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"Subsets" (Incremental Object)

IncrementalObject["Subsets"] [list]

creates an object that incrementally returns values that are subsets of list.

IncrementalObject["Subsets"] [list,n]

creates an object that incrementally returns values that are subsets of list of at most length n.

IncrementalObject["Subsets"][list,{n}]

creates an object that incrementally returns values that are subsets of list of length n.

IncrementalObject["Subsets"][list,{nmin,nmax}]

creates an object that incrementally returns values that are subsets of list of length between nmin and nmax.

IncrementalObject["Subsets"][list,nspec,s]

creates an object that incrementally returns values that are subsets of list limiting the results to the first s subsets.

IncrementalObject["Subsets"][list,nspec,{smin,smax}]

creates an object that incrementally returns values that are subsets of list running from positions smin to smax.

Details

  • A "Subsets" incremental object creates and returns subsets one at a time without having to generate all of them at once.
  • The following functions are also supported:
  • dsi===dsjTrue, if dsi equals dsj
    FullForm[ds]full form of ds
    InputForm[ds]input form of ds

Examples

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Basic Examples  (1)

Create a new "Subsets" incremental object:

Wolfram Language code: obj = IncrementalObject["Subsets"][{a, b}]

The first value:

Wolfram Language code: NextValue[obj]

The next value:

Wolfram Language code: NextValue[obj]

The next value:

Wolfram Language code: NextValue[obj]

The next value:

Wolfram Language code: NextValue[obj]

There are no more values, and a failure object is returned:

Wolfram Language code: NextValue[obj]

Scope  (5)

An incremental object can be used in Table:

Wolfram Language code: obj = IncrementalObject["Subsets"][{a, b, c}, {2}]; Table[e, {e, obj}]

An incremental object can be used in Do:

Wolfram Language code: obj = IncrementalObject["Subsets"][{a, b, c}, {2}]; Do[Echo[e], {e, obj}]

Subsets can be processed incrementally even if the total number of permutations is very long:

Wolfram Language code: obj = IncrementalObject["Subsets"][Range[50], {4}]; Do[NextValue[obj], 10000]
Wolfram Language code: NextValue[obj]

Subsets can be processed incrementally even if the total number is very long:

Wolfram Language code: obj = IncrementalObject["Subsets"][Range[50], {4}]; Do[NextValue[obj], 10000]
Wolfram Language code: NextValue[obj]

Processing subsets incrementally uses very significantly less memory:

Wolfram Language code: (obj = IncrementalObject["Select"][IncrementalObject["Subsets"][Range[20]], !OrderedQ[#]&]; Table[elem, {elem, obj}])//MaxMemoryUsed
Wolfram Language code: Select[Subsets[Range[20]], !OrderedQ[#]&]//MaxMemoryUsed

Properties & Relations  (3)

The values return by a "Subsets" incremental object are the same as those returned by Subsets.

Wolfram Language code: obj = IncrementalObject["Subsets"][{a, b, c, d}, 2]; Table[e, {e, obj}]
Wolfram Language code: Subsets[{a, b, c, d}, 2]

InputForm  (1)

InputForm returns the serialized contents of a "Subsets" incremental object:

Wolfram Language code: InputForm[IncrementalObject["Subsets"][{a, b, c}, 2]]

This serialized form can be used to recreate the incremental object:

Wolfram Language code: IncrementalObject["Subsets", {"Initial" :> True, "CountData" :> {1, 1, -1}, "Length" :> 3, "KData" :> {0, 0, 2}, "Data" :> {}, "Source" :> {a, b, c}}]

SameQ  (1)

SameQ can be used to test whether two incremental objects contain the same sequence at the same position:

Wolfram Language code: obj1 = IncrementalObject["Subsets"][{a, b, c, d}]; obj2 = IncrementalObject["Subsets"][{a, b, c, d}]; obj1 === obj2

If one objects moves to the next value, the two objects are no longer the same:

Wolfram Language code: NextValue[obj1]; obj1 === obj2

Advancing the other object means that they are both now the same:

Wolfram Language code: NextValue[obj2]; obj1 === obj2