Problem A: Maximizing Happiness on the Bus
The key to maximizing happiness is to seat family members together as much as possible. If two members of the same family sit in the same row, both will be happy, and we only use two seats. However, if they are seated separately, only one person is happy, but two seats are still used. Therefore, we prioritize seating family pairs together first.
Once all possible pairs are seated, there may still be some family members left to seat. If a family has an odd number of members, one person will be left without a pair. Ideally, we want to seat this person alone in a row to make them happy. However, if there are no remaining rows to seat them alone, we’ll have to seat them with someone from another family. This means the other person might no longer be happy since they are no longer seated alone.
The easiest way to handle part 2 is to check the number of remaining rows and people. If the number of remaining rows is greater than or equal to the number of unpaired people, all unpaired individuals can sit alone and remain happy. Otherwise, some people will have to share a row, and their happiness will be affected. In that case, the number of unhappy people will be 2 × remaining rows - remaining people.
