Gale and shapley published their paper on the stable matching problem in 1962; but a version of their algorithm had already been in use for ten years by the national resident matching program, for the problem of assigning medical residents to hospitals.
basically, the situation was the following. there were m hospitals, each with a certain number of available positions for hiring residents. there were n medical students graduating in a given year, each interested in joining one of the hospitals. each hospital had a ranking of the students in order of preference, and each student had a ranking of the hospitals in order of preference. we will assume that there were more students graduating than there were slots available in the m hospitals. the interest, naturally, was in finding a way of assigning each student to at most one hospital, in such a way that all
available positions in all hospitals were filled. (since we are assuming a surplus of students, there would be some students who do not get assigned to any hospital.)
we say that an assignment of students to hospitals is stable if neither of the following situations arises.

• first type of instability: there are students s and s′, and a hospital h, so that
a) s is assigned to h, and
b) s′ is assigned to no hospital, and
c) h prefers s′ to s.

• second type of instability: there are students s and s′, and hospitals h and h′, so that
a) s is assigned to h, and
b) s′ is assigned to h′, and
c) h prefers s′ to s, and
d) s′ prefers h to h′.

so we basically have the stable matching problem, except that (i) hospitals generally want more than one resident, and (ii) there is a surplus of medical students.
show that there is always a stable assignment of students to hospitals, and give an algorithm to nd one.

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[java] create an application called registrar that has the following classes: a. a student class that minimally stores the following data fields for a student: - name - student id number - number of credits - total grade points earned and this class should also be provides the following methods: - a constructor that initializes the name and id fields - a method that returns the student name field - a method that returns the student id field - methods to set and retrieve the total number of credits - methods to set and retrieve the total number of grade points earned. - a method that returns the gpa (grade points divided by credits) b. an instructor class that minimally stores the following data fields for an instructor: - name - faculty id number - department the following methods should be provided: - a constructor that initializes the name and id fields - methods to set and retrieve the instructor’s department. c. a course class that minimally stores the following data for a course: - name of the course- course registration code- maximum number of 35 students- instructor- number of students- students registered in the course (an array)the following methods should also be provided: - a constructor that initializes the name, registration code, and maximum number of students- methods to set and retrieve the instructor- a method to search for a student in the course; the search should be based on an id number.- a method to add a student to the course. if the course is hill, then an exception with an appropriate message should be raised (try creating your own exception class for this). also, be sure that the student is not already registered in the course. the list of students should be in the order that they registered.- a method to remove a student from the course. if the student is not found, then an exception with an appropriate message should be raised (use the same exception class mentioned a method that will allow course objects to be output to a file using object serialization- a method that will allow course objects to be read in from a file created with object serializationyou will note that the student and instructor classes described above have some commonality. create aperson class that captures this commonality and uses it as a base class for student and instructor. this class should be responsible for the name and id fields and also provide atostring method that returns a string of the form name, id. this will be the inheritedtostring method for the student and instructor classes.1. draw a uml diagram for diss application.2. implement the previous classes in java. write a main program that can serve as a test class that tests all of the methods created and demonstrates that they are working