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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Slides</title>
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<section>
<h1>Data Structures & Ruby</h1>
<p>By</p>
<h2>Aarti Parikh</h2>
<aside class="notes">Introduction, background
</aside>
</section>
<section>
<h1>Why study DS?</h1>
<ol>
<li> Search, Organize and Manipulate information</li>
<li> Reduces complexity </li>
<li> Efficiency in solving algorithms </li>
</ol>
</section>
<section>
<aside class="notes">Data Structures are building blocks that enable us to search, organize and manipulate information so we can discover meaning and solve problems.
Maintainable code for complex problems
Picking the right ds can reduces complexity
</aside>
<h2>Terms, Definitions & Properties</h2>
<ol>
<li>Linear Vs Non Linear</li>
<li>Abstract Data type </li>
<li>Time, Space Complexity & Big O Notation </li>
<li>Ordering in a data structure</li>
<li>Mutable vs Immutable</li>
<li>Concurrent</li>
<li>Duplication </li>
</ol>
<p>Learn more <a href="http://xlinux.nist.gov/dads//">NIST- Official dictionary</a></p>
<aside class="notes">Linear Data structures, Arrays & Lists
Non Linear Data structures, Trees, Graphs
Abstract Data type is a Model: Functional definition of a DS
separate from its implementation, set of functions and
constraints.
Properties ( how they store data)
What is the run time of ( insert, search, read )
What is the space complexity to store
Is ther ordering
How does the ds deal with concurrency
Are duplicates allowed.
</aside>
</section>
<section>
<h2>Big (O) notation</h2>
<p>Growth rate of a function or a program</p>
<pre><code> # O(n)
a = [1..1000]
a.each { |n| print n}
</code></pre>
<pre><code> # O(n^2)
a,b = (1..10),(1..10)
a.each do |m|
b.each do |n|
p m*n
end
end
</code></pre>
<pre><code> # O(n!) All possible permuattions of a string
"ruby".chars.to_a.permutation.map &:join
=> ["ruby", "ruyb", "rbuy", "rbyu", "ryub", "rybu", "urby", "uryb", "ubry", "ubyr", "uyrb", "uybr", "bruy", "bryu", "bury", "buyr", "byru", "byur", "yrub", "yrbu", "yurb", "yubr", "ybru", "ybur"]
</code></pre>
<aside class="notes"> The letter O is used because the growth rate of a function is also referred to as order of the function.
Performance as data increases
Number of loops
</aside>
</section>
<section>
<h2>Big (O) continued</h2>
<p>Classic example <a href="http://rosettacode.org/wiki/Binary_search#Ruby">Binary Search</a> in sorted array</p>
<pre><code class="ruby"> # O(log(n))
class Array
def binary_search(val, low=0, high=(length - 1))
return nil if high < low
mid = (low + high) / 2
case
when self[mid] > val then binary_search(val, low, mid-1)
when self[mid] < val then binary_search(val, mid+1, high)
else mid
end
end
end
</code></pre>
<pre><code class="ruby"> # O(2^n) Recursive or Naive Fibonacci
def fibonacci(n)
n <= 1 ? n : fibonacci( n - 1 ) + fibonacci( n - 2 )
end
</code></pre>
</section>
<section>
<h2>Big(O) enables selection of DS</h2>
<ol>
<li>Insert</li>
<li>Search </li>
<li>Retrieve</li>
<li>Space Used</li>
</ol>
<p><a href="http://bigocheatsheet.com/">Handy Cheatsheet</a></p>
<aside class="notes">We look at big O properties of DS to determine the choice based on problem domain
</aside>
</section>
<section>
<h2>Common DS</h2>
<ul>
<li>Array</li>
<li>Hash, Bloom Filter</li>
<li>Stack, Queue, Dequeue</li>
<li>Linked Lists, Circular Buffers</li>
<li>Set, BitArray</li>
<li>Tree, Binary Search Tree, Heap, Trie</li>
<li>Graph</li>
</ul>
<aside class="notes">Grouped by properties, some of the one one we will look at
</aside>
</section>
<section>
<h2>DS in Ruby Core & Std</h2>
<ul>
<li>Array</li>
<li>Hash</li>
<li>Set, SortedSet</li>
<li>Matrix</li>
<li>Vector</li>
<li>Range </li>
</ul>
<aside class="notes">Not that many to choose from
</aside>
</section>
<section>
<h2>DS in Java</h2>
<p>Java Collections Framework</p>
<p><img src="./images/java-collections.png"></p>
<p>Extensive use of DS not in Java Core</p>
<ul>
<li>
<a href="http://commons.apache.org/proper/commons-collections/">Apache commons Collection</a><br>
</li>
<li><a href="https://code.google.com/p/google-collections/">Google Guave</a></li>
</ul>
<p>Enough DS to choose from that there is a <a href="http://www.sergiy.ca/guide-to-selecting-appropriate-map-collection-in-java/">flowchart</a> for selecting the right one. </p>
</section>
<section>
<h2>Why DS not as distinct in Ruby</h2>
<p>Ruby's API blends queues, stacks, sets, arrays and lists in a few classes, for a richer api.</p>
</section>
<section>
<h2>Array</h2>
<ul>
<li>Stack/Queue/Dequeue all in one</li>
<li>LIFO and FIFO methods</li>
<li>O(1) operations<br>
<ul>
<li>pop</li>
<li>shift</li>
</ul>
</li>
<li>Ruby's Array has more then <a href="https://github.com/ruby/ruby/blob/trunk/array.c#L5683">100</a> methods!</li>
<li><a href="http://anorwell.com/index.php?id=53">Performance benchmarks for Array</a></li>
</ul>
</section>
<section>
<h1>Hash</h1>
<ul>
<li>Key/Vaue Pair</li>
<li>O(1) insert, search, delete</li>
<li>Internally an array</li>
<li>Uses a hash function & division method to fit data into an array</li>
</ul>
<h2>How it works</h2>
<p><a href="http://www.gotealeaf.com/blog/how-the-hash-works-in-ruby">How the Hash works in Ruby</a></p>
<h2>How to implement one in Ruby</h2>
<p><a href="http://bigocheatsheet.com/">Hash implementation</a></p>
</section>
<section>
<h2>Implementing DS in Ruby</h2>
<ul>
<li>Understand Ruby API's and implementation better</li>
<li>A nice refresher/ academic exercise</li>
<li>Discover libraries</li>
</ul>
<p>Let's start </p>
</section>
<section>
<h2>Stack</h2>
<ul>
<li>FIFO</li>
<li>Operations supported
<ul>
<li>push</li>
<li>pop</li>
<li>peek</li>
</ul>
</li>
<li>Implementation varies
<ul>
<li>Array</li>
<li>LinkedList</li>
</ul>
</li>
</ul>
<p><a href="https://github.com/aarti/data-structures-ruby/blob/gh-pages/code/stack/stack.rb">Stack Implementation using Array as storage</a> </p>
</section>
<section>
<h2>Queue</h2>
<ul>
<li>LIFO</li>
<li>Operations supported
<ul>
<li>shift</li>
<li>unshift</li>
</ul>
</li>
<li>Implementation varies
<ul>
<li>Array</li>
<li>LinkedList</li>
</ul>
</li>
</ul>
<p><a href="http://www.java-samples.com/showtutorial.php?tutorialid=1125">Queue Implementation using Forwardable and delgates so Storage is again Array</a> </p>
</section>
<section>
<h2>Deque</h2>
<ul>
<li>Double ended Queue </li>
<li>LIFO & FIFO</li>
<li>Implementation with <a href="https://github.com/aarti/data-structures-ruby/blob/gh-pages/code/deque/deque.rb">storage as Linked List</a> </li>
</ul>
</section>
<section>
<h1>Set</h1>
<ul>
<li>Unordered elements</li>
<li>Distinct elements</li>
<li>Tests for membership/inclusion not necessarily retrieval</li>
<li>No set in Core till 1.9.3</li>
<li>MRI Ruby implemented as a Hash</li>
<li>Faster then [1,2,3].uniq! since it is just a Hash</li>
<li>No literal notation, use Set.new</li>
<li>The expected operations in a Set
-member?
-union |
-intersection &
-difference -
-xor ^</li>
<li>Used in rails for routing, caching etc.</li>
</ul>
</section>
<section>
<h1>SortedSet</h1>
<ul>
<li>Same properties of Set but ordered elements<br>
</li>
<li>MRI Ruby implements natively in C with a Red-Black Tree DS</li>
<li>Sets in Java are also implemented in a similiar way.
<ul>
<li>Java 's TreeSet ~ Ruby's SortedSet </li>
<li>Java 's HashSet ~ Set</li>
</ul>
</li>
</ul>
</section>
<section>
<h1>CustomSet</h1>
<ul>
<li>Internally stored as an array</li>
<li>Supports instantiation with any enumerable type</li>
<li>Includes Enumerable and implements <code>each</code> to get some methods for free</li>
<li>Return types should enable chaining</li>
<li>Return types should not allow access to internal DS.</li>
</ul>
<p><a href="https://github.com/aarti/data-structures-ruby/blob/gh-pages/code/set/custom_set.rb">Implementation</a></p>
</section>
<section>
<h1>MultiSet</h1>
<ul>
<li> members allowed to appear more than once.
<ul>
<li>
<code>{a, a, b}</code><br>
</li>
</ul>
</li>
<li>the order of elements is irrelevant: The multisets
<ul>
<li>{a, a, b} and {a, b, a} are equal.</li>
</ul>
</li>
<li>it provides the count or multiplicity of an element in the set.
<ul>
<li>
<code>count (a) = 2</code> </li>
</ul>
</li>
<li>it can return the distinct elements of the set.
<ul>
<li><code>{a, b}</code></li>
</ul>
</li>
<li>it returns the cardinality of the set, total number of elements including duplicates.<br>
<ul>
<li><code>6</code></li>
</ul>
</li>
</ul>
<p><a href="https://github.com/aarti/data-structures-ruby/blob/gh-pages/code/multiset/multiset.rb">Implementation</a></p>
</section>
<section>
<h1>BitArray</h1>
<ul>
<li>Set like DS, but dense packed bits</li>
<li>Implemented using an array as storage</li>
</ul>
<p><a href="https://github.com/aarti/data-structures-ruby/blob/gh-pages/code/bitarray/bit-array.rb">Implementation</a></p>
</section>
<section>
<h1>Bloom Filter</h1>
<ul>
<li>Check membership in a set</li>
<li>Always gives a right answer if element is not present</li>
<li>false positive if present</li>
<li>Great for disk I/O</li>
<li>Safe browsing</li>
<li>Mix of hash & Set</li>
<li>uses multiple hash functions to verify membership</li>
</ul>
</section>
<section>
<h1>LinkedList</h1>
<ul>
<li><p>No LinkedList in Ruby</p></li>
<li><p>Unshift is expensive in Ruby, adding elements to end of list is cheaper</p></li>
<li><p><a href="http://www.sitepoint.com/rubys-missing-data-structure/">http://www.sitepoint.com/rubys-missing-data-structure/</a></p></li>
<li><p>a couple implementations</p></li>
</ul>
</section>
<section>
<h1>Circular Buffer</h1>
<ul>
<li>Implemented using an array as storage</li>
<li>Overwrites after full</li>
</ul>
</section>
<section>
<h1>Tree</h1>
<ul>
<li>Hierarchical DS</li>
<li>n-Ary tree</li>
<li>Binary Tree</li>
<li>Binary Search Tree</li>
<li>Heap</li>
<li>Trie</li>
<li>quick terminolgy
<ul>
<li>root</li>
<li>leaf</li>
<li>level</li>
<li>path</li>
<li>siblings</li>
</ul>
</li>
<li>Real world usage, File system, RDBMS</li>
</ul>
</section>
<section>
<h1>BST</h1>
<ul>
<li>Binary tree with ordering</li>
<li>left < right</li>
<li>no duplicates,</li>
<li>Search/Insert/delete O(log n)</li>
</ul>
</section>
<section>
<h1>Heap</h1>
<ul>
<li>Binary tree</li>
<li>Max/Min at root</li>
<li>No order left/right</li>
<li>Max heap, min heap</li>
</ul>
</section>
<section>
<h1>Trie</h1>
<ul>
<li>A tree with prefix stored</li>
<li>Space efficient when there is repetition</li>
<li>Example storing urls</li>
</ul>
<pre><code> www -> meetup -> com -> ruby -> sv ->
-> java
-> hiking
-> net
</code></pre>
</section>
<section>
<h1>Matrix</h1>
<ul>
<li>Creating multi dimensional arrays in Ruby</li>
</ul>
<pre><code> a =[][]
a = Array.new() {} n dimensional matrix
</code></pre>
<ul>
<li>Instead use Matrix class</li>
</ul>
<pre><code> Matrix.build(3, 3) {|row, col| 0 }
=> 0, 0, 0
0, 0, 0
0, 0, 0
</code></pre>
</section>
<section>
<h1>Graphs & other DS</h1>
<ul>
<li>Graphs
<ul>
<li>Singly linked list is a basic graph</li>
<li>Tree with loops</li>
</ul>
</li>
<li>Sparse Matrices<br>
</li>
<li>Space Partitioning Trees </li>
<li>K-D tree</li>
</ul>
</section>
<section>
<h1>Conclusion</h1>
<p><a href="https://github.com/aarti/data-structures-ruby">Github repo</a> </p>
<p>Please email feedback to [email protected]</p>
<p>Thanks for listening</p>
</section>
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