combinatorics

问题 This is somewhat of a combinatorial problem; I'm trying to figure out an efficient way to pair up all items in a data set. For example, I have an array of length 6: [1,2,3,4,5,6], and I want to make all possible pairings of the contents in the array as so: [1,2],[3,4],[5,6] [1,2],[3,5],[4,6] [1,2],[3,6],[4,5] [1,3],[2,4],[5,6] [1,3],[2,5],[4,6] ... and so on. In this example, there would be 15 combinations total. In general, the number of possibilities in this solution should be (N-1)!! where

问题 Let's define custom operators - let it be ++ , equals :- op(900, yfx, equals). :- op(800, xfy, ++). And fact: check(A equals A). I try to make predicate, let it be check/1 , that will return true in all following situations: check( a ++ b ++ c ++ d equals c ++ d ++ b ++ a ), check( a ++ b ++ c ++ d equals d ++ a ++ c ++ b), check( a ++ b ++ c ++ d equals d ++ b ++ c ++ a ), % and all permutations... of any amount of atoms check( a ++ ( b ++ c ) equals (c ++ a) ++ b), % be resistant to any

问题 Given an nxn array A of real positive numbers, I'm trying to find the minimum of the maximum of the element-wise minimum of all combinations of three rows of the 2-d array. Using for-loops, that comes out to something like this: import numpy as np n = 100 np.random.seed(2) A = np.random.rand(n,n) global_best = np.inf for i in range(n-2): for j in range(i+1, n-1): for k in range(j+1, n): # find the maximum of the element-wise minimum of the three vectors local_best = np.amax(np.array([A[i,:],

问题 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

问题 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

问题 I have some sets I would like to take the Cartesian product of, which is working well. However, I want to remove all elements of this new set which are identical under a permutation of the elements. For example, take the following code: import itertools as ittools x = 2 y = 3 z = 5 flist = list(ittools.product([x,y,z],repeat=3)) for f in flist: print reduce(lambda a,b: a*b, f) This code find the Cartesian product of the set {2,3,5} and returns the product of all three components of each

问题 I know that iterating over all subsets of a set of size n is a performance nightmare and will take O(2^n) time. How about iterating over all subsets of size k (for (0 <= k <= n))? Is that a performance nightmare? I know there are (n, k) = n! / k! (n - k)! possibilities. I know that if k is very close to 0 or very close to n, this is a small number. What is the worst case performance in terms of n and k? Is there a simpler way of saying it other than just O(n! / k! (n - k)!)? Is this

问题 I had a combinatorics assignment that involved getting every word with length less than or equal to 6 from a specific combination of strings. In this case, it was S = { 'a', 'ab', 'ba' }. The professor just started listing them off, but I thought it would be easier solved with a program. The only problem is that I can't get a good algorithm that would actually compute every possible option. If anyone could help, I'd appreciate it. I usually program in Python but really I just need help with

问题 Suppose we have n bins in which we are throwing k balls. What is a fast (i.e. using numpy/scipy instead of python code) way to generate all possible outcomes as a matrix? For example, if n = 4 and k = 3 , we'd want the following numpy.array : 3 0 0 0 2 1 0 0 2 0 1 0 2 0 0 1 1 2 0 0 1 1 1 0 1 1 0 1 1 0 2 0 1 0 1 1 1 0 0 2 0 3 0 0 0 2 1 0 0 2 0 1 0 1 2 0 0 1 1 1 0 1 0 2 0 0 3 0 0 0 2 1 0 0 1 2 0 0 0 3 Apologies if any permutation was missed, but this is the general idea. The generated

问题 Suppose we have n bins in which we are throwing k balls. What is a fast (i.e. using numpy/scipy instead of python code) way to generate all possible outcomes as a matrix? For example, if n = 4 and k = 3 , we'd want the following numpy.array : 3 0 0 0 2 1 0 0 2 0 1 0 2 0 0 1 1 2 0 0 1 1 1 0 1 1 0 1 1 0 2 0 1 0 1 1 1 0 0 2 0 3 0 0 0 2 1 0 0 2 0 1 0 1 2 0 0 1 1 1 0 1 0 2 0 0 3 0 0 0 2 1 0 0 1 2 0 0 0 3 Apologies if any permutation was missed, but this is the general idea. The generated