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?
> 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.
1,1,1,1,1,1 1,1,1,1,2 1,1,2,2 2,2,2 1,5
1,1,1,1,1 1,1,1,2 1,2,2 5
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Returns the number of different ways to make X pence using any number of coins. |
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