project_euler.problem_031.sol2

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

solution(→ int)

Returns the number of different ways to make X pence using any number of coins.

Module Contents

project_euler.problem_031.sol2.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