powerset

I have to write a brute-force implementation of the knapsack problem. Here's the pseudocode: computeMaxProfit(weight_capacity) max_profit = 0 S = {} // Each element of S is a weight-profit pair. while true if the sum of the weights in S <= weight_capacity if the sum of the profits in S > max_profit update max_profit if S contains all items // Then there is no next subset to generate return max generate the next subset S While the algorithm is fairly easy to implement, I haven't the slightest idea how to generate the power set of S, and to feed the subsets of the power set into each iteration

I want to calculate powerset of a set. Because I don't need the whole powerset at a time, it's better to generate it lazily. For example: powerset (set ["a"; "b"; "c"]) = seq { set []; set ["a"]; set ["b"]; set ["c"]; set ["a"; "b"]; set ["a"; "c"]; set ["b"; "c"]; set ["a";"b"; "c"]; } Since the result is a sequence, I prefer it in the above order. How can I do it in an idomatic way in F#? EDIT: This is what I'm going to use (based on BLUEPIXY's answer): let powerset s = let rec loop n l = seq { match n, l with | 0, _ -> yield [] | _, [] -> () | n, x::xs -> yield! Seq.map (fun l -> x::l)

I have a List of elements (1, 2, 3), and I need to get the superset (powerset) of that list (without repeating elements). So basically I need to create a List of Lists that looks like: {1} {2} {3} {1, 2} {1, 3} {2, 3} {1, 2, 3} What is the best (simplicity > efficiency in this case, the list won't be huge) way to implement this? Preferably in Java, but a solution in any language would be useful. Use bitmasks: int allMasks = (1 << N); for (int i = 1; i < allMasks; i++) { for (int j = 0; j < N; j++) if ((i & (1 << j)) > 0) //The j-th element is used System.out.print((j + 1) + " "); System.out

Let's say we have a Set S which contains a few subsets: - [a,b,c] - [a,b] - [c] - [d,e,f] - [d,f] - [e] Let's also say that S contains six unique elements: a, b, c, d, e and f . How can we find all possible subsets of S that contain each of the unique elements of S exactly once? The result of the function/method should be something like that: [[a,b,c], [d,e,f]]; [[a,b,c], [d,f], [e]]; [[a,b], [c], [d,e,f]]; [[a,b], [c], [d,f], [e]]. Is there any best practice or any standard way to achieve that? I would be grateful for a Pseudo-code, Ruby or Erlang example. It sounds like what you are looking

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? Combinations: from Mark Nelson's article on the same topic we have next_combination http://marknelson.us/2002/03/01/next-permutation Permutations: from STL we have std::next_permutation template <typename Iterator> inline bool next_combination(const Iterator first, Iterator k, const Iterator last) { if ((first == last) || (first == k) || (last == k)) return false; Iterator itr1 = first; Iterator itr2 = last; ++itr1; if (last == itr1) return false; itr1 =

I am studying for an interview and I stumbled upon this question online under the "Math" category. Generate power set of given set: int A[] = {1,2,3,4,5}; int N = 5; int Total = 1 << N; for ( int i = 0; i < Total; i++ ) { for ( int j = 0; j < N; j++) { if ( (i >> j) & 1 ) cout << A[j]; } cout <<endl; } Please I do not want an explicit answer. I just want clarifications and hints on how to approach this problem. I checked power set algorithm on google and I still do not understand how to address this problem. Also, could someone reiterate what the question is asking for. Thank you. Power set of

I have a Set of items of some type and want to generate its power set. I searched the web and couldn't find any Scala code that adresses this specific task. This is what I came up with. It allows you to restrict the cardinality of the sets produced by the length parameter. def power[T](set: Set[T], length: Int) = { var res = Set[Set[T]]() res ++= set.map(Set(_)) for (i <- 1 until length) res = res.map(x => set.map(x + _)).flatten res } This will not include the empty set. To accomplish this you would have to change the last line of the method simply to res + Set() Any suggestions how this can