# Is there a way to create a comprehensive set of conditional combinations

Hi I was just wondering if there was a way to generate a combinatorial collection subject to some condition. For example using the Combinatorics package If I can generate all combinations of some vector

``````collect(combinations(1:6,2))
15-element Vector{Vector{Int64}}:
[1, 2]
[1, 3]
[1, 4]
[1, 5]
[1, 6]
[2, 3]
[2, 4]
[2, 5]
[2, 6]
[3, 4]
[3, 5]
[3, 6]
[4, 5]
[4, 6]
[5, 6]
``````

However what if I only want the combinations where a certain condition is met, e.g. the second number minus the first is greater than one or the sum of the selected set is equal to some value. Is there a way to input these constraints as a parameter into combinations?

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`filter(x -> (x - x)>0 || sum(x) == value, collect(combinations(1:6,2)))`

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You should drop the `collect` to avoid allocating memory to store the discarded combos. If you must, add the `collect` outside `filter`.

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oh sorry, just copy-pasted!

note: filter() does not work without using collect() in this case without using `collect`.

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It appears that you need `Iterators.filter` if the second argument is an iterator.

`Iterators.filter(x → (x - x)>0 || sum(x) == value, combinations(1:6,2))`

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yes this is a more memory friendly version just because it consumes memory when needed only.

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thanks guys! this is really helpful. When I try to run it with Iterators.filter without collect rather than the actual combinations I get this. `Iterators.filter(x -> (x - x)>0 ||sum(x) == 6 ,combinations(1:6,2)) Base.Iterators.Filter{var"#15#16", Base.Generator{Combinatorics.Combinations, Combinatorics.var"#10#13"{Combinatorics.var"#reorder#11"{UnitRange{Int64}}}}}(var"#15#16"(), Base.Generator{Combinatorics.Combinations, Combinatorics.var"#10#13"{Combinatorics.var"#reorder#11"{UnitRange{Int64}}}}(Combinatorics.var"#10#13"{Combinatorics.var"#reorder#11"{UnitRange{Int64}}}(Combinatorics.var"#reorder#11"{UnitRange{Int64}}(1:6)), Combinatorics.Combinations(6, 2)))`

Is this normal?

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`Iterators.filter(x -> (x - x)>0 || sum(x) == value, combinations(1:6,2)) |> collect`

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awesome thanks! quick question what is the piping` |>` operator doing and how does that differ from your initial code ?

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Yes it only collects the result returned by the filtered one.

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gotcha thanks again!

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