# project euler – Problem 31

November 8, 2011
By

(This article was first published on YGC » R, and kindly contributed to R-bloggers)

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

1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).

It is possible to make £2 in the following way:

1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p

How many different ways can £2 be made using any number of coins?


Recursive algorithm is very straightforward.

?View Code RSPLUS
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  coins <- c(1,2,5,10,20,50,100,200) findChange <- function(money, numCoins) { if (numCoins ==1) return(1) s <- 0 for (i in 1:numCoins) { remain <- money-coins[i] if(remain==0) s <- s+1 if(remain>0) s <- s+findChange(remain,i) } return(s) }   print(findChange(200,length(coins)))
> system.time(source("Problem31.R"))
[1] 73682
user  system elapsed
0.89    0.00    0.89