Nirali Shah

Professor Evans

CS2102

Problem Set Ω

“5 Disney Princes”

To the tune of 5 Little Monkeys

5 Disney princes waiting to be wed,

Aladdin flew magic carpet,

And grabbed Jasmine’s hand.

Because she preferred him to wicked Jafar,

They tied the knot and rode afar.

4 Disney princes waiting to be wed,

In rides Prince Ferdinand,

to give true love’s kiss.

Matching with the dwarves? Not in her plan,

So Snow White won her royal man.

3 Disney princes waiting to be wed,

Prince Eric led his ship,

trying and trying to find his miss.

Her name was Ariel and her hair red,

The two left the sea witch gone and dead.

2 Disney princes waiting to be wed,
Prince Adam began with arrogance,

in his head.
Gaston loved Belle but Belle loved the beast,
They ended in love, to say the least.

1 Disney prince waiting to be wed,
Prince Philip fought Maleficent,

meeting Aurora at her bed.
They shared a magical love that broke the spell,
A classic fairytale in a nutshell.

No more Disney princes waiting to be wed!


Stable Matchings

Definition: M = {(a1, b1), (a2, b2), · · · , (an, bn)} is a stable matching between two sets A = {a1, · · · , an} and B = {b1, · · · , bn} with respective preference orderings ≺A and ≺B if there is no pair (ai , bj) where bi ≺ai bj and aj ≺bj ai.

Stable Matching Scenarios: According to the song “5 Disney Princes”, I will construct 2 scenarios of stable matching sets that will return the correct prince-princess matchings “M”, when passed through a Gale Shapley Algorithm (or other stable matching algorithm that takes in 2 sets of same cardinality).


Scenario #1:

This scenario matches each Disney prince with his respective Disney princess.

Sets:

A = Disney princes

B = Disney princesses

More specific sets:

A = {Aladdin, Ferdinand, Eric, Adam, Philip}

B = {Jasmine, Snow White, Ariel, Belle, Aurora}

M = {(Aladdin, Jasmine), (Ferdinand, Snow White), (Eric, Ariel), (Adam, Belle), (Philip, Aurora)}


Scenario #2:

This scenario matches each Disney princess by considering hypothetical alternate scenarios of the specific movie that the Disney prince and princess belong to.

Sets:

A1 = {Jasmine: [Aladdin, Jafar], Rajah: [Jafar, Aladdin]}

B1 = {Aladdin: [Jasmine, Rajah], Jafar: [Jasmine, Rajah]}

A2 = {Snow White: [Ferdinand, Dopey], The Queen: [Ferdinand, Dopey]}

B2 = {Ferdinand: [Snow White, The Queen], Dopey: [Snow White, The Queen]}

A3 = {Ariel: [Eric, Sebastian], Ursula: [Eric, Sebastian]}

B3 = {Eric: [Ariel, Ursula], Sebastian: [Ariel, Ursula]}

A4 = {Belle: [Adam, Gaston], Mrs.Potts: [Gaston, Adam]}

B4 = {Adam: [Belle, Mrs. Potts], Gaston: [Belle, Mrs. Potts]}

A5 = {Aurora: [Philip, Stefan], Maleficent: [Philip, Stefan]}

B5 = {Philip: [Aurora, Maleficent], Stefan: [Maleficent, Philip]}

M = {(Jasmine, Aladdin), (Snow White, Ferdinand), (Ariel, Eric), (Belle, Adam), (Aurora, Philip)}


Works Cited

"Kidsongs." Five Little Monkeys Lyrics. Together Again Video Productions Inc., n.d. Web. 05 Dec. 2016.

"List of Disney Princes." Disney Princess Wiki. Fandom Movies Community, n.d. Web. 05 Dec. 2016.