combinatorics

I know about itertools, but it seems it can only generate permutations without repetitions. for example, I'd like to generate all possible dice rolls for 2 dice. So I need all permutations of size 2 of [1, 2, 3, 4, 5, 6] including repetitions: (1, 1), (1, 2), (2, 1)... etc If possible I don't want to implement this from scratch 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, 6

There are n people numbered from 1 to n . I have to write a code which produces and print all different combinations of k people from these n . Please explain the algorithm used for that. I assume you're asking about combinations in combinatorial sense (that is, order of elements doesn't matter, so [1 2 3] is the same as [2 1 3] ). The idea is pretty simple then, if you understand induction / recursion: to get all K -element combinations, you first pick initial element of a combination out of existing set of people, and then you "concatenate" this initial element with all possible combinations

I'm looking for an algorithm to generate permutations of a set in such a way that I could make a lazy list of them in Clojure. i.e. I'd like to iterate over a list of permutations where each permutation is not calculated until I request it, and all of the permutations don't have to be stored in memory at once. Alternatively I'm looking for an algorithm where given a certain set, it will return the "next" permutation of that set, in such a way that repeatedly calling the function on its own output will cycle through all permutations of the original set, in some order (what the order is doesn't

I wish to produce the Cartesian product of 2 lists in Haskell, but I cannot work out how to do it. The cartesian product gives all combinations of the list elements: xs = [1,2,3] ys = [4,5,6] cartProd :: [a] -> [b] -> [(a,b)] cartProd xs ys ==> [(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)] This is not an actual homework question and is not related to any such question, but the way in which this problem is solved may help with one I am stuck on. This is very easy with list comprehensions. To get the cartesian product of the lists xs and ys , we just need to take the tuple (x,y) for