朱莉娅中se的所有子集

Question

你能帮我吗？ 我该怎么做才能找到集合中所有子集的代码

例如

我想用Julia编写此约束。这是一个子行程约束。但是我不知道如何找到S集的所有子集。

@constraint(ILRP,
            c7[k in totalK, t in totalH],
            sum(x[i,j,k,t] for i=1:totalS, j=1:totalS)<=size(S)-1);

非常感谢

Answer 1

您可以使用Combinatorics.jl软件包中的powerset函数来获取它，例如：

julia> using Combinatorics

julia> x = [1:5;]
5-element Array{Int64,1}:
 1
 2
 3
 4
 5

julia> powerset(x)
Base.Iterators.Flatten{Array{Combinatorics.Combinations{Array{Int64,1}},1}}(Combinatorics.Combinations{Array{Int64,1}}[Combinations{Array{Int64,1}}([1, 2, 3, 4, 5], 0), Combinations{Array{Int64,1}}([1, 2, 3, 4, 5], 1), Combinations{Array{Int64,1}}([1, 2, 3, 4, 5], 2), Combinations{Array{Int64,1}}([1, 2, 3, 4, 5], 3), Combinations{Array{Int64,1}}([1, 2, 3, 4, 5], 4), Combinations{Array{Int64,1}}([1, 2, 3, 4, 5], 5)])

julia> collect(powerset(x))
32-element Array{Array{Int64,1},1}:
 []
 [1]
 [2]
 [3]
 [4]
 [5]
 [1, 2]
 [1, 3]
 [1, 4]
 [1, 5]
 [2, 3]
 [2, 4]
 [2, 5]
 [3, 4]
 [3, 5]
 [4, 5]
 [1, 2, 3]
 [1, 2, 4]
 [1, 2, 5]
 [1, 3, 4]
 [1, 3, 5]
 [1, 4, 5]
 [2, 3, 4]
 [2, 3, 5]
 [2, 4, 5]
 [3, 4, 5]
 [1, 2, 3, 4]
 [1, 2, 3, 5]
 [1, 2, 4, 5]
 [1, 3, 4, 5]
 [2, 3, 4, 5]
 [1, 2, 3, 4, 5]

请注意，默认情况下，powerset返回一个迭代器，以避免分配所有子集。 另外，您可以向powerset传递第二个和第三个位置参数，以限制返回子集的最小和最大大小，例如：

julia> collect(powerset(x, 2, 3))
20-element Array{Array{Int64,1},1}:
 [1, 2]
 [1, 3]
 [1, 4]
 [1, 5]
 [2, 3]
 [2, 4]
 [2, 5]
 [3, 4]
 [3, 5]
 [4, 5]
 [1, 2, 3]
 [1, 2, 4]
 [1, 2, 5]
 [1, 3, 4]
 [1, 3, 5]
 [1, 4, 5]
 [2, 3, 4]
 [2, 3, 5]
 [2, 4, 5]
 [3, 4, 5]

Answer 2

不知道这是您要寻找的东西

  

使用组合语

   function subsets(A::AbstractArray,r::Union{AbstractArray,Integer})
  o= Array{Array{eltype(A),1},1}(undef,0)         
  if typeof(r)<:Integer
      r>length(A) && (r=[length(A)])
      r=[r...]
  elseif typeof(r)<:UnitRange
      r[end]>length(A) && (r=1:r[length(A)])
  else
      !issubset(r,1:length(A)) && (r=intersect(r,1:length(A)))
  end
  for n = r
      a=combinations(A,n)
      for i in a     
          push!(o,i)
      end
  end
  return o
end

subsets(A::AbstractArray) = subsets(A,1:length(A))

它可以列出所有子集或不超过一定限制（长度）的子集：例如：

 julia> subsets(1:3)
 7-element Array{Array{Int64,1},1}:
  [1]
  [2]
  [3]
  [1, 2]
  [1, 3]
  [2, 3]
  [1, 2, 3]
  julia> subsets(1:3,2)
  3-element Array{Array{Int64,1},1}:
  [1, 2]
  [1, 3]
  [2, 3]