inclusionExclusion3<T> static method

int inclusionExclusion3<T>(CustomSet<T> a, CustomSet<T> b, CustomSet<T> c)

Applies the inclusion-exclusion principle for three sets.

Formula: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

This extends the two-set formula to handle three sets.

Example:

final a = CustomSet<int>([1, 2, 3, 4]);
final b = CustomSet<int>([3, 4, 5, 6]);
final c = CustomSet<int>([5, 6, 7, 8]);
final count = AdvancedSetOperations.inclusionExclusion3(a, b, c);
print(count); // Output: 8

Implementation

static int inclusionExclusion3<T>(
  CustomSet<T> a,
  CustomSet<T> b,
  CustomSet<T> c,
) =>
    a.cardinality +
    b.cardinality +
    c.cardinality -
    SetOperations.intersection(a, b).cardinality -
    SetOperations.intersection(a, c).cardinality -
    SetOperations.intersection(b, c).cardinality +
    SetOperations.intersection(
      SetOperations.intersection(a, b),
      c,
    ).cardinality;