Partitioning a vector

General Usage
1

Dear all,
I have a vector: I = 1:55. I need to partition it into 10 subvectors, none of which must be empty and the length of each of which is a random number. What is the best way to do this? Could someone help me?

2

What is the use case? Do you have other constraints on the lengths? Why not take them constant?

3

I need different lenghts to insert in a optimization problem. Moreover, all components of ```I```` need to be used.

4

Okay but why do the lengths need to be different?
Do the subvectors need to be contiguous?

5

Here’s a simple code that does uniform assignment over the k subvectors.

n, k = 55, 10
x = 1:n
select = rand(1:k, n)
subvectors = Vector{Vector{eltype(x)}}(undef, k)
for i in 1:k
    subvectors[i] = x[select .== i]
end

Example result:

julia> subvectors
10-element Vector{Vector{Int64}}:
 [4, 5, 6, 31, 46, 53]
 [7, 17, 48]
 [3, 16, 26, 39, 41, 51, 52]
 [1, 10, 12, 13, 19, 21, 43, 54]
 []
 [9, 28, 32, 37, 42]
 [15, 23, 27, 30, 34, 40]
 [2, 11, 20, 22, 38, 44, 47]
 [8, 14, 24, 33, 36, 45, 50, 55]
 [18, 25, 29, 35, 49]

If you want none of them to be empty, one way would be to assign the first k elements of x deterministically for instance.

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7

Thanks a lot!!!

8

Using the prototypical decomposition of 55 = 1+2+…+10, it seems you might be looking for something like:

julia> using Random

julia> shuffle(getindex.(Ref(shuffle(1:55)),(:).(cumsum(0:9).+1,cumsum(1:10))))
10-element Vector{Vector{Int64}}:
 [29, 52, 30]
 [5, 24, 28, 21, 27, 22]
 [12, 38, 31, 26, 16, 23, 9, 36, 18]
 [13, 45, 46, 34, 14, 41, 19, 10, 3, 4]
 [8, 37, 7, 11]
 [51, 6]
 [54, 15, 40, 48, 20, 35, 50]
 [17, 53, 1, 2, 44]
 [39]
 [42, 43, 49, 32, 33, 25, 55, 47]

There are a few optimizations still possible on this expression, but is this in the direction you are looking?

9

Perhaps a similar discussion might be of interest

1 Like