Permutations with some identical elements: Difference between revisions
Permutations with some identical elements (view source)
Revision as of 07:19, 5 August 2022
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Line 1,267:
('B', 'B', 'C', 'A', 'A', 'B')
('A', 'C', 'B', 'B', 'A', 'B')
</pre>
Alternatively, generalized to accept any iterable.
<lang python>"""Permutations with some identical elements. Requires Python >= 3.7."""
from itertools import chain
from itertools import permutations
from itertools import repeat
from typing import Iterable
from typing import Tuple
from typing import TypeVar
T = TypeVar("T")
def permutations_repeated(
duplicates: Iterable[int],
symbols: Iterable[T],
) -> Iterable[Tuple[T, ...]]:
"""Return distinct permutations for `symbols` repeated `duplicates` times."""
iters = (repeat(sym, dup) for sym, dup in zip(symbols, duplicates))
return sorted(
set(
permutations(
chain.from_iterable(iters),
),
),
)
def main() -> None:
print(permutations_repeated([2, 3, 1], range(1, 4))) # 1-based
print(permutations_repeated([2, 3, 1], range(3))) # 0-based
print(permutations_repeated([2, 3, 1], ["A", "B", "C"])) # letters
if __name__ == "__main__":
main()
</lang>
{{out}}
<pre style="font-size:85%">
[(1, 1, 2, 2, 2, 3), (1, 1, 2, 2, 3, 2), (1, 1, 2, 3, 2, 2), (1, 1, 3, 2, 2, 2), (1, 2, 1, 2, 2, 3), (1, 2, 1, 2, 3, 2), (1, 2, 1, 3, 2, 2), (1, 2, 2, 1, 2, 3), (1, 2, 2, 1, 3, 2), (1, 2, 2, 2, 1, 3), (1, 2, 2, 2, 3, 1), (1, 2, 2, 3, 1, 2), (1, 2, 2, 3, 2, 1), (1, 2, 3, 1, 2, 2), (1, 2, 3, 2, 1, 2), (1, 2, 3, 2, 2, 1), (1, 3, 1, 2, 2, 2), (1, 3, 2, 1, 2, 2), (1, 3, 2, 2, 1, 2), (1, 3, 2, 2, 2, 1), (2, 1, 1, 2, 2, 3), (2, 1, 1, 2, 3, 2), (2, 1, 1, 3, 2, 2), (2, 1, 2, 1, 2, 3), (2, 1, 2, 1, 3, 2), (2, 1, 2, 2, 1, 3), (2, 1, 2, 2, 3, 1), (2, 1, 2, 3, 1, 2), (2, 1, 2, 3, 2, 1), (2, 1, 3, 1, 2, 2), (2, 1, 3, 2, 1, 2), (2, 1, 3, 2, 2, 1), (2, 2, 1, 1, 2, 3), (2, 2, 1, 1, 3, 2), (2, 2, 1, 2, 1, 3), (2, 2, 1, 2, 3, 1), (2, 2, 1, 3, 1, 2), (2, 2, 1, 3, 2, 1), (2, 2, 2, 1, 1, 3), (2, 2, 2, 1, 3, 1), (2, 2, 2, 3, 1, 1), (2, 2, 3, 1, 1, 2), (2, 2, 3, 1, 2, 1), (2, 2, 3, 2, 1, 1), (2, 3, 1, 1, 2, 2), (2, 3, 1, 2, 1, 2), (2, 3, 1, 2, 2, 1), (2, 3, 2, 1, 1, 2), (2, 3, 2, 1, 2, 1), (2, 3, 2, 2, 1, 1), (3, 1, 1, 2, 2, 2), (3, 1, 2, 1, 2, 2), (3, 1, 2, 2, 1, 2), (3, 1, 2, 2, 2, 1), (3, 2, 1, 1, 2, 2), (3, 2, 1, 2, 1, 2), (3, 2, 1, 2, 2, 1), (3, 2, 2, 1, 1, 2), (3, 2, 2, 1, 2, 1), (3, 2, 2, 2, 1, 1)]
[(0, 0, 1, 1, 1, 2), (0, 0, 1, 1, 2, 1), (0, 0, 1, 2, 1, 1), (0, 0, 2, 1, 1, 1), (0, 1, 0, 1, 1, 2), (0, 1, 0, 1, 2, 1), (0, 1, 0, 2, 1, 1), (0, 1, 1, 0, 1, 2), (0, 1, 1, 0, 2, 1), (0, 1, 1, 1, 0, 2), (0, 1, 1, 1, 2, 0), (0, 1, 1, 2, 0, 1), (0, 1, 1, 2, 1, 0), (0, 1, 2, 0, 1, 1), (0, 1, 2, 1, 0, 1), (0, 1, 2, 1, 1, 0), (0, 2, 0, 1, 1, 1), (0, 2, 1, 0, 1, 1), (0, 2, 1, 1, 0, 1), (0, 2, 1, 1, 1, 0), (1, 0, 0, 1, 1, 2), (1, 0, 0, 1, 2, 1), (1, 0, 0, 2, 1, 1), (1, 0, 1, 0, 1, 2), (1, 0, 1, 0, 2, 1), (1, 0, 1, 1, 0, 2), (1, 0, 1, 1, 2, 0), (1, 0, 1, 2, 0, 1), (1, 0, 1, 2, 1, 0), (1, 0, 2, 0, 1, 1), (1, 0, 2, 1, 0, 1), (1, 0, 2, 1, 1, 0), (1, 1, 0, 0, 1, 2), (1, 1, 0, 0, 2, 1), (1, 1, 0, 1, 0, 2), (1, 1, 0, 1, 2, 0), (1, 1, 0, 2, 0, 1), (1, 1, 0, 2, 1, 0), (1, 1, 1, 0, 0, 2), (1, 1, 1, 0, 2, 0), (1, 1, 1, 2, 0, 0), (1, 1, 2, 0, 0, 1), (1, 1, 2, 0, 1, 0), (1, 1, 2, 1, 0, 0), (1, 2, 0, 0, 1, 1), (1, 2, 0, 1, 0, 1), (1, 2, 0, 1, 1, 0), (1, 2, 1, 0, 0, 1), (1, 2, 1, 0, 1, 0), (1, 2, 1, 1, 0, 0), (2, 0, 0, 1, 1, 1), (2, 0, 1, 0, 1, 1), (2, 0, 1, 1, 0, 1), (2, 0, 1, 1, 1, 0), (2, 1, 0, 0, 1, 1), (2, 1, 0, 1, 0, 1), (2, 1, 0, 1, 1, 0), (2, 1, 1, 0, 0, 1), (2, 1, 1, 0, 1, 0), (2, 1, 1, 1, 0, 0)]
[('A', 'A', 'B', 'B', 'B', 'C'), ('A', 'A', 'B', 'B', 'C', 'B'), ('A', 'A', 'B', 'C', 'B', 'B'), ('A', 'A', 'C', 'B', 'B', 'B'), ('A', 'B', 'A', 'B', 'B', 'C'), ('A', 'B', 'A', 'B', 'C', 'B'), ('A', 'B', 'A', 'C', 'B', 'B'), ('A', 'B', 'B', 'A', 'B', 'C'), ('A', 'B', 'B', 'A', 'C', 'B'), ('A', 'B', 'B', 'B', 'A', 'C'), ('A', 'B', 'B', 'B', 'C', 'A'), ('A', 'B', 'B', 'C', 'A', 'B'), ('A', 'B', 'B', 'C', 'B', 'A'), ('A', 'B', 'C', 'A', 'B', 'B'), ('A', 'B', 'C', 'B', 'A', 'B'), ('A', 'B', 'C', 'B', 'B', 'A'), ('A', 'C', 'A', 'B', 'B', 'B'), ('A', 'C', 'B', 'A', 'B', 'B'), ('A', 'C', 'B', 'B', 'A', 'B'), ('A', 'C', 'B', 'B', 'B', 'A'), ('B', 'A', 'A', 'B', 'B', 'C'), ('B', 'A', 'A', 'B', 'C', 'B'), ('B', 'A', 'A', 'C', 'B', 'B'), ('B', 'A', 'B', 'A', 'B', 'C'), ('B', 'A', 'B', 'A', 'C', 'B'), ('B', 'A', 'B', 'B', 'A', 'C'), ('B', 'A', 'B', 'B', 'C', 'A'), ('B', 'A', 'B', 'C', 'A', 'B'), ('B', 'A', 'B', 'C', 'B', 'A'), ('B', 'A', 'C', 'A', 'B', 'B'), ('B', 'A', 'C', 'B', 'A', 'B'), ('B', 'A', 'C', 'B', 'B', 'A'), ('B', 'B', 'A', 'A', 'B', 'C'), ('B', 'B', 'A', 'A', 'C', 'B'), ('B', 'B', 'A', 'B', 'A', 'C'), ('B', 'B', 'A', 'B', 'C', 'A'), ('B', 'B', 'A', 'C', 'A', 'B'), ('B', 'B', 'A', 'C', 'B', 'A'), ('B', 'B', 'B', 'A', 'A', 'C'), ('B', 'B', 'B', 'A', 'C', 'A'), ('B', 'B', 'B', 'C', 'A', 'A'), ('B', 'B', 'C', 'A', 'A', 'B'), ('B', 'B', 'C', 'A', 'B', 'A'), ('B', 'B', 'C', 'B', 'A', 'A'), ('B', 'C', 'A', 'A', 'B', 'B'), ('B', 'C', 'A', 'B', 'A', 'B'), ('B', 'C', 'A', 'B', 'B', 'A'), ('B', 'C', 'B', 'A', 'A', 'B'), ('B', 'C', 'B', 'A', 'B', 'A'), ('B', 'C', 'B', 'B', 'A', 'A'), ('C', 'A', 'A', 'B', 'B', 'B'), ('C', 'A', 'B', 'A', 'B', 'B'), ('C', 'A', 'B', 'B', 'A', 'B'), ('C', 'A', 'B', 'B', 'B', 'A'), ('C', 'B', 'A', 'A', 'B', 'B'), ('C', 'B', 'A', 'B', 'A', 'B'), ('C', 'B', 'A', 'B', 'B', 'A'), ('C', 'B', 'B', 'A', 'A', 'B'), ('C', 'B', 'B', 'A', 'B', 'A'), ('C', 'B', 'B', 'B', 'A', 'A')]
</pre>
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