Basically, for each item from left to right, all the permutations of the remaining items are generated (and each one is added with the current elements). This can be done recursively (or iteratively if you like pain) until the last item is reached at which point there is only one possible order. So with the … Read more
You’re looking for expand.grid. expand.grid(0:1, 0:1, 0:1) Or, for the long case: n <- 14 l <- rep(list(0:1), n) expand.grid(l)
function pc_permute($items, $perms = array()) { if (empty($items)) { echo join(‘ ‘, $perms) . “<br />”; } else { for ($i = count($items) – 1; $i >= 0; –$i) { $newitems = $items; $newperms = $perms; list($foo) = array_splice($newitems, $i, 1); array_unshift($newperms, $foo); pc_permute($newitems, $newperms); } } } $arr = array(‘peter’, ‘paul’, ‘mary’); pc_permute($arr); or … Read more
You are looking for the Cartesian Product. In mathematics, a Cartesian product (or product set) is the direct product of two sets. In your case, this would be {1, 2, 3, 4, 5, 6} x {1, 2, 3, 4, 5, 6}. itertools can help you there: import itertools x = [1, 2, 3, 4, 5, … Read more
A Walk Through a Slice of Combinatorics in R* Below, we examine packages equipped with the capabilities of generating combinations & permutations. If I have left out any package, please forgive me and please leave a comment or better yet, edit this post. Outline of analysis: Introduction Combinations Permutations Multisets Summary Memory Before we begin, … Read more
A while back I had to do this in base R without loading any packages. permutations <- function(n){ if(n==1){ return(matrix(1)) } else { sp <- permutations(n-1) p <- nrow(sp) A <- matrix(nrow=n*p,ncol=n) for(i in 1:n){ A[(i-1)*p+1:p,] <- cbind(i,sp+(sp>=i)) } return(A) } } Usage: > matrix(letters[permutations(3)],ncol=3) [,1] [,2] [,3] [1,] “a” “b” “c” [2,] “a” “c” … Read more
You’re looking for the permutations formula: nPk = n!/(n-k)! In your case, you have 9 entries and you want to choose all of them, that’s 9P9 = 9! = 362880 You can find a PHP algorithm to permutate in recipe 4.26 of O’Reilly’s “PHP Cookbook”. pc_permute(array(0, 1, 2, 3, 4, 5, 7, 8)); Copied in … Read more
Here is a quite simple and short one using a recursive helper function: function cartesian(…args) { var r = [], max = args.length-1; function helper(arr, i) { for (var j=0, l=args[i].length; j<l; j++) { var a = arr.slice(0); // clone arr a.push(args[i][j]); if (i==max) r.push(a); else helper(a, i+1); } } helper([], 0); return r; } … Read more
class unique_element: def __init__(self,value,occurrences): self.value = value self.occurrences = occurrences def perm_unique(elements): eset=set(elements) listunique = [unique_element(i,elements.count(i)) for i in eset] u=len(elements) return perm_unique_helper(listunique,[0]*u,u-1) def perm_unique_helper(listunique,result_list,d): if d < 0: yield tuple(result_list) else: for i in listunique: if i.occurrences > 0: result_list[d]=i.value i.occurrences-=1 for g in perm_unique_helper(listunique,result_list,d-1): yield g i.occurrences+=1 a = list(perm_unique([1,1,2])) print(a) result: [(2, … Read more
First of all: it smells like recursion of course! Since you also wanted to know the principle, I did my best to explain it human language. I think recursion is very easy most of the times. You only have to grasp two steps: The first step All the other steps (all with the same logic) … Read more