project_euler.problem_031.sol2
==============================

.. py:module:: project_euler.problem_031.sol2

.. autoapi-nested-parse::

   Problem 31: https://projecteuler.net/problem=31

   Coin sums

   In England the currency is made up of pound, f, and pence, p, and there are
   eight coins in general circulation:

   1p, 2p, 5p, 10p, 20p, 50p, f1 (100p) and f2 (200p).
   It is possible to make f2 in the following way:

   1xf1 + 1x50p + 2x20p + 1x5p + 1x2p + 3x1p
   How many different ways can f2 be made using any number of coins?

   Hint:
       > There are 100 pence in a pound (f1 = 100p)
       > There are coins(in pence) are available: 1, 2, 5, 10, 20, 50, 100 and 200.
       > how many different ways you can combine these values to create 200 pence.

   Example:
       to make 6p there are 5 ways
         1,1,1,1,1,1
         1,1,1,1,2
         1,1,2,2
         2,2,2
         1,5
       to make 5p there are 4 ways
         1,1,1,1,1
         1,1,1,2
         1,2,2
         5



Functions
---------

.. autoapisummary::

   project_euler.problem_031.sol2.solution


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

.. py:function:: solution(pence: int = 200) -> int

   Returns the number of different ways to make X pence using any number of coins.
   The solution is based on dynamic programming paradigm in a bottom-up fashion.

   >>> solution(500)
   6295434
   >>> solution(200)
   73682
   >>> solution(50)
   451
   >>> solution(10)
   11