Determine Whether Two Horses Are Genetically Related

The International Horse Racing Committee maintains birth-certificate data for a collection of horses. Each record identifies a horse and, when known, its mother and father.

Each position i describes one horse:

• horseIds[i] is the horse's identifier.
• motherIds[i] is its mother's identifier, or the empty string "" when the mother is unknown.
• fatherIds[i] is its father's identifier, or the empty string "" when the father is unknown.

Relationship rule

For this exercise, assume every non-empty parent entry creates an undirected relationship edge between the horse and that parent. Two horses are genetically related when a path of one or more such parent-child edges connects them. A horse is also related to itself.