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|
<!DOCTYPE html>
<html>
<head>
<title>Well-Ordered</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="stylesheet" type="text/css" href="/well-ordered/static/styles.css">
<link rel="shortcut icon" type="image/x-icon" href="/well-ordered/static/favicon.ico">
</head>
<body>
<div class="container">
<div>
<a href="/" class="title">Well-Ordered</a><span>@</span><a href="https://cyfraeviolae.org">cyfraeviolae.org</a>
<span class="sep">|</span>
<a href="https://cyfraeviolae.org/git/well-ordered">source code</a>
</div>
<p>
The bibulous sorcerer Roseacrucis has depleted our distilled reserves. You must journey to obtain the
myriad ingredients necessary to recreate the seventy-seven official IBA cocktails—but your wallet runs
light, and your thirst grows deep. In what order do you obtain ingredients to make the most
drinks for the fewest drachma?
</p>
<noscript>Sorry, JavaScript is required to run Well-Ordered.</noscript>
<div id="form">
<form action="/" method="none">
<p>
Select any ingredients already owned or of negligible cost.
</p>
<div id="checkboxes">
<div class="ingredient">
<input type="checkbox" id="ingredient0" x-ingredient="0">
<label for="ingredient0">Absinthe</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient1" x-ingredient="1">
<label for="ingredient1">Angostura bitters</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient2" x-ingredient="2">
<label for="ingredient2">Aperol</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient3" x-ingredient="3">
<label for="ingredient3">Apricot brandy</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient4" x-ingredient="4">
<label for="ingredient4">Blackberry liqueur</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient5" x-ingredient="5">
<label for="ingredient5">Bourbon</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient6" x-ingredient="6">
<label for="ingredient6">Cachaca</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient7" x-ingredient="7">
<label for="ingredient7">Calvados</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient8" x-ingredient="8">
<label for="ingredient8">Campari</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient9" x-ingredient="9">
<label for="ingredient9">Champagne</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient10" x-ingredient="10">
<label for="ingredient10">Cherry liqueur</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient11" x-ingredient="11" checked>
<label for="ingredient11">Coconut milk</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient12" x-ingredient="12">
<label for="ingredient12">Coffee liqueur</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient13" x-ingredient="13">
<label for="ingredient13">Cognac</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient14" x-ingredient="14" checked>
<label for="ingredient14">Cola</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient15" x-ingredient="15" checked>
<label for="ingredient15">Cranberry juice</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient16" x-ingredient="16" checked>
<label for="ingredient16">Cream</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient17" x-ingredient="17">
<label for="ingredient17">Cream liqueur</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient18" x-ingredient="18">
<label for="ingredient18">Créme de Cacao</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient19" x-ingredient="19">
<label for="ingredient19">Créme de Cassis</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient20" x-ingredient="20">
<label for="ingredient20">Créme de Menthe</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient21" x-ingredient="21">
<label for="ingredient21">DOM Bénédictine</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient22" x-ingredient="22">
<label for="ingredient22">Dark rum</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient23" x-ingredient="23">
<label for="ingredient23">DiSaronno</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient24" x-ingredient="24">
<label for="ingredient24">Drambuie</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient25" x-ingredient="25">
<label for="ingredient25">Dry vermouth</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient26" x-ingredient="26">
<label for="ingredient26">Dry white wine</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient27" x-ingredient="27" checked>
<label for="ingredient27">Egg yolk</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient28" x-ingredient="28">
<label for="ingredient28">Galliano</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient29" x-ingredient="29">
<label for="ingredient29">Gin</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient30" x-ingredient="30" checked>
<label for="ingredient30">Ginger ale</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient31" x-ingredient="31" checked>
<label for="ingredient31">Ginger beer</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient32" x-ingredient="32" checked>
<label for="ingredient32">Grapefruit juice</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient33" x-ingredient="33">
<label for="ingredient33">Grenadine</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient34" x-ingredient="34" checked>
<label for="ingredient34">Hot coffee</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient35" x-ingredient="35">
<label for="ingredient35">Irish whiskey</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient36" x-ingredient="36">
<label for="ingredient36">Kirsch</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient37" x-ingredient="37" checked>
<label for="ingredient37">Lemon juice</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient38" x-ingredient="38">
<label for="ingredient38">Lillet Blonde</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient39" x-ingredient="39" checked>
<label for="ingredient39">Lime juice</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient40" x-ingredient="40">
<label for="ingredient40">Maraschino</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient41" x-ingredient="41" checked>
<label for="ingredient41">Olive juice</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient42" x-ingredient="42">
<label for="ingredient42">Orange bitters</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient43" x-ingredient="43">
<label for="ingredient43">Orange flower water</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient44" x-ingredient="44" checked>
<label for="ingredient44">Orange juice</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient45" x-ingredient="45">
<label for="ingredient45">Orgeat</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient46" x-ingredient="46">
<label for="ingredient46">Peach bitters</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient47" x-ingredient="47">
<label for="ingredient47">Peach puree</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient48" x-ingredient="48">
<label for="ingredient48">Peach schnapps</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient49" x-ingredient="49">
<label for="ingredient49">Peychaud's bitters</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient50" x-ingredient="50" checked>
<label for="ingredient50">Pineapple juice</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient51" x-ingredient="51">
<label for="ingredient51">Pisco</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient52" x-ingredient="52">
<label for="ingredient52">Prosecco</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient53" x-ingredient="53">
<label for="ingredient53">Raspberry liqueur</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient54" x-ingredient="54">
<label for="ingredient54">Raspberry syrup</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient55" x-ingredient="55">
<label for="ingredient55">Red Port</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient56" x-ingredient="56">
<label for="ingredient56">Rye</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient57" x-ingredient="57">
<label for="ingredient57">Scotch</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient58" x-ingredient="58" checked>
<label for="ingredient58">Soda water</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient59" x-ingredient="59">
<label for="ingredient59">Strawberry syrup</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient60" x-ingredient="60">
<label for="ingredient60">Sweet vermouth</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient61" x-ingredient="61" checked>
<label for="ingredient61">Syrup</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient62" x-ingredient="62">
<label for="ingredient62">Tequila</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient63" x-ingredient="63" checked>
<label for="ingredient63">Tomato juice</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient64" x-ingredient="64">
<label for="ingredient64">Triple Sec</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient65" x-ingredient="65">
<label for="ingredient65">Vodka</label>
</div>
<div class="ingredient">
<input type="checkbox" id="ingredient66" x-ingredient="66">
<label for="ingredient66">White rum</label>
</div>
</div>
<div>
<label for="limit">Time limit in seconds:</label>
<input id="limit" name="limit" type="number" value="60" min="10"></input>
</div>
<div>
<button type="submit" id="optimal">Compute ordering</button>
</div>
</form>
</div>
<div id="waiting"></div>
<div id="solution">
<p>The sample solution given the pre-selected ingredients:</p>
<ol>
<li>On-hand</li>
<li>
Vodka
<ul>
<li>Sea Breeze, Screwdriver, Bloody Mary, Moscow Mule</li>
</ul>
</li>
<li>
White rum
<ul>
<li>Mojito, Cuba Libre, Pina Colada, Daiquiri</li>
</ul>
</li>
<li>
Triple Sec
<ul>
<li>Lemon Drop Martini, Cosmopolitan, Kamikaze</li>
</ul>
</li>
<li>
Tequila
<ul>
<li>Margarita, Tommy's Margarita, Vampiro</li>
</ul>
</li>
<li>
Gin
<ul>
<li>Long Island Iced Tea, Gin Fizz, John Collins, White Lady</li>
</ul>
</li>
<li>
Cognac
<ul>
<li>Horse's Neck, Sidecar, Between the Sheets</li>
</ul>
</li>
<li>
Galliano
<ul>
<li>Yellow Bird, Golden Dream, Harvey Wallbanger</li>
</ul>
</li>
<li>
Grenadine
<ul>
<li>Bacardi, Tequila Sunrise</li>
</ul>
</li>
<li>
Cherry liqueur
<ul>
<li>Aviation, Mary Pickford, Hemingway Special</li>
</ul>
</li>
<li>
Bourbon
<ul>
<li>Whiskey Sour, Mint Julep</li>
</ul>
</li>
<li>
Dry vermouth
<ul>
<li>Dirty Martini, Dry Martini</li>
</ul>
</li>
<li>
Champagne
<ul>
<li>Mimosa, French 75</li>
</ul>
</li>
<li>
Angostura bitters
<ul>
<li>Old Fashioned, Champagne Cocktail</li>
</ul>
</li>
<li>
Dark rum
<ul>
<li>Planter's Punch, Dark 'n' Stormy</li>
</ul>
</li>
<li>
Coffee liqueur
<ul>
<li>Espresso Martini, Black Russian</li>
</ul>
</li>
<li>
DiSaronno
<ul>
<li>God Mother, French Connection</li>
</ul>
</li>
<li>
Créme de Cacao
<ul>
<li>Alexander</li>
</ul>
</li>
<li>
Créme de Menthe
<ul>
<li>Grasshopper, Stinger</li>
</ul>
</li>
<li>
Lillet Blonde
<ul>
<li>Vesper</li>
</ul>
</li>
<li>
Absinthe
<ul>
<li>Monkey Gland</li>
</ul>
</li>
<li>
Apricot brandy
<ul>
<li>Paradise</li>
</ul>
</li>
<li>
Pisco
<ul>
<li>Pisco Sour</li>
</ul>
</li>
<li>
Raspberry syrup
<ul>
<li>Clover Club</li>
</ul>
</li>
<li>
Orange bitters
<ul>
<li>Casino</li>
</ul>
</li>
<li>
Maraschino
<ul>
<li>Tuxedo</li>
</ul>
</li>
<li>
Red Port
<ul>
<li>Porto Flip</li>
</ul>
</li>
<li>
Scotch
<ul>
<li>God Father</li>
</ul>
</li>
<li>
Drambuie
<ul>
<li>Rusty Nail</li>
</ul>
</li>
<li>
Calvados
<ul>
<li>Angel Face</li>
</ul>
</li>
<li>
Prosecco
<ul>
<li>Barracuda</li>
</ul>
</li>
<li>
Peach puree
<ul>
<li>Bellini</li>
</ul>
</li>
<li>
Peach schnapps
<ul>
<li>Sex on the Beach</li>
</ul>
</li>
<li>
Cream liqueur
<ul>
<li>B52</li>
</ul>
</li>
<li>
Cachaca
<ul>
<li>Caipirinha</li>
</ul>
</li>
<li>
Raspberry liqueur
<ul>
<li>French Martini</li>
</ul>
</li>
<li>
Peach bitters
<ul>
<li>Derby</li>
</ul>
</li>
<li>
Aperol
<ul>
<li>Spritz Veneziano</li>
</ul>
</li>
<li>
Blackberry liqueur
<ul>
<li>Bramble</li>
</ul>
</li>
<li>Sweet vermouth</li>
<li>
Campari
<ul>
<li>Negroni, Americano</li>
</ul>
</li>
<li>
Rye
<ul>
<li>Manhattan</li>
</ul>
</li>
<li>
Orgeat
<ul>
<li>Mai-tai</li>
</ul>
</li>
<li>
Irish whiskey
<ul>
<li>Irish Coffee</li>
</ul>
</li>
<li>
DOM Bénédictine
<ul>
<li>Singapore Sling</li>
</ul>
</li>
<li>
Créme de Cassis
<ul>
<li>Russian Spring Punch</li>
</ul>
</li>
<li>
Peychaud's bitters
<ul>
<li>Sazerac</li>
</ul>
</li>
<li>
Orange flower water
<ul>
<li>Ramos Fizz</li>
</ul>
</li>
<li>
Dry white wine
<ul>
<li>Kir</li>
</ul>
</li>
<li>Kirsch</li>
<li>
Strawberry syrup
<ul>
<li>Rose</li>
</ul>
</li>
</ol>
</div>
<details>
<summary>Explain.</summary>
<p>
A recipe is a set of ingredients. The well-ordering problem: given
a set of recipes \(r_1\ldots{}r_m\) comprised of ingredients
\(y_1\ldots{}y_n\), find an ordering \(\sigma\) of the ingredients that maximizes
\[ \large\sum_{i=1}^{n}\sum_{j=1}^{m} p_\sigma(i, j) \]
where
\[ \large p_\sigma(i, j) = \begin{cases}
1 & r_j \subseteq \{y_{\sigma^{-1}(k)} \mid 1 \leq k \leq i\} \\
0 & \mathrm{otherwise.}
\end{cases} \]
</p>
<p>
In other words, we assign one point to each recipe in each round it is satisfiable by the already-collected
ingredients. We reduce the well-ordering problem to integer linear programming:
</p>
<p>
\[
\large
\begin{equation}
\begin{split}
\text{maximize } & \sum_{k=1}^n\sum_{j=1}^m v_{k,j} \\
\text{subject to } &
\begin{aligned}[t]
\sum_{i=0}^{n}c_{k, i} &= k & k \in [1, n] \\
c_{k,i} &\le c_{k+1, i} & i \in [1, n], k \in [1, n-1] \\
v_{k,j} &\ge -\lvert{}r_j\rvert + 1 + \sum_{i \in r_j}c_{k,i} & k \in [1, n], j \in [1, m] \\
v_{k,j} &\le c_{k,i} & k \in [1, n], j \in [1, m], i \in r_j \\
\end{aligned} \\
\text{binary } &
\begin{aligned}[t]
v_{k,j} & & k \in [1, n], j \in [1, m] \\
c_{k,i} & & k \in [1, n], i \in [1, n] \\
\end{aligned} \\
\end{split}
\end{equation}
\]
</p>
<p>
\(c_{k,i}\) is set when \(y_i\) is collected in rounds 1 through \(k\). \(v_{k,j}\) is set if \(r_j\) is
satisfiable in round \(k\). The first and second constraints ensure exactly one ingredient is added in each
round. The third and fourth constraints model that \(v_{k,j} = \bigwedge\limits_{i \in r_j} c_{k,i}\).
</p>
<p>
The system is solved in-browser using <a href="https://github.com/jvail/glpk.js">jvail's port</a> of
<a href="https://www.gnu.org/software/glpk/">GLPK</a> to WebAssembly. Alternatively, COIN-OR's
<a href="https://projects.coin-or.org/Cbc">cbc</a> can find the optimal solution in under thirty seconds on
a desktop computer. Recipes adapted from
<a href="https://github.com/teijo/iba-cocktails">teijo/iba-cocktails</a>.
</p>
</details>
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