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I am wanting to write the Gale-Shapely algorithm in python which can deal with an uneven number of pairings (i.e. more men than woman or more woman than men). The outcome should be the same number of stable matches as the lesser number of men and woman and any left over just do not match. The way in which I have currently implemented it works if number of woman>number of men, but if number of men>number of woman then this produces as infinite loop as the list of 'freeMen' is never empty and the while loop will iterate infinitely. I am struggling to work out how to implement this correctly. Code is below with two lists arguments first comprising a key for each man and values of preferred woman in order and vice versa for the second argument:

def gale_shapely_matching(men_preferences, woman_preferences):

    #create array to store the tempory pairings whilst iterating through matchings
    temporyMatches = []
    #create list of the free men
    freeMen = [user for user in list(men_preferences.keys())]

    #while loop to iterate while the freeMen array is not empty
    while len(freeMen)>0:
        for man in freeMen:
            for woman in man_preferences[man]:
                takenMatch=[match for match in temporyMatches if woman in match]

                if takenMatch:

                    #check if the the potential new matched man ranks higher in the womans preference (is a lower index). If man is higher preference amend match so as new man replaces previous match
                    if potential_new_match < current_match:
                        takenMatch[0][0] = man
                    temporyMatches.append([man, woman])
    return temporyMatches

What I have tried:

I have tried adding a list of freeWoman which can be removed from and changing the while loop so as it is while freeMen>0 and freeWoman>0, but not sure how to implement this to have the algorithm run as expected
Updated 9-Aug-22 8:07am

1 solution

Getting it to run does not mean your code is right! :laugh:
Think of the development process as writing an email: compiling successfully means that you wrote the email in the right language - English, rather than German for example - not that the email contained the message you wanted to send.

So now you enter the second stage of development (in reality it's the fourth or fifth, but you'll come to the earlier stages later): Testing and Debugging.

Start by looking at what it does do, and how that differs from what you wanted. This is important, because it give you information as to why it's doing it. For example, if a program is intended to let the user enter a number and it doubles it and prints the answer, then if the input / output was like this:
Input   Expected output    Actual output
  1            2                 1
  2            4                 4
  3            6                 9
  4            8                16
Then it's fairly obvious that the problem is with the bit which doubles it - it's not adding itself to itself, or multiplying it by 2, it's multiplying it by itself and returning the square of the input.
So with that, you can look at the code and it's obvious that it's somewhere here:
int Double(int value)
   return value * value;

Once you have an idea what might be going wrong, start using the debugger to find out why. Put a breakpoint on the first line of the method, and run your app. When it reaches the breakpoint, the debugger will stop, and hand control over to you. You can now run your code line-by-line (called "single stepping") and look at (or even change) variable contents as necessary (heck, you can even change the code and try again if you need to).
Think about what each line in the code should do before you execute it, and compare that to what it actually did when you use the "Step over" button to execute each line in turn. Did it do what you expect? If so, move on to the next line.
If not, why not? How does it differ?
Hopefully, that should help you locate which part of that code has a problem, and what the problem is.
This is a skill, and it's one which is well worth developing as it helps you in the real world as well as in development. And like all skills, it only improves by use!
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