combinatorics

This question is virtually the same as this SO post , only I'm looking for a VB.NET (.NET 4) solution. I've spun my wheels long enough trying to come up with a generic solution to solving this "power set" problem. Given: Dim choices As IEnumerable(Of String) = {"Coffee", "Tea", "Milk", "Cookies"} Dim choiceSets = choices.CombineAll() I'm looking for choiceSets to be an IEnumerable(Of IEnumerable(Of T)) so that I can do something like: For each choiceSet in choiceSets Console.WriteLine(String.Join(", ", choiceSet)) Next And get results that look like: Coffee Tea Milk Cookies Coffee, Tea Coffee,

I have a website where users submit questions (zero, one or multiple per day), vote on them and answer one question per day (more details here ). A user can see the question only once either by submitting, voting or answering it. I have a pool of questions that players have already seen. I need to remove 30 questions from the pool each month. I need to pick questions to remove in such way that I maximize the number of available questions left in the pool for player with least available questions. Example with pool of 5 questions (and need to remove 3): player A has seen questions 1, 3 and 5

I have some bins with different capacities and some objects with specified size. The goal is to pack these objects in the bins. Until now it is similar to the bin-packing problem. But the twist is that each object has a partial overlap with another. So while object 1 and 2 has sizes s1 and s2, when I put them in the same bin the filled space is less than s1+s2. Supposing that I know this overlapping value for each pair of objects, is there any approximation algorithm like the ones for original bin-packing for this problem too? Masood_mj The answer is to use a kind of tree that captures the

I guess my question has to do with a variant of the knapsack problem, but I can't really come up with a solution for this: Let's say you are in a hardware store and need to buy 21 screws. They only offer them in bags: Bag X - 16 Screws - 1.56$ per screw - 25$ Total Bag Y - 8 Screws - 2.25$ per screw - 18$ Total Bag Z - 4 Screws - 1.75$ per screw - 7$ Total Now you have to figure out which Bags you should buy to get your 21 screws (or more!) for the lowest possible price. So what I got is a table with all the bags and a variable to define the required amount. What I need as a result should be a

Consider the set, S , of all binary vectors of length n where each contains exactly m ones; so there are n-m zeros in each vector. My goal is to construct a number, k , of vectors from S such that these vectors are as different as possible from each other. As a simple example, take n =4, m =2 and k =2, then a possible solution is: [1,1,0,0] and [0,0,1,1]. It seems that this is an open problem in the coding theory literature (?). Is there any way (i.e. algorithm) to find a suboptimal yet good solution ? Is Hamming distance the right performance measure to use in this case ? Some thoughts: In