A collection of high performance functions implemented in C++ with Rcpp for solving problems in combinatorics and computational mathematics. Utilizes the RcppThread library for easy access to thread safe multithreading. We also make use of the RMatrix.h header file from RcppParallel for thread safe accessors for Rcpp matrices.

: Generate all combinations/permutations of a vector (including multisets) meeting specific criteria.`comboGeneral/permuteGeneral`

: Generate reproducible random samples of combinations/permutations`comboSample/permuteSample`

: Flexible iterators allow for bidirectional iteration as well as random access.`comboIter/permuteIter`

: Fast prime number generator`primeSieve`

: Prime counting function using Legendre’s formula`primeCount`

The `primeSieve`

function and the `primeCount`

function are both based off of the excellent work by Kim Walisch. The respective repos can be found here: kimwalisch/primesieve; kimwalisch/primecount

Additionally, many of the sieving functions make use of the fast integer division library libdivide by ridiculousfish.

```
install.packages("RcppAlgos")
## install the development version
devtools::install_github("jwood000/RcppAlgos")
```

```
## Generate prime numbers
primeSieve(50, 100)
[1] 53 59 61 67 71 73 79 83 89 97
## Count prime numbers less than n
primeCount(1e10)
[1] 455052511
## Find all 3-tuples combinations of 1:4
comboGeneral(4, 3)
[,1] [,2] [,3]
[1,] 1 2 3
[2,] 1 2 4
[3,] 1 3 4
[4,] 2 3 4
## Alternatively, iterate over combinations
a = comboIter(4, 3)
a$nextIter()
[1] 1 2 3
a$back()
[1] 2 3 4
a[[2]]
[1] 1 2 4
## Pass any atomic type vector
permuteGeneral(letters, 3, upper = 4)
[,1] [,2] [,3]
[1,] "a" "b" "c"
[2,] "a" "b" "d"
[3,] "a" "b" "e"
[4,] "a" "b" "f"
## Generate a reproducible sample
comboSample(10, 8, TRUE, n = 5, seed = 84)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 3 3 3 6 6 10 10 10
[2,] 1 3 3 4 4 7 9 10
[3,] 3 7 7 7 9 10 10 10
[4,] 3 3 3 9 10 10 10 10
[5,] 1 2 2 3 3 4 4 7
## Get combinations such that the product is between
## 3600 and 4000 (including 3600 but not 4000)
comboGeneral(5, 7, TRUE, constraintFun = "prod",
comparisonFun = c(">=","<"),
limitConstraints = c(3600, 4000),
keepResults = TRUE)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1 2 3 5 5 5 5 3750
[2,] 1 3 3 4 4 5 5 3600
[3,] 1 3 4 4 4 4 5 3840
[4,] 2 2 3 3 4 5 5 3600
[5,] 2 2 3 4 4 4 5 3840
[6,] 3 3 3 3 3 3 5 3645
[7,] 3 3 3 3 3 4 4 3888
```

- Function Documentation
- Computational Mathematics Overview
- Combination and Permutation Basics
- Combinatorial Sampling
- Constraints, Integer Partitions, and Compositions
- Attacking Problems Related to the Subset Sum Problem
- Combinatorial Iterators in RcppAlgos

I welcome any and all feedback. If you would like to report a bug, have a question, or have suggestions for possible improvements, please file an issue.