unionCardinalityN<T> static method

int unionCardinalityN<T>(List<CustomSet<T>> sets)

Calculates the cardinality of the union of multiple sets using the Generalized Inclusion-Exclusion Principle.

Formula for n sets: |A₁ ∪ A₂ ∪ ... ∪ Aₙ| = Σ|Aᵢ| - Σ|Aᵢ ∩ Aⱼ| + Σ|Aᵢ ∩ Aⱼ ∩ Aₖ| - ... + (-1)ⁿ⁻¹|A₁ ∩ A₂ ∩ ... ∩ Aₙ|

Note: This implementation is optimized for small numbers of sets (≤ 10). For larger numbers, consider alternative approaches.

Example:

final sets = [
  CustomSet<int>([1, 2, 3]),
  CustomSet<int>([3, 4, 5]),
  CustomSet<int>([5, 6, 7]),
];
print(CardinalityUtils.unionCardinalityN(sets)); // Output: 7

Implementation

static int unionCardinalityN<T>(List<CustomSet<T>> sets) {
  if (sets.isEmpty) return 0;
  if (sets.length == 1) return sets[0].cardinality;
  if (sets.length == 2) return unionCardinality(sets[0], sets[1]);
  if (sets.length == 3) return unionCardinality3(sets[0], sets[1], sets[2]);

  // For more than 3 sets, compute actual union
  CustomSet<T> result = sets[0];
  for (int i = 1; i < sets.length; i++) {
    result = SetOperations.union(result, sets[i]);
  }

  return result.cardinality;
}