https://github.com/deltam/perm
Permutation generator based on group theory written in Go
https://github.com/deltam/perm
golang permutation-generator
Last synced: 6 months ago
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Permutation generator based on group theory written in Go
- Host: GitHub
- URL: https://github.com/deltam/perm
- Owner: deltam
- License: mit
- Created: 2019-09-02T11:17:05.000Z (almost 7 years ago)
- Default Branch: master
- Last Pushed: 2021-11-20T06:19:41.000Z (over 4 years ago)
- Last Synced: 2024-06-19T23:14:05.824Z (about 2 years ago)
- Topics: golang, permutation-generator
- Language: Go
- Homepage:
- Size: 1.51 MB
- Stars: 4
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# perm
[](https://pkg.go.dev/github.com/deltam/perm)
Permutation generator based on group theory[^1].
- Fast
- Stateless
- generate next permutation from current permutation only.
- Permutation order is **NOT** lexical.
## Installation
```
go get github.com/deltam/perm
```
## Usage
Index only:
```go
func main() {
g, err := perm.New(3)
if err != nil {
log.Fatal(err)
}
for ; !g.Done(); g.Next() {
fmt.Println(p)
}
}
// Output:
// [1 2 0]
// [2 0 1]
// [0 2 1]
// [2 1 0]
// [0 1 2]
// [1 0 2]
```
Permutation of slice:
```go
func main() {
words := []rune("ABC")
g, err := perm.Iter(ss)
if err != nil {
log.Fatal(err)
}
for ; !g.Done(); g.Next() {
fmt.Printf("%v\t%s\n", g.Index(), string(words))
}
}
// Output:
// [1 2 0] ABC
// [2 0 1] BCA
// [0 2 1] CBA
// [2 1 0] BAC
// [0 1 2] CAB
// [1 0 2] ACB
```
## Performance
This algorithm is 40~50% faster than naive recursive algorithm.
time/op
Primitive-833.3µs ± 2%
Generator-839.1µs ± 2%
PermRecursive-866.9µs ± 1%
```go
func recPerm(p []int, n int, ignore []bool) {
if n == 0 {
return
}
for i := 0; i < len(p); i++ {
if !ignore[i] {
p[n-1] = i
ignore[i] = true
recPerm(p, n-1, ignore)
ignore[i] = false
}
}
}
```
## Background
See [paper](https://arxiv.org/abs/1307.2549)[^1] for details.
I also explained details on [my blog post](https://deltam.blogspot.com/2019/12/permutationgenerator.html)(Japanese only). [^3]
[Cayley graph](https://en.wikipedia.org/wiki/Cayley_graph) on permutation group generated by _sigma_ and _tau_ has a size two disjoint cycle cover and [Hamilton path](https://en.wikipedia.org/wiki/Hamiltonian_path).
sigma(rotation): (1, 2, ..., n) -> (2, 3, ..., n, 1)
tau(swap): (1, 2, ..., n) -> (2, 1, ..., n)
Below is the Hamilton path created by split and join the two cycles.
By observing above Hamilton path, you can discover local rule for generating that.
See `primitive.go` or this text[^2][^3] for details.
## License
MIT
Copyright 2019 deltam
[^1]: [Hamiltonicity of the Cayley Digraph on the Symmetric Group Generated by σ = (1 2 ... n) and τ = (1 2)](https://arxiv.org/abs/1307.2549)
[^2]: [The Williams Construction: Superpermutations — Greg Egan](https://www.gregegan.net/SCIENCE/Superpermutations/Superpermutations.html#WILLIAMS)
[^3]: [2つの操作のみで全順列を列挙する：対称群のグラフ上のハミルトン路にもとづく順列生成の紹介と実装 : サルノオボエガキ](https://deltam.blogspot.com/2019/12/permutationgenerator.html)