Convert simple recursive relation to functional program

Question

Hi I am trying to convert the following recursive pseudocode definition into a functional programming construct in R :

a = [ random numbers between 0 and 10 ]
b = [ random numbers between -5 and 5 ]
c = [ random numbers between 0 and -10 ]

x0 = 200
index = 0

function f(x) {
    index = index + 1
    if( x is between 200 and 220 ) return f(x + a[index])
    else if(x is between 220 and 250) return f(x + b[index])
    else if(x is 250 and above) return f(x + c[index])
}

Executable R code is :

a <- sample(1:10,size=50, replace=TRUE)
b <- sample(-5:5,size=50, replace=TRUE)
c <- sample(-1:-10,size=50, replace=TRUE)

index <- 0;


myfunc <- function(x){
  index <<- index + 1;
  if(index == 50) return(x)
  if(x <= 220){ return(myfunc(x + a[index])) }
  else if(x > 220 & x < 250){ return(myfunc(x + b[index])) }
  else {return( myfunc(x + c[index]))}
}
print(myfunc(200));

Would like to discuss any approach including Map/Filter/Reduce or Vectorisation. Many thanks in advance.

Furthermore, how can I retain the entire path of 50 x elements (rather than looking at just the one answer of x).

Answer 1

You can use the Reduce function with the accumulate option to save all the intermediate values.

To see how this works, try it out on the simple "sum" function

x = rep(200, 50)
Reduce(x=x, f=sum) 
Reduce(x=x, f=sum, accumulate=T)

The answer you're looking for requires you rewrite your special function so it can be passed to Reduce:

foo <- function(x, y = 0){
    if (200 <= x & x < 220){
        x + sample(1:10, 1)
    }
    else if(220 <= x & x < 250){
        x + sample(-5:5, 1)
    }
    else if (250 <= x){
        x + sample(-1:-10, 1)
    }
}

Reduce(x=rep(200, 50), f=foo, accumulate=T)