Part 2: Dorm Rooms (Sharp) With your new algorithms expertise, you've been hired by ResEd to help them with dorm room assignments. There are n ncoming students F = {f1.h, , and d single dorm rooms R = (r1, T2,... ,ra). Each student fi e F has a set of acceptable rooms A(f) C R, and a preference list in which they rank A(fi) in strict order. Given any student fi e F and any two rooms ry, Tk E FR f, is said to prefer rj to rk if {ry, A(f), and rj precedes rk on fi's preference list. Given any student fi e F and any two matchings M, M' (matching each f, to a room in A(f) or to no room at all), f is said to prefer M' to M if either (i) fi is assigned in M and unassigned in M, or (ii) fi is assigned in both M and M', and fi prefers M'(fi) to M(f). Part 2: Dorm Rooms (Sharp) With your new algorithms expertise, you've been hired by ResEd to help them with dorm room assignments. There are n ncoming students F = {f1.h, , and d single dorm rooms R = (r1, T2,... ,ra). Each student fi e F has a set of acceptable rooms A(f) C R, and a preference list in which they rank A(fi) in strict order. Given any student fi e F and any two rooms ry, Tk E FR f, is said to prefer rj to rk if {ry, A(f), and rj precedes rk on fi's preference list. Given any student fi e F and any two matchings M, M' (matching each f, to a room in A(f) or to no room at all), f is said to prefer M' to M if either (i) fi is assigned in M and unassigned in M, or (ii) fi is assigned in both M and M', and fi prefers M'(fi) to M(f)