User

Input: n men: m$1,...$ mn$,$ n women: w$1,...$ wn$,$ and a preference list for each person.

For all men, their preference list of the women are the same. For all women, the preference lists of the men are the same.

Output: A set of n marriages $\{($wi$1,$ mj$1),...,($win$,$ mjn$)\}$ such that everyone is married, and the marriages are stable. Prove that there exists a unique stable marriage.