mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 05:39:30 +00:00
61eedc16c3
* refactor: Fix matrix display deprecation * refactor: Remove useless `print` and `pass` statements * revert: Replace broken doctests * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * revert: Fix failing doctests * chore: Satisfy pre-commit Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
50 lines
1.9 KiB
Python
50 lines
1.9 KiB
Python
from __future__ import annotations
|
|
|
|
|
|
def stable_matching(
|
|
donor_pref: list[list[int]], recipient_pref: list[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]]
|
|
>>> 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
|