Gale Shapley Algorithm

graphs/gale_shapley_bigraph.py

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+def stable_matching(n: int, men_preferences: list, women_preferences: list) -> list:
+    '''
+    Finds the stable match in any bipartite graph, i.e a pairing where no 2 objects prefer each other over their partner.
+    Here marriage is used to make the variable names easier and so the algorithm can be intuitively understood.
+    The function accepts the preferences of the men and women (where both are named from 0 to n-1) and returns a list where index
+    position corresponds to the man and value at the index is the woman he is marrying.
+    E.g:
+    n = 4
+    men_preferences = [[0, 1, 3, 2], [0, 2, 3, 1], [1, 0, 2, 3], [0, 3, 1, 2]]
+    women_preferences = [[3, 1, 2, 0], [3, 1, 0, 2], [0, 3, 1, 2], [1, 0, 3, 2]]
+    >>>print(stable_matching(n,men_preferences,women_preferences))
+    [1,2,3,0]
+    P.S: Marriages are heterosexual since it is a bipartite graph where there must be 2 distinct sets of objects to be matched - i.e
+    patients and organ donors.
+    To better understand the algorithm, see also:
+    https://github.com/akashvshroff/Gale_Shapley_Stable_Matching (Detailed README).
+    https://www.youtube.com/watch?v=Qcv1IqHWAzg&t=13s (Numberphile YouTube Video).
+    '''
+    unmarried_men = [i for i in range(n)]
+    man_spouse = [None for i in range(n)]
+    woman_spouse = [None for i in range(n)]
+    num_proposals = [0 for i in range(n)]
+    while unmarried_men:
+        man = unmarried_men[0]
+        his_preferences = men_preferences[man]
+        woman = his_preferences[num_proposals[man]]
+        num_proposals[man] += 1
+        her_preferences = women_preferences[woman]
+        husb = woman_spouse[woman]
+        if husb != None:
+            if her_preferences.index(husb) > her_preferences.index(man):
+                woman_spouse[woman], man_spouse[man] = man, woman
+                unmarried_men.append(husb)
+                unmarried_men.remove(man)
+        else:
+            woman_spouse[woman], man_spouse[man] = man, woman
+            unmarried_men.remove(man)
+    return man_spouse