Hungarian method - 3 choices assignment - variable-assignment

Question

I have a question about the hungarian method for assigment problems.
In the examples I found from the hungarian method you have 1 to n prefereces.
So at the moment, we have in the school the task to create a programm where you have a school class (1 to n students). The students take exactly ONE gift to the class. So (1 to amount of students )
After that every student hast exactly three CHOICES(to pick one gift, e.g. gift 1, gift 5, gift 9) and our programm is supossed to output the best assignment for the class.
But as mentioned before the examples we found about the hungarian methods have 1- to n preferences. And we need exactly three.
How would we solve this specific task ?
Is the hungarian method still the best way to solve this task or should we look at another algorithm ?

Answer 1

I just saw your last question get closed without an answer.
I've implemented a practical way to solve this problem in C#, assuming the wishes are given in a csv file of the following format:
2,10,6
2,7,3
4,7,1
...
The number of columns, i.e. the number of preferences, doesn't matter for my implementation.
Obviously, there's room for performance improvements, but I chose to keep it more readable for the sake of the answer.
Here are the classes used in the code below:
public class Student
{
public int StudentNumber { get; set; }
public List<WishVote> WishVotes { get; set; }
}
public class WishVote
{
public int WishNumber { get; set; }
public int Order { get; set; }
public string Id { get; set; }
}
public class WishVoteResult
{
public int WishNumber { get; set; }
// wish order
// vote count for that order
// wish number
public List<Tuple<int, int, int>> Assignments { get; set; }
public int TotalVoteCount { get; set; }
}
And here is the code you could run in Main to output the wishes' numbers alongside the total number of votes in descending order:
var lines = File.ReadAllLines("wishes.csv").ToList();
int studentNumber = lines.Count;
var students = new List<Student>();
int currentLine = 0;
lines.ForEach(l =>
{
currentLine++;
var wishVotes = new List<WishVote>();
int wishOrder = 0;
l.Split(',').ToList().ForEach(w =>
{
wishOrder++;
wishVotes.Add(new WishVote
{
Id = Guid.NewGuid().ToString(),
Order = wishOrder,
WishNumber = Convert.ToInt32(w)
});
});
students.Add(new Student
{
StudentNumber = currentLine,
WishVotes = wishVotes
});
});
var allWishVotes = students.SelectMany(s => s.WishVotes).ToList();
List<int> uniqueWishes = allWishVotes.Select(w => w.WishNumber).Distinct().ToList();
var wishVoteResults = new List<WishVoteResult>();
// assuming every row in the file has the same number of columns
int orderCount = students.First().WishVotes.Max(w => w.Order);
uniqueWishes.ForEach(uw =>
{
var wishVoteResult = new WishVoteResult
{
WishNumber = uw,
TotalVoteCount = allWishVotes.Where(w => w.WishNumber == uw).Count(),
Assignments = new List<Tuple<int, int, int>>()
};
for(int i = 1; i <= orderCount; i++)
{
wishVoteResult.Assignments.Add(new Tuple<int, int, int>(i, allWishVotes.Where(w => w.Order == i && w.WishNumber == uw).Count(), uw));
}
wishVoteResults.Add(wishVoteResult);
});
var assignments = wishVoteResults.SelectMany(w => w.Assignments).OrderByDescending(a => a.Item2).ThenBy(a => a.Item1).ToList();
Console.WriteLine("Wish {wishNumber}: {voteCount} {wishOrder}");
foreach (var assignment in assignments)
{
Console.WriteLine($"Wish number {assignment.Item3}: {assignment.Item2} {assignment.Item1}");
}
Console.WriteLine("Finished.");
Effectively, what we're doing is creating all the possible assignments and then just sorting accordingly.