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<div class="section" id="solutions">
<h1>Solutions<a class="headerlink" href="#solutions" title="Permalink to this headline">¶</a></h1>
<div class="section" id="the-pi-wallis-solution">
<span id="pi-wallis"></span><h2>The Pi Wallis Solution<a class="headerlink" href="#the-pi-wallis-solution" title="Permalink to this headline">¶</a></h2>
<p>Compute the decimals of Pi using the Wallis formula:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""</span>
<span class="sd">The correction for the calculation of pi using the Wallis formula.</span>
<span class="sd">"""</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span>
<span class="n">pi</span> <span class="o">=</span> <span class="mf">3.14159265358979312</span>
<span class="n">my_pi</span> <span class="o">=</span> <span class="mf">1.</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">100000</span><span class="p">):</span>
<span class="n">my_pi</span> <span class="o">*=</span> <span class="mi">4</span><span class="o">*</span><span class="n">i</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="p">(</span><span class="mi">4</span><span class="o">*</span><span class="n">i</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mf">1.</span><span class="p">)</span>
<span class="n">my_pi</span> <span class="o">*=</span> <span class="mi">2</span>
<span class="k">print</span> <span class="n">pi</span>
<span class="k">print</span> <span class="n">my_pi</span>
<span class="k">print</span> <span class="nb">abs</span><span class="p">(</span><span class="n">pi</span> <span class="o">-</span> <span class="n">my_pi</span><span class="p">)</span>
<span class="c">################################################################################</span>
<span class="n">num</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">den</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">100000</span><span class="p">):</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="mi">4</span><span class="o">*</span><span class="n">i</span><span class="o">*</span><span class="n">i</span>
<span class="n">num</span> <span class="o">*=</span> <span class="n">tmp</span>
<span class="n">den</span> <span class="o">*=</span> <span class="n">tmp</span><span class="o">-</span><span class="mi">1</span>
<span class="n">better_pi</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="p">(</span><span class="n">num</span><span class="o">/</span><span class="n">den</span><span class="p">)</span>
<span class="k">print</span> <span class="n">pi</span>
<span class="k">print</span> <span class="n">better_pi</span>
<span class="k">print</span> <span class="nb">abs</span><span class="p">(</span><span class="n">pi</span> <span class="o">-</span> <span class="n">better_pi</span><span class="p">)</span>
<span class="k">print</span> <span class="nb">abs</span><span class="p">(</span><span class="n">my_pi</span> <span class="o">-</span> <span class="n">better_pi</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="the-quicksort-solution">
<span id="quick-sort"></span><h2>The Quicksort Solution<a class="headerlink" href="#the-quicksort-solution" title="Permalink to this headline">¶</a></h2>
<p>Implement the quicksort algorithm, as defined by wikipedia:</p>
<div class="highlight-python"><pre>function quicksort(array)
var list less, greater
if length(array) ≤ 1
return array
select and remove a pivot value pivot from array
for each x in array
if x ≤ pivot then append x to less
else append x to greater
return concatenate(quicksort(less), pivot, quicksort(greater))</pre>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""</span>
<span class="sd">Implement the quick sort algorithm.</span>
<span class="sd">"""</span>
<span class="k">def</span> <span class="nf">qsort</span><span class="p">(</span><span class="n">lst</span><span class="p">):</span>
<span class="sd">""" Quick sort: returns a sorted copy of the list.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">lst</span><span class="p">)</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">lst</span>
<span class="n">pivot</span><span class="p">,</span> <span class="n">rest</span> <span class="o">=</span> <span class="n">lst</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">lst</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
<span class="c"># Could use list comprehension:</span>
<span class="c"># less_than = [ lt for lt in rest if lt < pivot ]</span>
<span class="n">less_than</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">lt</span> <span class="ow">in</span> <span class="n">rest</span><span class="p">:</span>
<span class="k">if</span> <span class="n">lt</span> <span class="o"><</span> <span class="n">pivot</span><span class="p">:</span>
<span class="n">less_than</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">lt</span><span class="p">)</span>
<span class="c"># Could use list comprehension:</span>
<span class="c"># greater_equal = [ ge for ge in rest if ge >= pivot ]</span>
<span class="n">greater_equal</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">ge</span> <span class="ow">in</span> <span class="n">rest</span><span class="p">:</span>
<span class="k">if</span> <span class="n">ge</span> <span class="o">>=</span> <span class="n">pivot</span><span class="p">:</span>
<span class="n">greater_equal</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">ge</span><span class="p">)</span>
<span class="k">return</span> <span class="n">qsort</span><span class="p">(</span><span class="n">less_than</span><span class="p">)</span> <span class="o">+</span> <span class="p">[</span><span class="n">pivot</span><span class="p">]</span> <span class="o">+</span> <span class="n">qsort</span><span class="p">(</span><span class="n">greater_equal</span><span class="p">)</span>
<span class="c"># And now check that qsort does sort:</span>
<span class="k">assert</span> <span class="n">qsort</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">))</span> <span class="o">==</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="k">assert</span> <span class="n">qsort</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">)[::</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">==</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="k">assert</span> <span class="n">qsort</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span> <span class="o">==</span> <span class="nb">sorted</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
</pre></div>
</div>
</div>
<div class="section" id="fibonacci-sequence">
<span id="fibonacci"></span><h2>Fibonacci sequence<a class="headerlink" href="#fibonacci-sequence" title="Permalink to this headline">¶</a></h2>
<p>Write a function that displays the <tt class="docutils literal"><span class="pre">n</span></tt> first terms of the Fibonacci
sequence, defined by:</p>
<ul class="simple">
<li><tt class="docutils literal"><span class="pre">u_0</span> <span class="pre">=</span> <span class="pre">1;</span> <span class="pre">u_1</span> <span class="pre">=</span> <span class="pre">1</span></tt></li>
<li><tt class="docutils literal"><span class="pre">u_(n+2)</span> <span class="pre">=</span> <span class="pre">u_(n+1)</span> <span class="pre">+</span> <span class="pre">u_n</span></tt></li>
</ul>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">def</span> <span class="nf">fib</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="gp">... </span> <span class="sd">"""Display the n first terms of Fibonacci sequence"""</span>
<span class="gp">... </span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span>
<span class="gp">... </span> <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="gp">... </span> <span class="k">while</span> <span class="n">i</span> <span class="o"><</span> <span class="n">n</span><span class="p">:</span>
<span class="gp">... </span> <span class="k">print</span> <span class="n">b</span>
<span class="gp">... </span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="o">+</span><span class="n">b</span>
<span class="gp">... </span> <span class="n">i</span> <span class="o">+=</span><span class="mi">1</span>
<span class="gp">...</span>
<span class="gp">>>> </span><span class="n">fib</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="go">1</span>
<span class="go">1</span>
<span class="go">2</span>
<span class="go">3</span>
<span class="go">5</span>
<span class="go">8</span>
<span class="go">13</span>
<span class="go">21</span>
<span class="go">34</span>
<span class="go">55</span>
</pre></div>
</div>
</div>
<div class="section" id="the-directory-listing-solution">
<span id="dir-sort"></span><h2>The Directory Listing Solution<a class="headerlink" href="#the-directory-listing-solution" title="Permalink to this headline">¶</a></h2>
<p>Implement a script that takes a directory name as argument, and
returns the list of ‘.py’ files, sorted by name length.</p>
<p><strong>Hint:</strong> try to understand the docstring of list.sort</p>
<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""</span>
<span class="sd">Script to list all the '.py' files in a directory, in the order of file</span>
<span class="sd">name length.</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">os</span>
<span class="kn">import</span> <span class="nn">sys</span>
<span class="k">def</span> <span class="nf">filter_and_sort</span><span class="p">(</span><span class="n">file_list</span><span class="p">):</span>
<span class="sd">""" Out of a list of file names, returns only the ones ending by</span>
<span class="sd"> '.py', ordered with increasing file name length.</span>
<span class="sd"> """</span>
<span class="n">file_list</span> <span class="o">=</span> <span class="p">[</span><span class="n">filename</span> <span class="k">for</span> <span class="n">filename</span> <span class="ow">in</span> <span class="n">file_list</span>
<span class="k">if</span> <span class="n">filename</span><span class="o">.</span><span class="n">endswith</span><span class="p">(</span><span class="s">'.py'</span><span class="p">)]</span>
<span class="k">def</span> <span class="nf">key</span><span class="p">(</span><span class="n">item</span><span class="p">):</span>
<span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>
<span class="n">file_list</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">key</span><span class="o">=</span><span class="n">key</span><span class="p">)</span>
<span class="k">return</span> <span class="n">file_list</span>
<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">'__main__'</span><span class="p">:</span>
<span class="n">file_list</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">listdir</span><span class="p">(</span><span class="n">sys</span><span class="o">.</span><span class="n">argv</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">sorted_file_list</span> <span class="o">=</span> <span class="n">filter_and_sort</span><span class="p">(</span><span class="n">file_list</span><span class="p">)</span>
<span class="k">print</span> <span class="n">sorted_file_list</span>
</pre></div>
</div>
</div>
<div class="section" id="the-data-file-i-o-solution">
<span id="data-file"></span><h2>The Data File I/O Solution<a class="headerlink" href="#the-data-file-i-o-solution" title="Permalink to this headline">¶</a></h2>
<p>Write a function that will load the column of numbers in <tt class="docutils literal"><span class="pre">data.txt</span></tt>
and calculate the min, max and sum values.</p>
<p>Data file:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="mf">10.2</span>
<span class="mf">43.1</span>
<span class="mf">32.6</span>
<span class="mf">32.5</span>
<span class="mf">61.3</span>
<span class="mf">58.2</span>
</pre></div>
</div>
<p>Solution:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""Script to read in a column of numbers and calculate the min, max and sum.</span>
<span class="sd">Data is stored in data.txt.</span>
<span class="sd">"""</span>
<span class="k">def</span> <span class="nf">load_data</span><span class="p">(</span><span class="n">filename</span><span class="p">):</span>
<span class="n">fp</span> <span class="o">=</span> <span class="nb">open</span><span class="p">(</span><span class="n">filename</span><span class="p">)</span>
<span class="n">data_string</span> <span class="o">=</span> <span class="n">fp</span><span class="o">.</span><span class="n">read</span><span class="p">()</span>
<span class="n">fp</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
<span class="n">data</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">data_string</span><span class="o">.</span><span class="n">split</span><span class="p">():</span>
<span class="c"># Data is read in as a string. We need to convert it to floats</span>
<span class="n">data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
<span class="c"># Could instead use the following one line with list comprehensions!</span>
<span class="c"># data = [float(x) for x in data_string.split()]</span>
<span class="k">return</span> <span class="n">data</span>
<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">'__main__'</span><span class="p">:</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">load_data</span><span class="p">(</span><span class="s">'data.txt'</span><span class="p">)</span>
<span class="c"># Python provides these basic math functions</span>
<span class="k">print</span><span class="p">(</span><span class="s">'min: </span><span class="si">%f</span><span class="s">'</span> <span class="o">%</span> <span class="nb">min</span><span class="p">(</span><span class="n">data</span><span class="p">))</span>
<span class="k">print</span><span class="p">(</span><span class="s">'max: </span><span class="si">%f</span><span class="s">'</span> <span class="o">%</span> <span class="nb">max</span><span class="p">(</span><span class="n">data</span><span class="p">))</span>
<span class="k">print</span><span class="p">(</span><span class="s">'sum: </span><span class="si">%f</span><span class="s">'</span> <span class="o">%</span> <span class="nb">sum</span><span class="p">(</span><span class="n">data</span><span class="p">))</span>
</pre></div>
</div>
</div>
<div class="section" id="the-pythonpath-search-solution">
<span id="path-site"></span><h2>The PYTHONPATH Search Solution<a class="headerlink" href="#the-pythonpath-search-solution" title="Permalink to this headline">¶</a></h2>
<p>Write a program to search your PYTHONPATH for the module <tt class="docutils literal"><span class="pre">site.py</span></tt>.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""Script to search the PYTHONPATH for the module site.py"""</span>
<span class="kn">import</span> <span class="nn">os</span>
<span class="kn">import</span> <span class="nn">sys</span>
<span class="kn">import</span> <span class="nn">glob</span>
<span class="k">def</span> <span class="nf">find_module</span><span class="p">(</span><span class="n">module</span><span class="p">):</span>
<span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
<span class="c"># Loop over the list of paths in sys.path</span>
<span class="k">for</span> <span class="n">subdir</span> <span class="ow">in</span> <span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="p">:</span>
<span class="c"># Join the subdir path with the module we're searching for</span>
<span class="n">pth</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">subdir</span><span class="p">,</span> <span class="n">module</span><span class="p">)</span>
<span class="c"># Use glob to test if the pth is exists</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">glob</span><span class="o">.</span><span class="n">glob</span><span class="p">(</span><span class="n">pth</span><span class="p">)</span>
<span class="c"># glob returns a list, if it is not empty, the pth exists</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">res</span><span class="p">)</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="k">return</span> <span class="n">result</span>
<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">'__main__'</span><span class="p">:</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">find_module</span><span class="p">(</span><span class="s">'site.py'</span><span class="p">)</span>
<span class="k">print</span> <span class="n">result</span>
</pre></div>
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