Course Solutions Uncategorized (Solved) : 4a Given N Boys N Girls Many Ways Break N Pairs 4b Wish Assign Four Students B C D Two Roo Q31507345 . . . .

(Solved) : 4a Given N Boys N Girls Many Ways Break N Pairs 4b Wish Assign Four Students B C D Two Roo Q31507345 . . . .

 

4a) Given n boys and n girls, how many ways are there to break them into n pairs? 4b) You wish to assign four students A, B, C, and D to two rooms, two stu dents per room. Come up with a preference list for the students, where each of them ranks the remaining three possible roommates (without ties) such that no stable assignment exists. Provide the preferences of the students in a table similar to the one below Highly preferred Mildly preferred Not preferred| 4c) Show that the Gale-Shapley algorithm for pairing up n boys and n girls takes at most n(n - 1)1 rounds.

4a)

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