RcppAlgos 
A collection of high performance functions implemented in C++ for solving problems in combinatorics and computational mathematics.
Featured Functions
comboGeneral/permuteGeneral: Generate all combinations/permutations of a vector (including multisets) meeting specific criteria.partitionsGeneral: Efficient algorithms for partitioning numbers under various constraintscomboSample/permuteSample/partitionsSample: Generate reproducible random samples of combinations/permutations/partitionscomboIter/permuteIter/partitionsIter: Flexible iterators allow for bidirectional iteration as well as random access.primeSieve: Fast prime number generatorprimeCount: Prime counting function using Legendre's formula
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.
Benchmarks
Installation
install.packages("RcppAlgos")
## install the development version
devtools::install_github("jwood000/RcppAlgos")Basic Usage
## Generate prime numbers
primeSieve(50)
# [1] 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
## Many of the functions can produce results in
## parallel for even greater performance
p = primeSieve(1e15, 1e15 + 1e8, nThreads = 4)
head(p)
# [1] 1000000000000037 1000000000000091 1000000000000159
# [4] 1000000000000187 1000000000000223 1000000000000241
tail(p)
# [1] 1000000099999847 1000000099999867 1000000099999907
# [4] 1000000099999919 1000000099999931 1000000099999963
## 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"
## Flexible partitioning algorithms
partitionsGeneral(0:5, 3, freqs = rep(1:2, 3), target = 6)
# [,1] [,2] [,3]
# [1,] 0 1 5
# [2,] 0 2 4
# [3,] 0 3 3
# [4,] 1 1 4
# [5,] 1 2 3
## 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 3888Further Reading
- Function Documentation
- Computational Mathematics Overview
- Combination and Permutation Basics
- Combinatorial Sampling
- Constraints and Integer Partitions
- Attacking Problems Related to the Subset Sum Problem
- Combinatorial Iterators in RcppAlgos
- Cartesian Products and Partitions of Groups into Equal Size
Why RcppAlgos but no Rcpp?
Previous versions of RcppAlgos relied on Rcpp to ease the burden of exposing C++ to R. While the current version of RcppAlgos does not utilize Rcpp, it would not be possible without the myriad of excellent contributions to Rcpp.
Contact
If you would like to report a bug, have a question, or have suggestions for possible improvements, please file an issue.