Here is a recursive program that prints all the possible ways that an amount x (in cents) can be made up using Australian coins (which come in 5, 10, 20, 50, 100, and 200 cent denominations). To avoid repetition, each possible decomposition is ordered.

change <- function(x, y.vec = c()) {

# finds possible ways of making up amount x using Australian coins

# x is given in cents and we assume it is divisible by 5

# y.vec are coins already used (so total amount is x + sum(y.vec))

if (x == 0) {

cat(y.vec, "")

} else {

coins <- c(200, 100, 50, 20, 10, 5)

new.x <- x - coins

new.x <- new.x[new.x >= 0]

for (z in new.x) {

y.tmp <- c(y.vec, x - z)

if (identical(y.tmp, sort(y.tmp))) {

change(z, y.tmp)

}

}

}

return(invisible(NULL))

}

Rewrite this program so that instead of writing its output to the screen it returns it as a list, where each element is a vector giving a possible decomposition of x.

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