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queue 04 OCI
stack 04 Oci
linked list 047 OCI
keep an array N
t where
NextCm points to thepositions ofthe next woman he will beproposigto
on his pref Est
Man Pref m NextEMT
I
takes 04
keep an array
called currentG n
where current w is No11 if w issingle
setto w is engaged to me
takes 0 i
womanPrep t
12 34502
womanRanting
2 3 5 6
Men’s ID’s
A
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G.si enatais overall
OCn2 0Cn2
1
w
E
infavor
of m
5 To
i r
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l
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Discussion 1
1. Prove that every execution of the G-S algorithm (when men are proposing) results in the
same stable matching regardless of the order in which men propose.
2. Prove that when we run the G-S algorithm with men proposing, women end up with their
worst valid partners.
3. True or False:
In every stable matching that Gale–Shapley algorithm may end up with when men propose,
there is a man who is matched to his highest-ranked woman.
4. In a connected bipartite graph, is the bipartition unique? Justify your answer.