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"Permutations" (Incremental Object)

IncrementalObject["Permutations"] [list]

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

Details

  • A "Permutations" incremental object creates and returns permutations 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 "Permutations" incremental object:

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

The first 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  (4)

An incremental object can be used in Table:

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

An incremental object can be used in Do:

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

The permutation values never repeat themselves even if there are repeated elements in the input:

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

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

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

Properties & Relations  (3)

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

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

InputForm  (1)

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

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

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

Wolfram Language code: IncrementalObject["Permutations", {"Position" :> 1, "Length" :> 3, "Repetitions" :> False, "Data" :> {1, 2, 3, 1, 2, 3, 0, 0, 0}, "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["Permutations"][{a, b, c, d}]; obj2 = IncrementalObject["Permutations"][{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