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Derangement Generators

JNumberTools provides derangement (fixed-point-free permutation) generators for lists and integer ranges. All m^th generators are BigInteger compatible, enabling rapid access to very large ranks.

Currently Available Algorithms

1. Derangement in lex order
2. Every m^th derangement in lex order
3. Derangement random choice
4. Derangement random sample
5. Derangement of ranks

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1. Derangement in lex order

Generates all derangements of the given elements in lexicographical order. A derangement is a permutation where no element appears in its original position.

// All derangements of [0,1,2,3] in lex order
JNumberTools.derangements()
    .of(4)
    .lexOrder()
    .stream().forEach(System.out::println);

// All derangements of ["A","B","C","D"] in lex order
JNumberTools.derangements()
    .of("A", "B", "C", "D")
    .lexOrder()
    .stream().forEach(System.out::println);

2. Every m-th derangement in lex order

Generates every m^th derangement, starting from a given rank, without iterating through all prior derangements.

int m = 3;
int start = 0;

// Every 3rd derangement of [0,1,2,3,4] starting from rank 0
JNumberTools.derangements()
    .of(5)
    .lexOrderMth(m, start)
    .stream().forEach(System.out::println);

// Every 3rd derangement of ["A","B","C","D","E"] starting from rank 0
JNumberTools.derangements()
    .of("A", "B", "C", "D", "E")
    .lexOrderMth(m, start)
    .stream().forEach(System.out::println);

3. Derangement random choice

Generates random derangements with replacement (duplicates allowed).

// Generate any 5 derangements of [0,1,2,3] with duplicates allowed
JNumberTools.derangements()
    .of(4)
    .choice(5)
    .stream().forEach(System.out::println);

4. Derangement random sample

Generates random derangements without replacement (unique output).

// Generate 5 unique derangements of ["A","B","C","D","E"]
JNumberTools.derangements()
    .of("A", "B", "C", "D", "E")
    .sample(5)
    .stream().forEach(System.out::println);

5. Derangement of ranks

Generates derangements at indices specified by a custom rank sequence.

var ranks = List.of(
        BigInteger.ZERO,
        BigInteger.valueOf(2),
        BigInteger.valueOf(10),
        new BigInteger("1000000000000000000"));

// Generate derangements of size 8 at specific ranks
JNumberTools.derangements()
    .of(8)
    .byRanks(ranks)
    .stream().forEach(System.out::println);

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