Why is my recursive function so slow in R?

Question

The following takes about 30 seconds to run whereas I would expect it to be nearly instant. Is there a problem with my code?

x <- fibonacci(35);

fibonac         


        

Answer 1

A recursive implementation with linear cost:

fib3 <- function(n){
  fib <- function(n, fibm1, fibm2){
    if(n==1){return(fibm2)}
    if(n==2){return(fibm1)}
    if(n >2){
      fib(n-1, fibm1+fibm2, fibm1)  
    }
  }
fib(n, 1, 0)  
}

Comparing with the recursive solution with exponential cost:

> system.time(fibonacci(35))
  usuário   sistema decorrido 
   14.629     0.017    14.644 
> system.time(fib3(35))
  usuário   sistema decorrido 
    0.001     0.000     0.000

This solution can be vectorized with ifelse:

fib4 <- function(n){
    fib <- function(n, fibm1, fibm2){
        ifelse(n<=1, fibm2,
          ifelse(n==2, fibm1,
            Recall(n-1, fibm1+fibm2, fibm1)  
          ))
    }
    fib(n, 1, 0)  
}

fib4(1:30)
##  [1]      0      1      1      2      3      5      8
##  [8]     13     21     34     55     89    144    233
## [15]    377    610    987   1597   2584   4181   6765
## [22]  10946  17711  28657  46368  75025 121393 196418
## [29] 317811 514229

The only changes required are changing == to <= for the n==1 case, and changing each if block to the equivalent ifelse.