Homework 7

Background: 27.3.

Due November 4th:

• 7.1: Use a hash table to compute the mode of a list of n numbers in expected O(n) time.
• 7.2: For a set of n boys and n girls with rank-order lists, give an algorithm to check if a given marriage is stable.
• 7.3: The MATCH algorithm terminates when all boys are engaged. Argue that all girls are also engaged at this point.
• 7.4: Argue that MATCH returns the girl-pessimal stable marriage.
• 7.5: Argue that, if the boy-optimal and girl-optimal marriages are the same, then there is only one stable marriage.