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"Tuples" (Incremental Object)

IncrementalObject["Tuples"] [list,n]

creates an object that incrementally returns values that are n-tuples of list.

IncrementalObject["Tuples"] [{list1,list2,…}]

creates an object that incrementally returns values that are tuples whose i th element is from listi.

Details

  • A "Tuples" incremental object creates and returns tuples 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 "Tuples" incremental object:

Wolfram Language code: obj = IncrementalObject["Tuples"][{a, b}, 2]

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  (3)

An incremental object can be used in Table:

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

An incremental object can be used in Do:

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

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

Wolfram Language code: obj = IncrementalObject["Tuples"][Range[20], 4]; Do[NextValue[obj], 10000]
Wolfram Language code: NextValue[obj]

Properties & Relations  (3)

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

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

InputForm  (1)

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

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

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

Wolfram Language code: IncrementalObject["Tuples", {"Data" :> {0, 0, 0, 0}, "Exhausted" :> False, "Source" :> {{a, b, c}, {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["Tuples"][{a, b, c, d}, 2]; obj2 = IncrementalObject["Tuples"][{a, b, c, d}, 2]; 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