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slides/cse662fa2018/2018-08-31-FunctionalDS.html
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<!doctype html>
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<html lang="en">
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<head>
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<meta charset="utf-8">
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<title>CSE 662 - Languages and Runtimes for Big Data</title>
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<meta name="description" content="Material for the University at Buffalo's CSE-662 'Languages and Runtimes for Big Data'">
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<meta name="author" content="Oliver Kennedy">
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<div class="reveal">
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<!-- Any section element inside of this container is displayed as a slide -->
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<div class="slides">
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<section>
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<section>
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<h2>Functional Data Structures</h2>
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</section>
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<section>
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<h3>Reminder</h3>
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<p>Learned Index Structures due Weds (in class)</p>
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<p>One person from each group should email me...<ul>
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<li>[CSE-662] in the subject line</li>
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<li>A list of group members (Names + UBITs)</li>
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<li>The project seed that your group would like to work on</li>
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</ul></p>
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</section>
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</section>
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<section>
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<section>
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<p><span class="fragment highlight-red">Mutable</span> vs Immutable Data</p>
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</section>
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<section>
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<pre><code>
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X = [ "Alice", "Bob", "Carol", "Dave" ]
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</code></pre>
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<table class="fragment">
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<tr>
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<td style="font-size: 120%; font-weight: bold; font-family: fixed">X : </td>
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<td style="border-style: solid; border-width: 5px;">Alice</td>
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<td style="border-style: solid; border-width: 5px;">Bob</td>
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<td style="border-style: solid; border-width: 5px;">Carol</td>
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<td style="border-style: solid; border-width: 5px;">Dave</td>
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</tr>
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</table>
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<pre><code class="fragment">
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print(X[2]) // -> "Carol"
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</code></pre>
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<pre><code class="fragment">
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X[2] = "Eve"
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</code></pre>
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<table class="fragment">
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<tr>
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<td style="font-size: 120%; font-weight: bold; font-family: fixed">X : </td>
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<td style="border-style: solid; border-width: 5px;">Alice</td>
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<td style="border-style: solid; border-width: 5px;">Bob</td>
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<td style="border-style: solid; border-width: 5px; color: white; border-color: white">Eve</td>
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<td style="border-style: solid; border-width: 5px;">Dave</td>
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</tr>
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</table>
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<pre><code class="fragment">
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print(X[2]) // -> "Eve"
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</code></pre>
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</section>
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<section>
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<pre><code>
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X = [ Alice, Bob, Carol, Dave ]
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</code></pre>
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<table>
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<tr>
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<td style="font-size: 120%; font-weight: bold; font-family: fixed">X : </td>
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<td style="border-style: solid; border-width: 5px;">Alice</td>
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<td style="border-style: solid; border-width: 5px;">Bob</td>
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<td style="border-style: solid; border-width: 5px;">Carol</td>
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<td style="border-style: solid; border-width: 5px;">Dave</td>
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</tr>
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</table>
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<table style="margin-top: 80px">
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<thead class="fragment">
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<th style="width: 300px; text-align: center;">Thread 1</th>
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<th style="width: 300px; text-align: center;">Thread 2</th>
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</thead>
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<tr>
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<td><pre><code>
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X[2] = "Eve"
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</code></pre></td>
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<td><pre><code>
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print(X[2])
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</code></pre></td>
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</tr>
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<tr class="fragment"><td></td><td style="font-size: 300%;text-align: center">🤔</td></tr>
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</table>
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</section>
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<section>
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<h3>Mutable Data Structures</h3>
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<ul>
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<li class="fragment">The programmer's intended ordering is unclear.</li>
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<li class="fragment">Atomicity/Correctness requires locking.</li>
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<li class="fragment">Versioning requires copying the data structure.</li>
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<li class="fragment">Cache coherency is expensive.</li>
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</ul>
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<p style="font-weight: bold; margin-top: 50px;" class="fragment">Can these problems be avoided?</p>
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</section>
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</section>
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<section>
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<section>
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<p>Mutable vs <span class="fragment highlight-red">Immutable Data</span></p>
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</section>
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<section>
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<pre><code>
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X = [ "Alice", "Bob", "Carol", "Dave" ]
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</code></pre>
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<table>
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<tr>
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<td style="font-size: 120%; font-weight: bold; font-family: fixed">X : </td>
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<td style="border-style: solid; border-width: 5px;">Alice</td>
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<td style="border-style: solid; border-width: 5px;">Bob</td>
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<td style="border-style: solid; border-width: 5px;">Carol</td>
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<td style="border-style: solid; border-width: 5px;">Dave</td>
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</tr>
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</table>
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<pre><code class="fragment" data-fragment-index="1">
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print(X[2]) // -> "Carol"
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</code></pre>
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<pre><code class="fragment fade-in-then-semi-out" data-fragment-index="1">
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X[2] = "Eve"
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</code></pre>
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<p style="font-weight: bold; margin-top: 50px;" class="fragment">Don't allow writes!</p>
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<p style="font-weight: bold; margin-top: 50px;" class="fragment">But what if we need to update the structure?</p>
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</section>
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<section>
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<h3>Idea 1: Copy</h3>
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<table>
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<tr>
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<td style="font-size: 120%; font-weight: bold; font-family: fixed">X : </td>
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<td>Alice</td>
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<td>Bob</td>
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<td>Carol</td>
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<td>Dave</td>
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</tr>
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</table>
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<table>
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<tr>
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<td style="font-size: 120%; font-weight: bold; font-family: fixed">X' : </td>
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<td class="fragment">Alice</td>
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<td class="fragment">Bob</td>
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<td class="fragment">Eve</td>
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<td class="fragment">Dave</td>
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</tr>
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</table>
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<p style="font-weight: bold; margin-top: 50px;" class="fragment">Slooooooooooooooooooooooow!</p>
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</section>
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<section>
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<h3>Idea 2: Break it Down</h3>
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<svg data-src="graphics/2018-08-31-FunctionalTreeInsertion.svg" height="500px" style="background-color: lightgrey;" />
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<p class="fragment">Data is always added, not replaced!</p>
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</section>
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<section>
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<h4>Immutable Data Structures
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<div style="font-size: 50%">(aka 'Functional' or 'Persistent' Data Structures)</div></h4>
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<ul>
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<li class="fragment">Once an object is created it never changes.</li>
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<li class="fragment">The object persists until all pointers to it go away, at which point it is garbage collected.</li>
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<li class="fragment">Only the "root" pointer is ever allowed to change, to point to a new version.</li>
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</ul>
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</section>
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</section>
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<section>
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<section>
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<h2>Linked List Stacks</h2>
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</section>
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<section>
|
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<svg data-src="graphics/2018-08-31-FunctionalStack.svg" width="796px" height="493px" style="background-color: lightgrey;" stretch/>
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</section>
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</section>
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<section>
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<section>
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<h2>Class Exercise 1</h2>
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<p>How would you implement:</p>
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<pre><code>
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list update(list, index, new_value)
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</code></pre>
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</section>
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<section>
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<h2>Class Exercise 2</h2>
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<p>Implement a set with:</p>
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<pre><code>
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set init()
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boolean is_member(set, elem)
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set insert(set, elem)
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</code></pre>
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</section>
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</section>
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<section>
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<section>
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<h3 class="fragment" data-fragment-index="2">Lazy Evaluation</h3>
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<img src="graphics/2018-08-31-FunctionalStackMerge.svg" style="background-color: lightgrey" />
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<p class="fragment" data-fragment-index="1">Can we do better?</p>
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</section>
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<section>
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<h3>Putting off Work</h3>
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<table>
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<tr>
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<td style="vertical-align: middle; font-size: 150%;"><pre>x = "expensive()"</pre></td>
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<td class="fragment" style="text-align: center;">Fast<br/>(Just saving a 'todo')</td>
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</tr>
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<tr>
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<td style="vertical-align: middle; font-size: 150%;"><pre>print(x)</pre></td>
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<td class="fragment" style="text-align: center;">Slow<br/>(Performing the 'todo')</td>
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</tr>
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<tr>
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<td style="vertical-align: middle; font-size: 150%;"><pre>print(x)</pre></td>
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<td class="fragment" style="text-align: center;">Fast<br/>('todo' already done)</td>
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</tr>
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</table>
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</section>
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<section>
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<h2>Class Exercise 3</h2>
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<img src="graphics/2018-08-31-FunctionalStackMerge.svg" style="background-color: lightgrey" />
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<p>Make it better!</p>
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</section>
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<section>
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<h3>Putting off Work</h3>
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<pre><code>
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concatenate(a, b) {
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a', front = pop(a)
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if a' is empty {
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return (front, b)
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} else {
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return (front, "concatenate(a', b)")
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}
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}
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</code></pre>
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<p class="fragment">What is the time complexity of this concatenate?</p>
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<p class="fragment">What happens to reads?</p>
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</section>
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<section>
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<h3>Lazy Evaluation</h3>
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<p>Save work for later...
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<ul>
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<li>... and avoid work that is never requred.</li>
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<li>... to spread out work over multiple calls.</li>
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<li>... for better "amortized" costs.</li>
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</ul>
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</p>
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</section>
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</section>
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<section>
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<section>
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<h3>Amortized Analysis</h3>
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<p>Allow operation A to 'pay it forward' for another operation B that hasn't happened yet.</p>
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<p class="fragment">... or allow an operation B to 'borrow' from another operation A that hasn't happened yet.</p>
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<ul class="fragment">
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<li>A's time complexity goes up by X.</li>
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<li>B's time complexity goes down by X.</li>
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</ul>
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</section>
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<section>
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<h4>Example: Amortized Queues</h4>
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<img src="graphics/2018-08-31-AmortizedQueue.svg" style="background-color: lightgrey" height="600px" />
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</section>
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<section>
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<h4>Example: Amortized Queues</h4>
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<pre><code>
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queue enqueue(queue, item) {
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return {
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current : queue.current,
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todo : push(queue.todo, item)
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)
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}
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</code></pre>
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<p class="fragment">What is the cost?</p>
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</section>
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<section>
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<h4>Example: Amortized Queues</h4>
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<pre><code>
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queue dequeue(queue) {
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if(queue.current != NULL){
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return { current: pop(queue.current), todo: queue.todo }
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} else if(queue.todo != NULL) {
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return { current: reverse(queue.todo), todo: NULL }
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} else {
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return { current: NULL, todo: NULL }
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}
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}
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</code></pre>
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<p class="fragment">What is the cost?</p>
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</section>
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<section>
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<h4>Example: Amortized Analysis</h4>
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<dl>
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<dt class="fragment">enqueue(): Push onto todo stack</dt>
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<dd class="fragment">$O(1) + \text{create } 1 \text{ credit}$</dd>
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<dt class="fragment">dequeue(): Pop current OR Reverse todo </dt>
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<dd class="fragment">Either:<ul>
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<li>Pop current queue: <span class="fragment">$O(1)$</span></li>
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<li>Reverse stack: <span class="fragment">$O(1) + \text{consume } N \text{ credits}$</span></li>
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</ul>
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</dl>
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<p class="fragment">Critical requirement of amortized analysis: Must ensure that every credit consumed is created.</p>
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</section>
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</section>
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</div>
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slides/cse662fa2018/graphics/2018-08-31-AmortizedQueue.svg
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