mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
25d9d819a2
* 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
|
|
|
|
|
|
def stable_matching(donor_pref: List[int], recipient_pref: List[int]) -> List[int]:
|
|
"""
|
|
Finds the stable match in any bipartite graph, i.e a pairing where no 2 objects
|
|
prefer each other over their partner. The function accepts the preferences of
|
|
oegan donors and recipients (where both are assigned numbers from 0 to n-1) and
|
|
returns a list where the index position corresponds to the donor and value at the
|
|
index is the organ recipient.
|
|
|
|
To better understand the algorithm, see also:
|
|
https://github.com/akashvshroff/Gale_Shapley_Stable_Matching (README).
|
|
https://www.youtube.com/watch?v=Qcv1IqHWAzg&t=13s (Numberphile YouTube).
|
|
|
|
>>> donor_pref = [[0, 1, 3, 2], [0, 2, 3, 1], [1, 0, 2, 3], [0, 3, 1, 2]]
|
|
>>> recipient_pref = [[3, 1, 2, 0], [3, 1, 0, 2], [0, 3, 1, 2], [1, 0, 3, 2]]
|
|
>>> print(stable_matching(donor_pref, recipient_pref))
|
|
[1, 2, 3, 0]
|
|
"""
|
|
assert len(donor_pref) == len(recipient_pref)
|
|
n = len(donor_pref)
|
|
unmatched_donors = list(range(n))
|
|
donor_record = [-1] * n # who the donor has donated to
|
|
rec_record = [-1] * n # who the recipient has received from
|
|
num_donations = [0] * n
|
|
while unmatched_donors:
|
|
donor = unmatched_donors[0]
|
|
donor_preference = donor_pref[donor]
|
|
recipient = donor_preference[num_donations[donor]]
|
|
num_donations[donor] += 1
|
|
rec_preference = recipient_pref[recipient]
|
|
prev_donor = rec_record[recipient]
|
|
if prev_donor != -1:
|
|
if rec_preference.index(prev_donor) > rec_preference.index(donor):
|
|
rec_record[recipient] = donor
|
|
donor_record[donor] = recipient
|
|
unmatched_donors.append(prev_donor)
|
|
unmatched_donors.remove(donor)
|
|
else:
|
|
rec_record[recipient] = donor
|
|
donor_record[donor] = recipient
|
|
unmatched_donors.remove(donor)
|
|
return donor_record
|