cartesianProductN<T> static method

CustomSet<List<T>> cartesianProductN<T>(List<CustomSet<T>> sets)

Returns the Cartesian product of n sets.

Notation: A₁ × A₂ × ... × Aₙ = {(a₁, a₂, ..., aₙ) | aᵢ ∈ Aᵢ}

Returns all possible n-tuples where each element comes from the corresponding set in the list.

If any set is empty or the list is empty, returns an empty set.

Implementation

static CustomSet<List<T>> cartesianProductN<T>(List<CustomSet<T>> sets) {
  if (sets.isEmpty) return CustomSet.empty();
  if (sets.any((s) => s.isEmpty)) return CustomSet.empty();

  List<List<T>> result = [[]];
  for (var set in sets) {
    final List<List<T>> newResult = [];
    for (var prefix in result) {
      for (var element in set.elements) {
        newResult.add([...prefix, element]);
      }
    }
    result = newResult;
  }

  return CustomSet(result);
}