https://github.com/python/cpython/commit/e1e85204edbf8c0c9ba1e50c74ac8708553585d8
commit: e1e85204edbf8c0c9ba1e50c74ac8708553585d8
branch: main
author: Raymond Hettinger <[email protected]>
committer: rhettinger <[email protected]>
date: 2025-02-06T18:35:55-06:00
summary:
Add multinomial to the itertools recipes docs (gh-129760)
files:
M Doc/library/itertools.rst
diff --git a/Doc/library/itertools.rst b/Doc/library/itertools.rst
index eb61453718bd3c..fbbec42ce9dae7 100644
--- a/Doc/library/itertools.rst
+++ b/Doc/library/itertools.rst
@@ -838,10 +838,10 @@ and :term:`generators <generator>` which incur
interpreter overhead.
.. testcode::
- from collections import deque
+ from collections import Counter, deque
from contextlib import suppress
from functools import reduce
- from math import sumprod, isqrt
+ from math import comb, prod, sumprod, isqrt
from operator import itemgetter, getitem, mul, neg
def take(n, iterable):
@@ -1127,6 +1127,12 @@ The following recipes have a more mathematical flavor:
n -= n // prime
return n
+ def multinomial(*counts):
+ "Number of distinct arrangements of a multiset."
+ # Counter('abracadabra').values() -> 5 2 1 1 2
+ # multinomial(5, 2, 1, 1, 2) → 83160
+ return prod(map(comb, accumulate(counts), counts))
+
.. doctest::
:hide:
@@ -1730,6 +1736,12 @@ The following recipes have a more mathematical flavor:
>>> ''.join(it)
'DEF1'
+ >>> multinomial(5, 2, 1, 1, 2)
+ 83160
+ >>> word = 'coffee'
+ >>> multinomial(*Counter(word).values()) == len(set(permutations(word)))
+ True
+
.. testcode::
:hide:
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