Arduino library with a number of statistic helper functions.
This library contains functions that have the goal to help with some basic statistical calculations.
returns how many different ways one can choose a set of k elements from a set of n. The order does matter. The limits mentioned is the n for which all k still work.
- uint32_t permutations(n, k) exact up to 12
- uint64_t permutations64(n, k) exact up to 20
- double dpermutations(n, k) not exact up to 34 (4 byte) or 170 (8 byte)
If you need a larger n but k is near 0 the functions will still work, but to which k differs per value for n. (no formula found, and an overflow detection takes overhead).
- nextPermutation(array, size) given an array of type T it finds the next permutation of that array in a lexicographical way. ABCD --> ABDC. Based upon // http://www.nayuki.io/page/next-lexicographical-permutation-algorithm although other same code examples exist.
- uint32_t factorial(n) exact up to 12!
- uint64_t factorial64(n) exact up to 20! (Print 64 bit ints with my printHelpers)
- double dfactorial(n) not exact up to 34! (4 byte) or 170! (8 byte)
- double stirling(n) approximation function for factorial (right magnitude)
dfactorial() is quite accurate over the whole range. stirling() is up to 3x faster for large n (> 100), but accuracy is less than the dfactorial(), see example.
returns how many different ways one can choose a set of k elements from a set of n. The order does not matter. The number of combinations grows fast so n is limited per function. The limits mentioned is the n for which all k still work.
- uint32_t combinations(n, k) n = 0 .. 30 (iterative version)
- uint64_t combinations64(n, k) n = 0 .. 61 (iterative version)
- uint32_t rcombinations(n, k) n = 0 .. 30 (recursive version, slightly slower)
- uint64_t rcombinations64(n, k) n = 0 .. 61 (recursive version, slightly slower)
- double dcombinations(n, k) n = 0 .. 125 (4bit) n = 0 .. 1020 (8 bit)
If you need a larger n but k is near 0 or near n the functions will still work, but for which k differs per value for n. (no formula found, and an overflow detection takes overhead).
- combPascal(n, k) n = 0 .. 30 but due to double recursion per iteration it takes time and a lot of it for larger values. Added for recreational purposes, limited tested.
- perm1 is a sketch in the examples that shows a recursive permutation algorithm. It generates all permutations of a given char string. It allows you to process every instance. It is added to this library as it fits in the context.
- code & example for get Nth Permutation
- investigate valid range detection for a given (n, k) for combinations and permutations.