cartesianProduct<T, U> static method

CustomSet<(T, U)> cartesianProduct<T, U>(CustomSet<T> a, CustomSet<U> b)

Returns the Cartesian product of two sets.

Notation: A × B = {(a, b) | a ∈ A and b ∈ B}

The Cartesian product contains all ordered pairs where the first element is from set A and the second is from set B.

If either set is empty, the result is an empty set. |A × B| = |A| × |B|

Example:

final c = CustomSet<int>([1, 2, 3]);
final d = CustomSet<String>(['a', 'b']);
final result = AdvancedSetOperations.cartesianProduct(c, d);
// result = {(1, 'a'), (1, 'b'), (2, 'a'), (2, 'b'), (3, 'a'), (3, 'b')}

Implementation

static CustomSet<(T, U)> cartesianProduct<T, U>(
  CustomSet<T> a,
  CustomSet<U> b,
) {
  if (a.isEmpty || b.isEmpty) return CustomSet.empty();

  final List<(T, U)> pairs = [];
  for (var elementA in a.elements) {
    for (var elementB in b.elements) {
      pairs.add((elementA, elementB));
    }
  }

  return CustomSet(pairs);
}