# [R] Merge sort

Duncan Murdoch murdoch.duncan at gmail.com
Tue Apr 19 23:51:40 CEST 2016

```On 19/04/2016 3:39 PM, Gaston wrote:
> Hello everyone,
>
> I am learning R since recently, and as a small exercise I wanted to
> write a recursive mergesort. I was extremely surprised to discover that
> my sorting, although operational, is deeply inefficient in time. Here is
> my code :
>
>> merge <- function(x,y){
>>    if (is.na(x)) return(y)
>>    else if (is.na(y)) return(x)
>>    else if (x<y) return(c(x,merge(x[-1],y)))
>>    else return(c(y,merge(x,y[-1])))
>> }
>>
>> division <- function(x){
>>    if (is.na(x)) return(cbind(x,x))
>>    else
>> return(cbind(c(x,division(x[-c(1,2)])[,1]),c(x,division(x[-c(1,2)])[,2])))
>> }
>>
>> mergesort <- function(x){
>>    if (is.na(x)) return(x)
>>    else{
>>      print(x)
>>      t=division(x)
>>      return(merge(mergesort(t[,1]),mergesort(t[,2])))
>>    }
>> }
>
> I tried my best to write it "the R-way", but apparently I failed. I
> suppose some of the functions I used are quite heavy. I would be
> grateful if you could give a hint on how to change that!
>
> I hope I made myself clear and wish you a nice day,

Your use of is.na() looks strange.  I don't understand why you are
testing element 2 in mergesort(), and element 1 in merge(), and element
3 in division.  Are you using it to test the length?  It's better to use
the length() function for that.

The division() function returns a matrix.  It would make more R-sense to
return a list containing the two parts, because they might not be the
same length.

Generally speaking, function calls are expensive in R, so the recursive
merge you're using looks like it would be the bottleneck.  You'd almost
certainly be better off to allocate something of length(x) + length(y),
and do the assignments in a loop.

Here's a merge sort I wrote as an illustration in a class.  It's
designed for clarity rather than speed, but I'd guess it would be faster
than yours:

mergesort <- function(x) {

n <- length(x)
if (n < 2) return(x)

# split x into two pieces of approximately equal size, x1 and x2

x1 <- x[1:(n %/% 2)]
x2 <- x[(n %/% 2 + 1):n]

# sort each of the pieces
x1 <- mergesort(x1)
x2 <- mergesort(x2)

# merge them back together
result <- c()
i <- 0
while (length(x1) > 0 && length(x2) > 0) {
# compare the first values
if (x1 < x2) {
result[i + 1] <- x1
x1 <- x1[-1]
} else {
result[i + 1] <- x2
x2 <- x2[-1]
}
i <- i + 1
}

# put the smaller one into the result
# delete it from whichever vector it came from
# repeat until one of x1 or x2 is empty
# copy both vectors (one is empty!) onto the end of the results
result <- c(result, x1, x2)
result
}

If I were going for speed, I wouldn't modify the x1 and x2 vectors, and
I'd pre-allocate result to the appropriate length, rather than growing
it in the while loop.  But that was a different class!

Duncan Murdoch

```