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Add itertools recipe for directly finding the n-th combination #5161

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Jan 13, 2018
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Add itertools recipe for directly finding the n-th combination #5161

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544f23b
Add nth_combination recipe and test
rhettinger Jan 12, 2018
b629ad9
Use same parameter names as the other recipes
rhettinger Jan 12, 2018
da2746c
Move range check to start of function. Expand tests to include negat…
rhettinger Jan 13, 2018
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23 changes: 23 additions & 0 deletions Doc/library/itertools.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -859,6 +859,29 @@ which incur interpreter overhead.
indices = sorted(random.randrange(n) for i in range(r))
return tuple(pool[i] for i in indices)

def nth_combination(iterable, r, index):
'Equivalent to list(combinations(iterable, r))[index]'
pool = tuple(iterable)
n = len(pool)
if r < 0 or r > n:
raise ValueError
c = 1
k = min(r, n-r)
for i in range(1, k+1):
c = c * (n - k + i) // i
if index < 0:
index += c
if index < 0 or index >= c:
raise IndexError
result = []
while r:
c, n, r = c*r//n, n-1, r-1
while index >= c:
index -= c
c, n = c*(n-r)//n, n-1
result.append(pool[-1-n])
return tuple(result)

Note, many of the above recipes can be optimized by replacing global lookups
with local variables defined as default values. For example, the
*dotproduct* recipe can be written as::
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33 changes: 33 additions & 0 deletions Lib/test/test_itertools.py
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Expand Up @@ -2262,6 +2262,30 @@ def test_permutations_sizeof(self):
... # first_true([a,b], x, f) --> a if f(a) else b if f(b) else x
... return next(filter(pred, iterable), default)

>>> def nth_combination(iterable, r, index):
... 'Equivalent to list(combinations(iterable, r))[index]'
... pool = tuple(iterable)
... n = len(pool)
... if r < 0 or r > n:
... raise ValueError
... c = 1
... k = min(r, n-r)
... for i in range(1, k+1):
... c = c * (n - k + i) // i
... if index < 0:
... index += c
... if index < 0 or index >= c:
... raise IndexError
... result = []
... while r:
... c, n, r = c*r//n, n-1, r-1
... while index >= c:
... index -= c
... c, n = c*(n-r)//n, n-1
... result.append(pool[-1-n])
... return tuple(result)


This is not part of the examples but it tests to make sure the definitions
perform as purported.

Expand Down Expand Up @@ -2345,6 +2369,15 @@ def test_permutations_sizeof(self):
>>> first_true('ABC0DEF1', '9', str.isdigit)
'0'

>>> population = 'ABCDEFGH'
>>> for r in range(len(population) + 1):
... seq = list(combinations(population, r))
... for i in range(len(seq)):
... assert nth_combination(population, r, i) == seq[i]
... for i in range(-len(seq), 0):
... assert nth_combination(population, r, i) == seq[i]


"""

__test__ = {'libreftest' : libreftest}
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