R Under development (unstable) (2024-10-17 r87242 ucrt) -- "Unsuffered Consequences"
Copyright (C) 2024 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(randtoolbox)
Loading required package: rngWELL
This is randtoolbox. For an overview, type 'help("randtoolbox")'.
> 
> #compare two implementations
> 
> f <- function(n)
+ {
+   res <- numeric(n+1)
+   res[1:2] <- c(0,1)   
+   
+   for(i in 1:(n-1))
+   {
+     # i <- 1
+     k <- 1:(i+1) -1
+     res[1:(i+2)] <- c(k * res[1:(i+1)], 0) + c(0, res[1:(i+1)]) 
+   }
+   res
+ }
> 
> g <- function(n)
+ {
+   if( n == 0)
+     res <- 1
+   if(n > 0)
+     res <- c(0,1)   
+   
+   if(n > 1)
+   {
+     for(i in 1:(n-1))
+     {
+       k <- 1:length(res) -1
+       res <- c(k * res, 0) + c(0, res) 
+     }
+   }
+   return(res)    
+ }
> 
> cbind(stirling(3) , f(3))
     [,1] [,2]
[1,]    0    0
[2,]    1    1
[3,]    3    3
[4,]    1    1
> cbind(stirling(4) , f(4))
     [,1] [,2]
[1,]    0    0
[2,]    1    1
[3,]    7    7
[4,]    6    6
[5,]    1    1
> 
> if(FALSE)
+ {
+   cbind(stirling(10) , f(10))
+   cbind(stirling(12) , f(12))
+   
+   system.time(f(2000))
+   system.time(stirling(2000))
+   
+   # library(microbenchmark)
+   # microbenchmark(f(1000), g(1000))
+   # microbenchmark(f(2000), g(2000))
+   
+ }
> 
> proc.time()
   user  system elapsed 
   0.21    0.12    0.34