stable match algorithm for different sizes groups and limited places

I want to write a program that oriented student to their specialty in university depending on their choices and their range in the specialty.

each specialty can take multiple student (in this case cnm =1 , dsi=2 , rss=2),and the number of student can be more than the number of places (in this case one student not gonna have a place because there is only 5 places ).

The program run with out a problem but the output is not correct .(and I couldn’t know why ) . The output for this example should be ((a,cnm),(c,rss),(b,dsi),(e,dsi),(f,rss))

i found a video on youtube (https://youtu.be/FhRf0j068ZA ,the source code https://github.com/Schachte/stable-matching-algorithm) where the person explain and write a code for stable matching problem , i liked that code so i toke it and i tried to edited so it can be solve my problem

If anyone could help me out I would really appreciate it.

*****this is my code

students = {
'A': ['CNM', 'DSI', 'RSS'],
'B': ['CNM', 'DSI', 'RSS'],
'C': ['DSI', 'CNM', 'RSS'],
'D': ['DSI', 'RSS', 'CNM'],
'E': ['RSS', 'DSI', 'CNM'],
'F': ['RSS', 'CNM', 'DSI']
    }

choices = {
   'DSI': ['C', 'E','D', 'B','F','A'],
   'RSS': ['B','F','A', 'E', 'D','C'],
   'CNM': ['A', 'B','C', 'D','E','F']
   }

rss=2
cnm = 1
dsi=2
results = []
students_with_out_choice =[]

for student in students:
     students_with_out_choice.append(student)

while (len(students_with_out_choice) > 0 ):
      for i in range (3):
          for student in students_with_out_choice:
              for choice in students[student]:
                    if ((choice == "DSI" and dsi != 0) or (choice == "RSS" and rss != 0) or (choice == "CNM" and cnm != 0)):
                       results.append([student, choice])
                       students_with_out_choice.remove(student)
                       if (choice == "DSI"):
                          dsi -= 1
                       if (choice == "RSS"):
                          rss -= 1
                       if (choice == "CNM"):
                          cnm -= 1
                       break

                    else:
                       for key, value in results:
                          if choice == value:
                             a= key

                       etudiant_actuel = choices[choice].index(a)
                       etudiant_proposer = choices[choice].index(student)

                       if (etudiant_actuel >etudiant_proposer):
                           students_with_out_choice.remove(student)

                           students_with_out_choice.append(a)

                           a = student
                           break
                       elif(i==2):
                            students_with_out_choice.remove(student)
                            break

print(results)

Answer

One problem in your code could be that you are changing a list (students_with_out_choice) while iterating over it. This often leads to unexpected results.

As @enke has pointed out, the deferred acceptance algorithm is the method of choice here. An implementation of this algorithm could look something like this with your example:

s = {
    'A': ['CNM', 'DSI', 'RSS'],
    'B': ['CNM', 'DSI', 'RSS'],
    'C': ['DSI', 'CNM', 'RSS'],
    'D': ['DSI', 'RSS', 'CNM'],
    'E': ['RSS', 'DSI', 'CNM'],
    'F': ['RSS', 'CNM', 'DSI']
}

r = {
    'DSI': ['C', 'E', 'D', 'B', 'F', 'A'],
    'RSS': ['B', 'F', 'A', 'E', 'D', 'C'],
    'CNM': ['A', 'B', 'C', 'D', 'E', 'F']
}

p = {
    'DSI': 2,
    'RSS': 2,
    'CNM': 1
}


def get_matched_students(students, rankings, places):

    waiting_students = [student for student in students]
    matching_results = {choice: [] for choice in places}

    def get_waiting_list_without_student(student):
        return [x for x in waiting_students if x != student]

    def get_sorted_results_with_student(student, choice):
        matching_results[choice].append(student)
        return [x for x in rankings[choice] if x in matching_results[choice]]

    while waiting_students:
        for student in waiting_students.copy():
            if not students[student]:
                waiting_students = get_waiting_list_without_student(student)
                continue
            choice = students[student].pop(0)
            if len(matching_results[choice]) < places[choice]:
                matching_results[choice] = get_sorted_results_with_student(student, choice)
                waiting_students = get_waiting_list_without_student(student)
            else:
                if rankings[choice].index(student) < rankings[choice].index(matching_results[choice][-1]):
                    matching_results[choice] = get_sorted_results_with_student(student, choice)
                    waiting_students = get_waiting_list_without_student(student)
                    waiting_students.append(matching_results[choice].pop())

    return matching_results


print(get_matched_students(s, r, p))

This will give you the lists of students that have been matched to each subject: {'DSI': ['C', 'E'], 'RSS': ['B', 'F'], 'CNM': ['A']}

If you want to see the results from the student’s perspective, you can do something like this:

results = get_matched_students(s, r, p)

results_by_students = [[student, course] for student in s for course, result in results.items() if student in result]

print(results_by_students)

# Output: [['A', 'CNM'], ['B', 'RSS'], ['C', 'DSI'], ['E', 'DSI'], ['F', 'RSS']]