You must assign n students to m summer programs as evenly as possible. Each student has provided a list of programs he or she is willing to attend, and every program has at least one interested student. Ideally, the students would be evenly spread between the programs, so that no program takes more than d n m e students. However, this will likely be impossible. Required:
Design a polynomial-time algorithm to find an assignment that minimizes the number of students assigned to the fullest program.