powerset - Developer IT

[C++] next_permutation for combinations or subsets in powerset

- by bobber205

Is there some equivalent library or function that will give me the next combination of a set of values like next_permutation in does for me?

Time complexity of a powerset generating function

I'm trying to figure out the time complexity of a function that I wrote (it generates a power set for a given string): public static HashSet<string> GeneratePowerSet(string input) { HashSet<string> powerSet = new HashSet<string>(); if (string.IsNullOrEmpty(input)) return powerSet; int powSetSize = (int)Math.Pow(2.0, (double)input.Length); // Start at 1 to skip the empty string case for (int i = 1; i < powSetSize; i++) { string str = Convert.ToString(i, 2); string pset = str; for (int k = str.Length; k < input.Length; k++) { pset = "0" + pset; } string set = string.Empty; for (int j = 0; j < pset.Length; j++) { if (pset[j] == '1') { set = string.Concat(set, input[j].ToString()); } } powerSet.Add(set); } return powerSet; } So my attempt is this: let the size of the input string be n in the outer for loop, must iterate 2^n times (because the set size is 2^n). in the inner for loop, we must iterate 2*n times (at worst). 1. So Big-O would be O((2^n)*n) (since we drop the constant 2)... is that correct? And n*(2^n) is worse than n^2. if n = 4 then (4*(2^4)) = 64 (4^2) = 16 if n = 100 then (10*(2^10)) = 10240 (10^2) = 100 2. Is there a faster way to generate a power set, or is this about optimal?

Read the article

What algorithm can calculate the power set of a given set?

- by ross

I would like to efficiently generate a unique list of combinations of numbers based on a starting list of numbers. example start list = [1,2,3,4,5] but the algorithm should work for [1,2,3...n] result = [1],[2],[3],[4],[5] [1,2],[1,3],[1,4],[1,5] [1,2,3],[1,2,4],[1,2,5] [1,3,4],[1,3,5],[1,4,5] [2,3],[2,4],[2,5] [2,3,4],[2,3,5] [3,4],[3,5] [3,4,5] [4,5] Note. I don't want duplicate combinations, although I could live with them, eg in the above example I don't really need the combination [1,3,2] because it already present as [1,2,3]

Read the article

What is your favourite cleverly written functional code?

- by sdcvvc

What are your favourite short, mind-blowing snippets in functional languages? My two favourite ones are (Haskell): powerset = filterM (const [True, False]) foldl f v xs = foldr (\x g a -> g (f a x)) id xs v -- from Hutton's tutorial (I tagged the question as Haskell, but examples in all languages - including non-FP ones - are welcome as long as they are in functional spirit.)

Read the article

What scalability problems have you solved using a NoSQL data store?

- by knorv

NoSQL refers to non-relational data stores that break with the history of relational databases and ACID guarantees. Popular open source NoSQL data stores include: Cassandra (tabular, written in Java, used by Facebook, Twitter, Digg, Rackspace, Mahalo and Reddit) CouchDB (document, written in Erlang, used by Engine Yard and BBC) Dynomite (key-value, written in C++, used by Powerset) HBase (key-value, written in Java, used by Bing) Hypertable (tabular, written in C++, used by Baidu) Kai (key-value, written in Erlang) MemcacheDB (key-value, written in C, used by Reddit) MongoDB (document, written in C++, used by Sourceforge, Github, Electronic Arts and NY Times) Neo4j (graph, written in Java, used by Swedish Universities) Project Voldemort (key-value, written in Java, used by LinkedIn) Redis (key-value, written in C, used by Engine Yard, Github and Craigslist) Riak (key-value, written in Erlang, used by Comcast and Mochi Media) Ringo (key-value, written in Erlang, used by Nokia) Scalaris (key-value, written in Erlang, used by OnScale) ThruDB (document, written in C++, used by JunkDepot.com) Tokyo Cabinet/Tokyo Tyrant (key-value, written in C, used by Mixi.jp (Japanese social networking site)) I'd like to know about specific problems you - the SO reader - have solved using data stores and what NoSQL data store you used. Questions: What scalability problems have you used NoSQL data stores to solve? What NoSQL data store did you use? What database did you use before switching to a NoSQL data store? I'm looking for first-hand experiences, so please do not answer unless you have that.

Read the article

An unusual type signature

- by Travis Brown

In Monads for natural language semantics, Chung-Chieh Shan shows how monads can be used to give a nicely uniform restatement of the standard accounts of some different kinds of natural language phenomena (interrogatives, focus, intensionality, and quantification). He defines two composition operations, A_M and A'_M, that are useful for this purpose. The first is simply ap. In the powerset monad ap is non-deterministic function application, which is useful for handling the semantics of interrogatives; in the reader monad it corresponds to the usual analysis of extensional composition; etc. This makes sense. The secondary composition operation, however, has a type signature that just looks bizarre to me: (<?>) :: (Monad m) => m (m a -> b) -> m a -> m b (Shan calls it A'_M, but I'll call it <?> here.) The definition is what you'd expect from the types; it corresponds pretty closely to ap: g <?> x = g >>= \h -> return $ h x I think I can understand how this does what it's supposed to in the context of the paper (handle question-taking verbs for interrogatives, serve as intensional composition, etc.). What it does isn't terribly complicated, but it's a bit odd to see it play such a central role here, since it's not an idiom I've seen in Haskell before. Nothing useful comes up on Hoogle for either m (m a -> b) -> m a -> m b or m (a -> b) -> a -> m b. Does this look familiar to anyone from other contexts? Have you ever written this function?

Read the article

(Ordered) Set Partitions in fixed-size Blocks

- by Eugen

Here is a function I would like to write but am unable to do so. Even if you don't / can't give a solution I would be grateful for tips. For example, I know that there is a correlation between the ordered represantions of the sum of an integer and ordered set partitions but that alone does not help me in finding the solution. So here is the description of the function I need: The Task Create an efficient* function List<int[]> createOrderedPartitions(int n_1, int n_2,..., int n_k) that returns a list of arrays of all set partions of the set {0,...,n_1+n_2+...+n_k-1} in number of arguments blocks of size (in this order) n_1,n_2,...,n_k (e.g. n_1=2, n_2=1, n_3=1 -> ({0,1},{3},{2}),...). Here is a usage example: int[] partition = createOrderedPartitions(2,1,1).get(0); partition[0]; // -> 0 partition[1]; // -> 1 partition[2]; // -> 3 partition[3]; // -> 2 Note that the number of elements in the list is (n_1+n_2+...+n_n choose n_1) * (n_2+n_3+...+n_n choose n_2) * ... * (n_k choose n_k). Also, createOrderedPartitions(1,1,1) would create the permutations of {0,1,2} and thus there would be 3! = 6 elements in the list. * by efficient I mean that you should not initially create a bigger list like all partitions and then filter out results. You should do it directly. Extra Requirements If an argument is 0 treat it as if it was not there, e.g. createOrderedPartitions(2,0,1,1) should yield the same result as createOrderedPartitions(2,1,1). But at least one argument must not be 0. Of course all arguments must be = 0. Remarks The provided pseudo code is quasi Java but the language of the solution doesn't matter. In fact, as long as the solution is fairly general and can be reproduced in other languages it is ideal. Actually, even better would be a return type of List<Tuple<Set>> (e.g. when creating such a function in Python). However, then the arguments wich have a value of 0 must not be ignored. createOrderedPartitions(2,0,2) would then create [({0,1},{},{2,3}),({0,2},{},{1,3}),({0,3},{},{1,2}),({1,2},{},{0,3}),...] Background I need this function to make my mastermind-variation bot more efficient and most of all the code more "beautiful". Take a look at the filterCandidates function in my source code. There are unnecessary / duplicate queries because I'm simply using permutations instead of specifically ordered partitions. Also, I'm just interested in how to write this function. My ideas for (ugly) "solutions" Create the powerset of {0,...,n_1+...+n_k}, filter out the subsets of size n_1, n_2 etc. and create the cartesian product of the n subsets. However this won't actually work because there would be duplicates, e.g. ({1,2},{1})... First choose n_1 of x = {0,...,n_1+n_2+...+n_n-1} and put them in the first set. Then choose n_2 of x without the n_1 chosen elements beforehand and so on. You then get for example ({0,2},{},{1,3},{4}). Of course, every possible combination must be created so ({0,4},{},{1,3},{2}), too, and so on. Seems rather hard to implement but might be possible. Research I guess this goes in the direction I want however I don't see how I can utilize it for my specific scenario. http://rosettacode.org/wiki/Combinations

Developer IT