Combinatorics Class |
Enumerative Combinatorics and Counting.
Inheritance HierarchyNamespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
SyntaxC#
public static class Combinatorics
The Combinatorics type exposes the following members.
Methods| Name | Description | |
|---|---|---|
  | Combinations | Count the number of possible combinations without repetition. The order does not matter and each object can be chosen only once. |
| CombinationsWithRepetition | Count the number of possible combinations with repetition. The order does not matter and an object can be chosen more than once. |
| GenerateCombination(Int32, Random) | Generate a random combination, without repetition, by randomly selecting some of N elements. |
| GenerateCombination(Int32, Int32, Random) | Generate a random combination, without repetition, by randomly selecting k of N elements. |
| GenerateCombinationWithRepetition | Generates a random combination, with repetition, by randomly selecting k of N elements. |
| GeneratePermutation | Generate a random permutation, without repetition, by generating the index numbers 0 to N-1 and shuffle them randomly. Implemented using Fisher-Yates Shuffling. |
| GenerateVariation(BigInteger, Int32, Random) |
Generate a random variation, without repetition, by randomly selecting k of n elements with order. This is an O(k) space-complexity implementation optimized for very large N. The space complexity of Fisher-Yates Shuffling is O(n+k). When N is very large, the algorithm will be unexecutable in limited memory, and a more memory-efficient algorithm is needed. You can explicitly cast N to BigInteger if N is out of range of Int32 or memory, so that this special implementation is called. However, this implementation is slower than Fisher-Yates Shuffling: don't call it if time is more critical than space. The K of type BigInteger seems impossible, because the returned array is of size K and must all be stored in memory. |
| GenerateVariation(Int32, Int32, Random) | Generate a random variation, without repetition, by randomly selecting k of n elements with order. Implemented using partial Fisher-Yates Shuffling. |
| GenerateVariationWithRepetition | Generate a random variation, with repetition, by randomly selecting k of n elements with order. |
| Permutations | Count the number of possible permutations (without repetition). |
 | SelectCombinationT | Select a random combination, without repetition, from a data sequence by selecting k elements in original order. |
| SelectCombinationWithRepetitionT | Select a random combination, with repetition, from a data sequence by selecting k elements in original order. |
| SelectPermutationT | Select a random permutation from a data sequence by returning the provided data in random order. Implemented using Fisher-Yates Shuffling. |
| SelectPermutationInplaceT | Select a random permutation, without repetition, from a data array by reordering the provided array in-place. Implemented using Fisher-Yates Shuffling. The provided data array will be modified. |
| SelectVariationT | Select a random variation, without repetition, from a data sequence by randomly selecting k elements in random order. Implemented using partial Fisher-Yates Shuffling. |
| SelectVariationWithRepetitionT | Select a random variation, with repetition, from a data sequence by randomly selecting k elements in random order. |
| Variations | Count the number of possible variations without repetition. The order matters and each object can be chosen only once. |
| VariationsWithRepetition | Count the number of possible variations with repetition. The order matters and each object can be chosen more than once. |
See Also