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#!/usr/bin/env python
# The gale_shapley implementation is taken from
# https://johnlekberg.com/blog/2020-08-22-stable-matching.html
from collections import deque
# Track the number of total proposals per proposer for order O questions
number_of_proposals = dict()
def pref_to_rank(pref):
return {a: {b: idx for idx, b in enumerate(a_pref)} for a, a_pref in pref.items()}
def gale_shapley(*, A, B, A_pref, B_pref):
"""Create a stable matching using the
Gale-Shapley algorithm.
A -- set[str].
B -- set[str].
A_pref -- dict[str, list[str]].
B_pref -- dict[str, list[str]].
Output: list of (a, b) pairs.
"""
B_rank = pref_to_rank(B_pref)
ask_list = {a: deque(bs) for a, bs in A_pref.items()}
pair = {}
remaining_A = set(A)
while len(remaining_A) > 0:
a = remaining_A.pop()
b = ask_list[a].popleft()
if b not in pair:
pair[b] = a
print(f"Matching {a} with {b} (a)")
number_of_proposals[a] += 1
else:
a0 = pair[b]
b_prefer_a0 = B_rank[b][a0] < B_rank[b][a]
if b_prefer_a0:
remaining_A.add(a)
print(f"{a} is rejected by {b} because {a0} is more preffered (c)")
number_of_proposals[a] += 1
else:
remaining_A.add(a0)
print(f"Matching {a} with {b}, {a0} is now free (b)")
number_of_proposals[a] += 1
pair[b] = a
return [(a, b) for b, a in pair.items()]
if __name__ == "__main__":
women = list(range(1, 27))
men = [chr(x + 65) for x in range(26)]
n = int(input("n: "))
men = men[:n]
# because algorithms are 1 indexed, compromise
women = ["0"] + women[:n]
men_pref = dict()
women_pref = dict()
# For 1 to n-1, men's preference lists look like
# Mk = Wk Wk+1 ... Wn-1 W1 W2 ... Wn
for (cur, m) in enumerate(men, start=1):
# last man n has the same preference list as n-1
if cur == n:
cur = cur - 1
prefs = list()
k = cur
# Wk .. Wn-1
while k < n:
prefs.append(women[k])
k += 1
# W1 .. Wn-1
k = 1
while k < cur:
prefs.append(women[k])
k += 1
# last woman n is always last at everyone's preference list
prefs.append(women[n])
men_pref[m] = prefs
# women's preference list for 1-n-2 look like
# Wk = Wk+1 Wk
# n-1 looks like
# Wn-1 = W1 Wn
# last women's preference list doesn't matter
for (cur, w) in enumerate(women, start=-1):
prefs = list()
# again, compromise between 1 indexed algorithms and nice code
if cur == -1:
continue
# last woman
if cur == n - 1:
k = 0
while k < n:
prefs.append(men[k])
k += 1
women_pref[w] = prefs
continue
# n-1th woman
if cur == n - 2:
prefs.append(men[0])
prefs.append(men[n - 1])
k = 0
while k < n:
if k == n - 1:
k += 1
continue
if k == 0:
k += 1
continue
prefs.append(men[k])
k += 1
women_pref[w] = prefs
continue
# rest of the women obey the general rule
prefs.append(men[cur + 1])
prefs.append(men[cur])
# we need n - k more men to fill, they don't matter
k = 0
while k < n:
if k == cur:
k += 1
continue
if k == cur + 1:
k += 1
continue
prefs.append(men[k])
k += 1
women_pref[w] = prefs
print("Men Preference Table")
for (k,v) in men_pref.items():
print(f'{k:2}| {" ".join([str(x) for x in v])}')
print("----")
print("Women Preference Table")
for (k,v) in women_pref.items():
print(f'{k:2}| {" ".join(v)}')
print("----")
number_of_proposals = {a: 0 for a in men}
matchings= gale_shapley(A=men, B=women, A_pref=men_pref, B_pref=women_pref)
print(f"Final pairings:")
for (m,w) in matchings:
print(f"{m} - {w}")
print()
total = 0
for (men, times) in number_of_proposals.items():
total += times
print(f"{men} proposed {times} times")
print(f"total of {total} times with n(n-1) + 1 = {n*(n-1) + 1}")
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