = 3x² -8x -17
"""
# polynomial_derivative([1, -4, -17, 60]) → [3, -8, -17]
n = len(coefficients)
powers = reversed(range(1, n))
return list(map(operator.mul, coefficients, powers))
def sieve(n):
"Primes less than n."
# sieve(30) → 2 3 5 7 11 13 17 19 23 29
if n > 2:
yield 2
data = bytearray((0, 1)) * (n // 2)
for p in iter_index(data, 1, start=3, stop=math.isqrt(n) + 1):
data[p*p : n : p+p] = bytes(len(range(p*p, n, p+p)))
yield from iter_index(data, 1, start=3)
def factor(n):
"Prime factors of n."
# factor(99) → 3 3 11
# factor(1_000_000_000_000_007) → 47 59 360620266859
# factor(1_000_000_000_000_403) → 1000000000000403
for prime in sieve(math.isqrt(n) + 1):
while not n % prime:
yield prime
n //= prime
if n == 1:
return
if n > 1:
yield n
def totient(n):
"Count of natural numbers up to n that are coprime to n."
# https://mathworld.wolfram.com/TotientFunction.html
# totient(12) → 4 because len([1, 5, 7, 11]) == 4
for prime in set(factor(n)):
n -= n // prime
return n