# [R] Speeding up a loop

Petr Savicky savicky at cs.cas.cz
Fri Jul 20 16:26:34 CEST 2012

```On Fri, Jul 20, 2012 at 05:45:30AM -0700, wwreith wrote:
> General problem: I have 20 projects that can be invested in and I need to
> decide which combinations meet a certain set of standards. The total
> possible combinations comes out to 2^20. However I know for a fact that the
> number of projects must be greater than 5 and less than 13. So far the the
> code below is the best I can come up with for iteratively creating a set to
> check against my set of standards.
>
> Code
> x<-matrix(0,nrow=1,ncol=20)
> for(i in 1:2^20)
> {
> x<-x+1
>   for(j in 1:20)
>   {
>     if(x[j]>1)
>     {
>       x[j]=0
>       if(j<20)
>       {
>         x[j+1]=x[j+1]+1
>       }
>     }
>   }
> if(sum(x)>5 && sum(x)<13)
> {
> # insert criteria here.
> }
> }
>
> my code forces me to create all 2^20 x's and then use an if statement to
> decide if x is within my range of projects. Is there a faster way to
> increment x. Any ideas on how to kill the for loop so that it won't attempt
> to process an x where the sum is greater than 12 or less than 6?

Hi.

The restriction on the sum of the rows between 6 and 12 eliminates the
tails of the distribution, not the main part. So, the final number of
rows is not much smaller than 2^20. More exactly, it is

sum(choose(20, 6:12))

which is about 0.8477173 * 2^20. On the other hand, all combinations
may be created using expand.grid() faster than using a for loop.

Try the following

g <- as.matrix(expand.grid(rep(list(0:1), times=20)))
s <- rowSums(g)
x <- g[s > 5 & s < 13, ]
nrow(x)

 888896

Hope this helps.

Petr Savicky.

```