---
title: Plots
layout: plots
groups:
  - navbar
navbar_link: <span class="glyphicon glyphicon-th-large"></span>&nbsp;Plots
custom_css: plots.css
plot_kinds:
  - sorted
  - randomized
  - reversed
plots:
  - codename: bubble
    brief_name: Bubble sort
    display_name: Bubble sort
    min_length: 0
    max_length: 200
    repetitions:
      sorted: 1000
      randomized: 100
      reversed: 100
    complexity:
      sorted: O(<var>n</var>)
      randomized: O(<var>n</var><sup>2</sup>)
      reversed: O(<var>n</var><sup>2</sup>)
  - codename: bubble_optimized
    brief_name: "&hellip; \"optimized\""
    display_name: "\"Optimized\" bubble sort"
    min_length: 0
    max_length: 200
    repetitions:
      sorted: 1000
      randomized: 100
      reversed: 100
    complexity:
      sorted: O(<var>n</var>)
      randomized: O(<var>n</var><sup>2</sup>)
      reversed: O(<var>n</var><sup>2</sup>)
  - codename: heap
    brief_name: Heapsort
    display_name: Heapsort
    min_length: 0
    max_length: 200
    repetitions: 100
    complexity: O(<var>n</var> log <var>n</var>)
  - codename: insertion
    brief_name: Insertion sort
    display_name: Insertion sort
    min_length: 0
    max_length: 200
    repetitions:
      sorted: 1000
      randomized: 100
      reversed: 100
    complexity:
      sorted: O(<var>n</var>)
      randomized: O(<var>n</var><sup>2</sup>)
      reversed: O(<var>n</var><sup>2</sup>)
  - codename: merge
    brief_name: Merge sort
    display_name: Merge sort
    min_length: 0
    max_length: 200
    repetitions: 100
    complexity: O(<var>n</var> log <var>n</var>)
  - codename: quick_first
    brief_name: Quicksort (first element as pivot)
    display_name: Quicksort (first element as pivot)
    min_length: 0
    max_length: 200
    repetitions: 100
    complexity:
      sorted: O(<var>n</var><sup>2</sup>)
      randomized: O(<var>n</var> log <var>n</var>)
      reversed: O(<var>n</var><sup>2</sup>)
  - codename: quick_second
    brief_name: "&hellip; second element&hellip;"
    display_name: Quicksort (second element as pivot)
    min_length: 0
    max_length: 200
    repetitions: 100
    complexity:
      sorted: O(<var>n</var><sup>2</sup>)
      randomized: O(<var>n</var> log <var>n</var>)
      reversed: O(<var>n</var><sup>2</sup>)
  - codename: quick_middle
    brief_name: "&hellip; middle element&hellip;"
    display_name: Quicksort (middle element as pivot)
    min_length: 0
    max_length: 200
    repetitions: 100
    complexity: O(<var>n</var> log <var>n</var>)
  - codename: quick_last
    brief_name: "&hellip; last element&hellip;"
    display_name: Quicksort (last element as pivot)
    min_length: 0
    max_length: 200
    repetitions: 100
    complexity:
      sorted: O(<var>n</var><sup>2</sup>)
      randomized: O(<var>n</var> log <var>n</var>)
      reversed: O(<var>n</var><sup>2</sup>)
  - codename: quick_random
    brief_name: "&hellip; random element&hellip;"
    display_name: Quicksort (random element as pivot)
    min_length: 0
    max_length: 200
    repetitions: 100
    complexity: O(<var>n</var> log <var>n</var>)
  - codename: selection
    brief_name: Selection sort
    display_name: Selection sort
    min_length: 0
    max_length: 200
    repetitions: 100
    complexity: O(<var>n</var><sup>2</sup>)
---
<h1>Plots</h1>

<div class="row">
<div class="col-xs-12 col-sm-9 col-md-6">
<p class="text-muted">The goals of this "project" include a) familiarizing
myself with a few sorting algorithms by examining their (possibly, simplified)
implementations and b) studying the way algorithm's running time changes in
relation to the length of its input (a.k.a. identifying its time
complexity).</p>
<p class="text-muted">A simple way to visualize the way algorithm's running
time changes would be to make appropriate measurements and plot them on a nice
graph.
The results of course are highly dependent on the hardware used, while the
graph's look depends on the software used for rendering.</p>
<p class="text-muted">Both the hardware &amp; the software that were used to
produce the plots are listed below.</p>
<table class="table table-bordered">
  <tr>
    <th>CPU</th>
    <td><a href="http://ark.intel.com/products/58917">Intel Atom N2800</a></td>
  </tr>
  <tr>
    <th>OS</th>
    <td>Windows 7 Professional Service Pack 1</td>
  </tr>
  <tr>
    <th>Python</th>
    <td>3.4.1</td>
  </tr>
  <tr>
    <th>matplotlib</th>
    <td>1.4.0</td>
  </tr>
</table>
</div>
</div>

{% if page.plots and page.plots != empty %}
<div class="row">
  <div class="col-xs-12 col-sm-10 col-md-8">
    <p>The table &amp; plots below are just an attempt to nicely lay out the
data generated using the code from the project repository's <code>master</code>
branch.
Visit <a href="https://github.com/egor-tensin/sorting_algorithms/">https://github.com/egor-tensin/sorting_algorithms/</a> for more details.</p>

    <p>In short, each of the implemented algorithms was provided with three
input sequences:</p>
<ul>
  <li>a list of n consecutive numbers sorted in ascending order ("sorted" input),</li>
  <li>&hellip; in descending order ("reversed" input),</li>
  <li>&hellip; in random order ("randomized" input).</li>
</ul>
    <p>Use the table below to quickly navigate to the plots for the
corresponding algorithm.</p>
    <table class="table table-bordered table-hover">
      <thead>
        <tr>
          <th class="text-center" rowspan="2">Algorithm</th>
          <th class="text-center" colspan="{{ page.plot_kinds.size }}">Complexity</th>
        </tr>
        <tr>
          {% for kind in page.plot_kinds %}
            <th class="text-center">{{ kind }}</th>
          {% endfor %}
        </tr>
      </thead>
      <tbody>
{% for algorithm in page.plots %}
<tr>
  <td><a href="#plots_{{ algorithm.codename }}">{{ algorithm.brief_name }}</a></td>
  {% for kind in page.plot_kinds %}
    <td>{% if algorithm.complexity[kind] %}{{ algorithm.complexity[kind] }}{% else %}{{ algorithm.complexity }}{% endif %}</td>
  {% endfor %}
</tr>
{% endfor %}
      </tbody>
    </table>
  </div>
</div>

{% for algorithm in page.plots %}
<a id="plots_{{ algorithm.codename }}"></a>
<h3>{{ algorithm.display_name }}</h3>
<div class="row">
  {% for kind in page.plot_kinds %}
  {% if algorithm.repetitions[kind] %}
    {% assign repetitions = algorithm.repetitions[kind] %}
  {% else %}
    {% assign repetitions = algorithm.repetitions %}
  {% endif %}
  {% capture stem %}{{ algorithm.codename }}_{{ repetitions }}_{{ kind }}_{{ algorithm.min_length }}_{{ algorithm.max_length }}{% endcapture %}
  <div class="col-xs-12 col-sm-6 col-md-4">
    <div class="thumbnail">
      <a class="thumbnail" href="{{ site.baseurl }}/img/plots/full_size/{{ stem }}.png">
        <img class="img-responsive" src="{{ site.baseurl }}/img/plots/previews/{{ stem }}.jpg"/>
      </a>
      <div class="caption">
        <strong>{{ algorithm.display_name }}</strong><br/>
        <strong>Input:</strong> {{ kind }}<br/>
        <strong>Complexity:</strong> {% if algorithm.complexity[kind] %}{{ algorithm.complexity[kind] }}{% else %}{{ algorithm.complexity }}{% endif %}<br/>
      </div>
    </div>
  </div>
  {% endfor %}
</div>
{% endfor %}

{% else %}
<h3>Sorry, not plots have been added yet.</h3>
<hr/>
{% endif %}