A collection of high performance functions implemented in C++ for solving problems in combinatorics and computational mathematics.

: Generate all combinations/permutations of a vector (including multisets) meeting specific criteria.`{combo|permute}General`

: Efficient algorithms for partitioning numbers under various constraints`{partitions|compositions}General`

: Generate reproducible random samples`{combo|permute|partitions|compositions}Sample`

: Flexible iterators allow for bidirectional iteration as well as random access.`{combo|permute|partitions|compositions}Iter`

: 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)
# [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
## And compositions
compositionsGeneral(0:3, repetition = TRUE)
# [,1] [,2] [,3]
# [1,] 0 0 3
# [2,] 0 1 2
# [3,] 0 2 1
# [4,] 1 1 1
## 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, Partitions, and Compositions
- Attacking Problems Related to the Subset Sum Problem
- Combinatorial Iterators in RcppAlgos
- Cartesian Products and Partitions of Groups

`RcppAlgos`

`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`

.

If you would like to report a bug, have a question, or have suggestions for possible improvements, please file an issue.

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