JuliaMath / JuliaMath/Combinatorics.jl
Allow & include empty partitions among sets from `partitions(::Vector, ::Int)`
- Dominant language
- Julia
- Stars
- 230
- Forks
- 62
- PR merge metrics
- No merged PRs in 30d
Description
For some applications, it can be helpful to include in the set of partitions of a vector, the option of taking nothing, i.e., to include empty-partitions. Currently, however, `partitions(s::AbstractVector, m::Int)` will only consider non-empty partitions. I think it would be nice to allow the former as well, enabled e.g., by a keyword argument (e.g., `allow_empty`).
By example, this would turn the two following examples from:
```jl
julia> partitions([1,2,3], 2) |> collect
[[1, 2], [3]]
[[1, 3], [2]]
[[1], [2, 3]]
julia> partitions([1,2,3,4], 3) |> collect
[[1, 2], [3], [4]]
[[1, 3], [2], [4]]
[[1], [2, 3], [4]]
[[1, 4], [2], [3]]
[[1], [2, 4], [3]]
[[1], [2], [3, 4]]
```
to:
```jl
julia> partitions([1,2,3], 2; allow_empty=true) |> collect
[[1, 2], [3]]
[[1, 3], [2]]
[[1], [2, 3]]
[[1, 2, 3], []] # additional permutation
julia> partitions([1,2,3,4], 3; allow_empty=true) |> collect
[[1, 2], [3], [4]]
[[1, 3], [2], [4]]
[[1], [2, 3], [4]]
[[1, 4], [2], [3]]
[[1], [2, 4], [3]]
[[1], [2], [3, 4]]
[[1, 2, 3], [], [4]] # additional permutation
[[1, 2, 4], [3], []] # additional permutation
[[1, 2], [3, 4], []] # additional permutation
...
```
NB: This can currently be "simulated" by appending some token element, e.g., `0`, onto the input vector `m-1` times, and then considering token-elements as empty. I.e., `partitions(vcat(s, fill(0, m-1)), m)`. But this seems inelegant and generates redundant possibilities that need to be filtered out subsequently.
Contributor guide
No contributing guide indexed for this repository
Assessment
This issue has not been assessed yet.