R中的递归函数

Question

I want to understand this problem. I stop understanding after the for statement.

This is a recursive program (prints all the possible ways that an amount x (in cents) can be made up using Australian coins (5, 10, 20, 50, 100, and 200 cent denominations)). Each 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, "\n")
    } 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.

Answer 1

Since the algorithm considers every coin every time through the loop, it would be possible to come up with multiple results for the same set of coins, (for example 35 = 5+10+20 = 5+20+10 = 10+20+5 are the same answer three different ways). The logic inside the loop ensures the answer is only given once, sorted by low to high value coins, since if (identical(y.tmp, sort(y.tmp))) evaluates to TRUE only once, the first time it is encountered. (Replace the logic inside the loop with change(z, c(y.vec, x - z)) in order to see the difference).