Ball

A ball is participated by $n$ students from Kumpula and $n$ students from Viikki. The students of each campus are numbered $1,2,\dots,n$.

Each dancing pair has one student from Kumpula and one from Viikki, and you know all pairs that are willing to dance with each other. Each student can belong to at most one dancing pair. What is the maximum number of pairs that can be formed?

In a file ball.py, implement the class Ball with the following methods:

• add_pair declares that a student $a$ from Kumpula and a student $b$ from Viikki are willing to dance with each other
• max_pairs returns the maximum number of dancing pairs

class Ball:
    def __init__(self, n):
        # TODO

    def add_pair(self, a, b):
        # TODO

    def max_pairs(self):
        # TODO

if __name__ == "__main__":
    ball = Ball(4)

    print(ball.max_pairs()) # 0

    ball.add_pair(1, 2)
    print(ball.max_pairs()) # 1

    ball.add_pair(1, 3)
    ball.add_pair(3, 2)
    print(ball.max_pairs()) # 2

    ball.add_pair(2, 1)
    print(ball.max_pairs()) # 3

In the example above, the situation at the end allows three dancing pairs, for instance:

• The Kumpula student $1$ dances with the Viikki student $3$
• The Kumpula student $2$ dances with the Viikki student $1$
• The Kumpula student $3$ dances with the Viikki student $2$

Notice that each campus has $n$ students. For example the Kumpula student $1$ and the Viikki student $1$ are two different students.