combinatorics

Edit: I'm sorry, but I forgot to mention that I'll need the values of the counter variables. So making one loop isn't a solution I'm afraid. I'm not sure if this is possible at all, but I would like to do the following. To a function, an array of numbers is passed. Each number is the upper limit of a for loop, for example, if the array is [2, 3, 5] , the following code should be executed: for(var a = 0; a < 2; a++) { for(var b = 0; b < 3; b++) { for(var c = 0; c < 5; c++) { doSomething([a, b, c]); } } } So the amount of nested for loops is equal to the length of the array. Would there be any

I am studying the code in the Data.List module and can't exactly wrap my head around this implementation of permutations: permutations :: [a] -> [[a]] permutations xs0 = xs0 : perms xs0 [] where perms [] _ = [] perms (t:ts) is = foldr interleave (perms ts (t:is)) (permutations is) where interleave xs r = let (_,zs) = interleave' id xs r in zs interleave' _ [] r = (ts, r) interleave' f (y:ys) r = let (us,zs) = interleave' (f . (y:)) ys r in (y:us, f (t:y:us) : zs) Can somebody explain in detail how these nested functions connect/work with each other? Twan van Laarhoven Sorry about the late

Suppose we need to write a function that gives the list of all the subsets of a set. The function and the doctest is given below. And we need to complete the whole definition of the function def subsets(s): """Return a list of the subsets of s. >>> subsets({True, False}) [{False, True}, {False}, {True}, set()] >>> counts = {x for x in range(10)} # A set comprehension >>> subs = subsets(counts) >>> len(subs) 1024 >>> counts in subs True >>> len(counts) 10 """ assert type(s) == set, str(s) + ' is not a set.' if not s: return [set()] element = s.pop() rest = subsets(s) s.add(element) It has to

What is the fastest way to calculate all possible length-r combinations of n possible elements without resorting to brute force techniques or anything that requires STL? While working on an Apriori algorithm for my final project in my data structures class, I developed an interesting solution that uses bit-shifting and recursion, which i will share in an answer below for anyone who is interested. However, is this the fastest way of achieving this (without using any common libraries)? I ask more out of curiosity than anything else, as the algorithm i currently have works just fine for my

I want to pre-compute some values for each combination in a set of combinations. For example, when choosing 3 numbers from 0 to 12, I'll compute some value for each one: >>> for n in choose(range(13), 3): print n, foo(n) (0, 1, 2) 78 (0, 1, 3) 4 (0, 1, 4) 64 (0, 1, 5) 33 (0, 1, 6) 20 (0, 1, 7) 64 (0, 1, 8) 13 (0, 1, 9) 24 (0, 1, 10) 85 (0, 1, 11) 13 etc... I want to store these values in an array so that given the combination, I can compute its and get the value. For example: >>> a = [78, 4, 64, 33] >>> a[magic((0,1,2))] 78 What would magic be? Initially I thought to just store it as a 3-d

I am looking to create a special type of combination in which no two sets have more than one intersecting element. Let me explain with an example: Let us say we have 9 letter set that contains A, B, C, D, E, F, G, H, and I If you create the standard non-repeating combinations of three letters you will have 9C3 sets. These will contain sets like ABC, ABD, BCD, etc. I am looking to create sets that have at the most only 1 common letter. So in this example, we will get following sets: ABC, ADG, AEI, AFH, BEH, BFG, BDI, CFI, CDH, CEG, DEF, and GHI - note that if you take any two sets there are no

I need to generate all combinations of size @k in a given set of size @n . Can someone please review the following SQL and determine first if the following logic is returning the expected results, and second if is there a better way? /*CREATE FUNCTION dbo.Factorial ( @x int ) RETURNS int AS BEGIN DECLARE @value int IF @x <= 1 SET @value = 1 ELSE SET @value = @x * dbo.Factorial( @x - 1 ) RETURN @value END GO*/ SET NOCOUNT ON; DECLARE @k int = 5, @n int; DECLARE @set table ( [value] varchar(24) ); DECLARE @com table ( [index] int ); INSERT @set VALUES ('1'),('2'),('3'),('4'),('5'),('6'); SELECT