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* Gale Shapley Algorithm Implementation of a Nobel prize-winning algorithm that determines a stable matching in a bipartite graph. * Update graphs/gale_shapley_bigraph.py Co-authored-by: Christian Clauss <cclauss@me.com> * Fixed some flake8 issues. * Updated it to donors and recipients * description changes Co-authored-by: Christian Clauss <cclauss@me.com> * description changes Co-authored-by: Christian Clauss <cclauss@me.com> * description changes Co-authored-by: Christian Clauss <cclauss@me.com> * Edited the line lengths * Update gale_shapley_bigraph.py * Update gale_shapley_bigraph.py Co-authored-by: Christian Clauss <cclauss@me.com>
45 lines
1.9 KiB
Python
45 lines
1.9 KiB
Python
from typing import List
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def stable_matching(donor_pref: List[int], recipient_pref: List[int]) -> List[int]:
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"""
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Finds the stable match in any bipartite graph, i.e a pairing where no 2 objects
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prefer each other over their partner. The function accepts the preferences of
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oegan donors and recipients (where both are assigned numbers from 0 to n-1) and
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returns a list where the index position corresponds to the donor and value at the
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index is the organ recipient.
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To better understand the algorithm, see also:
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https://github.com/akashvshroff/Gale_Shapley_Stable_Matching (README).
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https://www.youtube.com/watch?v=Qcv1IqHWAzg&t=13s (Numberphile YouTube).
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>>> donor_pref = [[0, 1, 3, 2], [0, 2, 3, 1], [1, 0, 2, 3], [0, 3, 1, 2]]
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>>> recipient_pref = [[3, 1, 2, 0], [3, 1, 0, 2], [0, 3, 1, 2], [1, 0, 3, 2]]
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>>> print(stable_matching(donor_pref, recipient_pref))
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[1, 2, 3, 0]
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"""
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assert len(donor_pref) == len(recipient_pref)
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n = len(donor_pref)
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unmatched_donors = list(range(n))
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donor_record = [-1] * n # who the donor has donated to
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rec_record = [-1] * n # who the recipient has received from
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num_donations = [0] * n
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while unmatched_donors:
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donor = unmatched_donors[0]
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donor_preference = donor_pref[donor]
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recipient = donor_preference[num_donations[donor]]
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num_donations[donor] += 1
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rec_preference = recipient_pref[recipient]
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prev_donor = rec_record[recipient]
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if prev_donor != -1:
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if rec_preference.index(prev_donor) > rec_preference.index(donor):
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rec_record[recipient] = donor
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donor_record[donor] = recipient
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unmatched_donors.append(prev_donor)
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unmatched_donors.remove(donor)
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else:
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rec_record[recipient] = donor
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donor_record[donor] = recipient
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unmatched_donors.remove(donor)
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return donor_record
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