- Reference See "Modern Applied Statistics with S-PLUS", 2ed, by W.N. Venables and B.D. Ripley. ISBN 0-387-98214-0 Springer-Verlag. Chapter 4.7, page 149-150. - Author's suggestion It should be used cautiously as it can lead to slow and memory-intensive code. In a few cases it can provide a neat and effective solution to an intrinsically recursive problem. - Example Generating all possible subsets of size r from a set of elements of size n. - subsets 1 If the size of the result is not too large an efficient way to do this is to store the subsets as the rows of an array. Here, create a file "<a href="./example/recursive/subsets_1.r" target="_blank">subsets_1.r</a>" as follows, ``` # File name: subsets_1.r subsets <- function(r, n, v = 1 : n){ if(r <= 0) NULL else if(r >= n) v[1 : n] else rbind(cbind(v[1], subsets(r - 1, n - 1, v[-1])), subsets(r, n - 1, v[-1])) } ``` - subsets 2 If we re-assign the function body to another name and use the name "subsets" for something else, or discard it, our function body will cease to work. It would be useful to have a function body that continued to work regardless of the name given it. Here, create a file "<a href="./example/recursive/subsets_2.r" target="_blank">subsets_2.r</a>" as follows, ``` # File name: subsets_2.r subsets <- function(r, n, v = 1 : n){ if(r <= 0) NULL else if(r >= n) v[1 : n] else rbind(cbind(v[1], Recall(r - 1, n - 1, v[-1])), Recall(r, n - 1, v[-1])) } ``` - R commands to list all combinations and permutations For R version 2.4 or newer, there are some commands that you can use to list all combinations by given total elements and how many you want to choose, and all permutations by given total elements. ``` choose(10,5) # compute choose(10,5) factoral(5) # compute numbers of permutations of 5 elements library(combinat) combn(10,5) # list all combinations of choose(10,5) permn(5) # list all permutations of 5 elements library(gtools) combinations(10,5) # list all combinations of choose(10,5) permutations(5,5) # list all permutations of 5 elements permutations(5,3) # list all permutations of the elements from choose(5,3) # i.e. total C(5,3) * 3! possible outcomes ``` --- <div w3-include-html="../preamble_tail_date.html"></div>