There are n students in the CS program, and each of them must take the Algorithms course. There

are m sections of Algorithms offered: A1, ...,Am. They begin at times T1, ...,Tm. Each student can

sign up for at most one section. Because students also have other courses to take, each student can

only attend some subset of the Algorithms sections. This varies by student: some may only be free

during one or two sections, while others might be able to attend all of them. In addition, each

section Ai has a cap Ci on the total enrollment, so you cannot put more than Ci students in that

section. Your goal is to assign students to sections so that as many students as possible are enrolled

in a section of Algorithms (note that it might be impossible to enroll everybody into a section: this is

fine). Design an algorithm to solve this problem by using network flows