dynamic_programming.integer_partition
=====================================

.. py:module:: dynamic_programming.integer_partition

.. autoapi-nested-parse::

   The number of partitions of a number n into at least k parts equals the number of
   partitions into exactly k parts plus the number of partitions into at least k-1 parts.
   Subtracting 1 from each part of a partition of n into k parts gives a partition of n-k
   into k parts. These two facts together are used for this algorithm.
   * https://en.wikipedia.org/wiki/Partition_(number_theory)
   * https://en.wikipedia.org/wiki/Partition_function_(number_theory)



Attributes
----------

.. autoapisummary::

   dynamic_programming.integer_partition.n


Functions
---------

.. autoapisummary::

   dynamic_programming.integer_partition.partition


Module Contents
---------------

.. py:function:: partition(m: int) -> int

   >>> partition(5)
   7
   >>> partition(7)
   15
   >>> partition(100)
   190569292
   >>> partition(1_000)
   24061467864032622473692149727991
   >>> partition(-7)
   Traceback (most recent call last):
       ...
   IndexError: list index out of range
   >>> partition(0)
   Traceback (most recent call last):
       ...
   IndexError: list assignment index out of range
   >>> partition(7.8)
   Traceback (most recent call last):
       ...
   TypeError: 'float' object cannot be interpreted as an integer


.. py:data:: n