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README.rst
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Raymond Hettinger
Add subfactorial()
10 июн 2026, 06:06
10 июн 2026, 06:06
842a2b1
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============== More Itertools ============== .. image:: https://readthedocs.org/projects/more-itertools/badge/?version=latest :target: https://more-itertools.readthedocs.io/en/stable/ Python's ``itertools`` library is a gem - you can compose elegant solutions for a variety of problems with the functions it provides. In ``more-itertools`` we collect additional building blocks, recipes, and routines for working with Python iterables. +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Grouping | `chunked <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.chunked>`_, | | | `ichunked <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.ichunked>`_, | | | `chunked_even <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.chunked_even>`_, | | | `sliced <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.sliced>`_, | | | `constrained_batches <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.constrained_batches>`_, | | | `distribute <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.distribute>`_, | | | `divide <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.divide>`_, | | | `split_at <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.split_at>`_, | | | `split_before <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.split_before>`_, | | | `split_after <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.split_after>`_, | | | `split_into <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.split_into>`_, | | | `split_when <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.split_when>`_, | | | `bucket <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.bucket>`_, | | | `unzip <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.unzip>`_, | | | `batched <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.batched>`_, | | | `grouper <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.grouper>`_, | | | `partition <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.partition>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Lookahead and lookback | `spy <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.spy>`_, | | | `peekable <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.peekable>`_, | | | `seekable <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.seekable>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Windowing | `windowed <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.windowed>`_, | | | `substrings <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.substrings>`_, | | | `substrings_indexes <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.substrings_indexes>`_, | | | `stagger <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.stagger>`_, | | | `windowed_complete <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.windowed_complete>`_, | | | `pairwise <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.pairwise>`_, | | | `triplewise <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.triplewise>`_, | | | `sliding_window <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.sliding_window>`_, | | | `subslices <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.subslices>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Augmenting | `count_cycle <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.count_cycle>`_, | | | `intersperse <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.intersperse>`_, | | | `padded <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.padded>`_, | | | `repeat_each <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.repeat_each>`_, | | | `mark_ends <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.mark_ends>`_, | | | `repeat_last <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.repeat_last>`_, | | | `adjacent <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.adjacent>`_, | | | `groupby_transform <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.groupby_transform>`_, | | | `pad_none <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.pad_none>`_, | | | `ncycles <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.ncycles>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Combining | `collapse <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.collapse>`_, | | | `sort_together <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.sort_together>`_, | | | `interleave <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.interleave>`_, | | | `interleave_longest <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.interleave_longest>`_, | | | `interleave_evenly <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.interleave_evenly>`_, | | | `interleave_randomly <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.interleave_randomly>`_, | | | `zip_offset <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.zip_offset>`_, | | | `zip_broadcast <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.zip_broadcast>`_, | | | `flatten <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.flatten>`_, | | | `roundrobin <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.roundrobin>`_, | | | `prepend <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.prepend>`_, | | | `value_chain <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.value_chain>`_, | | | `partial_product <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.partial_product>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Concurrency | `concurrent_tee <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.concurrent_tee>`_, | | | `serialize <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.serialize>`_, | | | `synchronized <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.synchronized>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Summarizing | `ilen <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.ilen>`_, | | | `unique_to_each <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.unique_to_each>`_, | | | `sample <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.sample>`_, | | | `consecutive_groups <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.consecutive_groups>`_, | | | `run_length <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.run_length>`_, | | | `map_reduce <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.map_reduce>`_, | | | `join_mappings <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.join_mappings>`_, | | | `exactly_n <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.exactly_n>`_, | | | `is_sorted <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.is_sorted>`_, | | | `all_equal <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.all_equal>`_, | | | `all_unique <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.all_unique>`_, | | | `argmin <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.argmin>`_, | | | `argmax <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.argmax>`_, | | | `minmax <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.minmax>`_, | | | `first_true <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.first_true>`_, | | | `quantify <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.quantify>`_, | | | `iequals <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.iequals>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Selecting | `islice_extended <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.islice_extended>`_, | | | `first <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.first>`_, | | | `last <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.last>`_, | | | `one <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.one>`_, | | | `only <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.only>`_, | | | `strictly_n <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.strictly_n>`_, | | | `strip <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.strip>`_, | | | `lstrip <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.lstrip>`_, | | | `rstrip <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.rstrip>`_, | | | `filter_except <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.filter_except>`_, | | | `map_except <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.map_except>`_, | | | `filter_map <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.filter_map>`_, | | | `iter_suppress <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.iter_suppress>`_, | | | `nth_or_last <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.nth_or_last>`_, | | | `extract <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.extract>`_, | | | `unique_in_window <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.unique_in_window>`_, | | | `before_and_after <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.before_and_after>`_, | | | `nth <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.nth>`_, | | | `take <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.take>`_, | | | `tail <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.tail>`_, | | | `unique_everseen <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.unique_everseen>`_, | | | `unique_justseen <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.unique_justseen>`_, | | | `unique <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.unique>`_, | | | `duplicates_everseen <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.duplicates_everseen>`_, | | | `duplicates_justseen <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.duplicates_justseen>`_, | | | `classify_unique <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.classify_unique>`_, | | | `longest_common_prefix <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.longest_common_prefix>`_, | | | `takewhile_inclusive <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.takewhile_inclusive>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Math | `dft <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.dft>`_, | | | `idft <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.idft>`_, | | | `convolve <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.convolve>`_, | | | `dotproduct <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.dotproduct>`_, | | | `matmul <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.matmul>`_, | | | `polynomial_from_roots <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.polynomial_from_roots>`_, | | | `polynomial_derivative <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.polynomial_derivative>`_, | | | `polynomial_eval <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.polynomial_eval>`_, | | | `reshape <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.reshape>`_, | | | `sum_of_squares <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.sum_of_squares>`_, | | | `transpose <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.transpose>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Integer math | `factor <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.factor>`_, | | | `is_prime <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.is_prime>`_, | | | `multinomial <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.multinomial>`_, | | | `nth_prime <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.nth_prime>`_, | | | `sieve <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.sieve>`_, | | | `subfactorial <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.subfactorial>`_, | | | `totient <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.totient>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Statistics | `running_min <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.running_min>`_, | | | `running_max <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.running_max>`_, | | | `running_mean <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.running_mean>`_, | | | `running_median <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.running_median>`_, | | | `running_statistics <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.running_statistics>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Combinatorics | `circular_shifts <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.circular_shifts>`_, | | | `derangements <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.derangements>`_, | | | `gray_product <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.gray_product>`_, | | | `outer_product <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.outer_product>`_, | | | `partitions <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.partitions>`_, | | | `set_partitions <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.set_partitions>`_, | | | `powerset <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.powerset>`_, | | | `powerset_of_sets <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.powerset_of_sets>`_ | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | | `distinct_combinations <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.distinct_combinations>`_, | | | `distinct_permutations <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.distinct_permutations>`_ | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | | `combination_index <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.combination_index>`_, | | | `combination_with_replacement_index <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.combination_with_replacement_index>`_, | | | `permutation_index <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.permutation_index>`_, | | | `product_index <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.product_index>`_ | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | | `nth_combination <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.nth_combination>`_, | | | `nth_combination_with_replacement <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.nth_combination_with_replacement>`_, | | | `nth_permutation <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.nth_permutation>`_, | | | `nth_product <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.nth_product>`_ | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | | `random_combination <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.random_combination>`_, | | | `random_combination_with_replacement <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.random_combination_with_replacement>`_, | | | `random_derangement <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.random_derangement>`_, | | | `random_permutation <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.random_permutation>`_, | | | `random_product <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.random_product>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Wrapping | `always_iterable <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.always_iterable>`_, | | | `always_reversible <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.always_reversible>`_, | | | `countable <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.countable>`_, | | | `consumer <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.consumer>`_, | | | `iter_except <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.iter_except>`_, | | | `sized_iterator <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.sized_iterator>`_ | | | `with_iter <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.with_iter>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Others | `locate <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.locate>`_, | | | `rlocate <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.rlocate>`_, | | | `replace <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.replace>`_, | | | `numeric_range <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.numeric_range>`_, | | | `side_effect <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.side_effect>`_, | | | `iterate <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.iterate>`_, | | | `loops <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.loops>`_, | | | `difference <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.difference>`_, | | | `make_decorator <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.make_decorator>`_, | | | `SequenceView <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.SequenceView>`_, | | | `time_limited <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.time_limited>`_, | | | `map_if <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.map_if>`_, | | | `iter_index <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.iter_index>`_, | | | `consume <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.consume>`_, | | | `tabulate <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.tabulate>`_, | | | `repeatfunc <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.repeatfunc>`_, | | | `doublestarmap <https://more-itertools.readthedocs.io/en/stable/api.html#more_itertools.doublestarmap>`_ | +------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Getting started =============== To get started, install the library with `pip <https://pip.pypa.io/en/stable/>`_: .. code-block:: shell pip install more-itertools The recipes from the `itertools docs <https://docs.python.org/3/library/itertools.html#itertools-recipes>`_ are included in the top-level package: .. code-block:: python >>> from more_itertools import flatten >>> iterable = [(0, 1), (2, 3)] >>> list(flatten(iterable)) [0, 1, 2, 3] Several new recipes are available as well: .. code-block:: python >>> from more_itertools import chunked >>> iterable = [0, 1, 2, 3, 4, 5, 6, 7, 8] >>> list(chunked(iterable, 3)) [[0, 1, 2], [3, 4, 5], [6, 7, 8]] >>> from more_itertools import spy >>> iterable = (x * x for x in range(1, 6)) >>> head, iterable = spy(iterable, n=3) >>> list(head) [1, 4, 9] >>> list(iterable) [1, 4, 9, 16, 25] For the full listing of functions, see the `API documentation <https://more-itertools.readthedocs.io/en/stable/api.html>`_. Links elsewhere =============== Blog posts about ``more-itertools``: * `Yo, I heard you like decorators <https://www.bbayles.com/index/decorator_factory>`__ * `Tour of Python Itertools <https://martinheinz.dev/blog/16>`__ (`Alternate <https://dev.to/martinheinz/tour-of-python-itertools-4122>`__) * `Real-World Python More Itertools <https://python.plainenglish.io/real-world-more-itertools-gideons-blog-a3901c607550>`_ Development =========== ``more-itertools`` is maintained by `@erikrose <https://github.com/erikrose>`_ and `@bbayles <https://github.com/bbayles>`_, with help from `many others <https://github.com/more-itertools/more-itertools/graphs/contributors>`_. If you have a problem or suggestion, please file a bug or pull request in this repository. Thanks for contributing! Version History =============== The version history can be found in `documentation <https://more-itertools.readthedocs.io/en/stable/versions.html>`_.