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Set/Subset Generators

JNumberTools provides the following 7 generators for sets and subsets. All m^th generators are BigInteger compatible, enabling rapid generation of subsets at very large indices, such as 10¹⁰⁰.

Currently Available Algorithms

1. All subsets in lex order
2. Every m^th subsets in lex order
3. All subsets of given size range in lex order
4. Every m^th subsets in a given size range in lex order
5. Random subset choice
6. Random subset sample
7. Subsets of ranks

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1. All subsets in lex order

Generates all subsets of a given set in lexicographical order, including the empty set (φ). For example, for the set ["A", "B", "C"], it generates: [], [A], [B], [C], [A, B], [A, C], [B, C], [A, B, C].

// All subsets of ["Apple", "Banana", "Guava"] in lex order
JNumberTools.subsets()
    .of("Apple", "Banana", "Guava")
    .all()
    .lexOrder()
    .stream().forEach(System.out::println);

2. Every m-th subsets in lex order

Generates every m^th subset of a given set in lexicographical order, starting from a given index. This API directly generates the desired subset without iterating through preceding subsets, making it highly efficient.

// Every 1 billionth subset of numbers in range [0,40) starting from 0th index
JNumberTools.subsets()
    .of(40)
    .all()
    .lexOrderMth(1_000_000_000, 0)
    .stream().forEach(System.out::println);

3. All subsets of given size range in lex order

Generates all subsets within a specified size range in lexicographical order. For example, for the set ["A", "B", "C"] with size range [2,3], it generates: [A, B], [A, C], [B, C], [A, B, C].

// All subsets of ["Apple", "Banana", "Guava"] in size range [2,3] in lex order
JNumberTools.subsets()
    .of("Apple", "Banana", "Guava")
    .inRange(2, 3)
    .lexOrder()
    .stream().forEach(System.out::println);

4. Every m-th subsets in range in lex order

Generates every m^th subset within a specified size range in lexicographical order, starting from a given index. This API directly generates the desired subset without computing preceding subsets.

// Every 1 billionth subset of numbers in range [0,40) with size range [10,39] starting from 0th index
JNumberTools.subsets()
    .of(40)
    .inRange(10, 39)
    .lexOrderMth(1_000_000_000, 0)
    .stream().forEach(System.out::println);

5. Random subset choice

Generates n random subsets with duplicates allowed.

// Generate 5 random subsets of numbers in range [0,10) with duplicates
JNumberTools.subsets()
    .of(10)
    .all()
    .choice(5)
    .stream().forEach(System.out::println);

// Generate 5 random subsets of ["Apple", "Banana", "Guava"] with duplicates
JNumberTools.subsets()
    .of("Apple", "Banana", "Guava")
    .all()
    .choice(5)
    .stream().forEach(System.out::println);

6. Random subset sample

Generates n random subsets without duplicates.

// Generate 5 random subsets of numbers in range [0,10) without duplicates
JNumberTools.subsets()
    .of(10)
    .all()
    .sample(5)
    .stream().forEach(System.out::println);

// Generate 5 random subsets of ["Apple", "Banana", "Guava"] without duplicates
JNumberTools.subsets()
    .of("Apple", "Banana", "Guava")
    .all()
    .sample(5)
    .stream().forEach(System.out::println);

7. Subsets of ranks

Generates subsets at indices specified by a custom sequence.

// Generates subsets of numbers in range [0,100) at specified indices
var iterable = List.of(10, 20, 1_000_000_000L, new BigInteger("1000000000000000000000"));
JNumberTools.subsets()
    .of(100)
    .all()
    .byRanks(iterable)
    .stream().forEach(System.out::println);

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