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Euler has design of a homepage and there is a link back to the overview for each solution.

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Felix Martin
2018-06-14 20:11:26 -04:00
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<title>EulerProblem019</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
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<h1 id="Euler-Problem-19">Euler Problem 19<a class="anchor-link" href="#Euler-Problem-19">&#182;</a></h1><p>You are given the following information, but you may prefer to do some research for yourself.</p>
<h1 id="Euler-Problem-19">Euler Problem 19<a class="anchor-link" href="#Euler-Problem-19"></a></h1><p><a href="/euler">Back to overview.</a></p><p>You are given the following information, but you may prefer to do some research for yourself.</p>
<ul>
<li>1 Jan 1900 was a Monday.</li>
<li>Thirty days has September,
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<li>A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.</li>
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<p>How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?</p>
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<p>We have one hundred years which equal 1200 months. Every month starts with a weekday and $\frac{1}{7}$ of all weekdays are Sundays. So, 1200 divided by 7 is 171 point something.</p>
<p>Which turns out to be the correct solution.</p>
<p>Let's still code a solution because we were not that smart back then. We create two generators, zip, them and search for 1st and Sunday.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">weekday_generator_function</span><span class="p">():</span>
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<span class="k">yield</span> <span class="s1">&#39;Monday&#39;</span>
<span class="k">yield</span> <span class="s1">&#39;Tuesday&#39;</span>
<span class="k">yield</span> <span class="s1">&#39;Wednesday&#39;</span>
<span class="k">yield</span> <span class="s1">&#39;Thursday&#39;</span>
<span class="k">yield</span> <span class="s1">&#39;Friday&#39;</span>
<span class="k">yield</span> <span class="s1">&#39;Saturday&#39;</span>
<span class="k">yield</span> <span class="s1">&#39;Sunday&#39;</span>
<span class="k">yield</span> <span class="s1">'Monday'</span>
<span class="k">yield</span> <span class="s1">'Tuesday'</span>
<span class="k">yield</span> <span class="s1">'Wednesday'</span>
<span class="k">yield</span> <span class="s1">'Thursday'</span>
<span class="k">yield</span> <span class="s1">'Friday'</span>
<span class="k">yield</span> <span class="s1">'Saturday'</span>
<span class="k">yield</span> <span class="s1">'Sunday'</span>
<span class="k">def</span> <span class="nf">day_of_month_generator_function</span><span class="p">():</span>
<span class="n">day</span><span class="p">,</span> <span class="n">month</span><span class="p">,</span> <span class="n">year</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1901</span>
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<span class="n">ds</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="n">weekday_generator_function</span><span class="p">(),</span> <span class="n">day_of_month_generator_function</span><span class="p">())</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">len</span><span class="p">([</span><span class="mi">1</span> <span class="k">for</span> <span class="n">weekday</span><span class="p">,</span> <span class="n">date</span> <span class="ow">in</span> <span class="n">ds</span> <span class="k">if</span> <span class="n">weekday</span> <span class="o">==</span> <span class="s2">&quot;Sunday&quot;</span> <span class="ow">and</span> <span class="n">date</span> <span class="o">==</span> <span class="mi">1</span><span class="p">])</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">len</span><span class="p">([</span><span class="mi">1</span> <span class="k">for</span> <span class="n">weekday</span><span class="p">,</span> <span class="n">date</span> <span class="ow">in</span> <span class="n">ds</span> <span class="k">if</span> <span class="n">weekday</span> <span class="o">==</span> <span class="s2">"Sunday"</span> <span class="ow">and</span> <span class="n">date</span> <span class="o">==</span> <span class="mi">1</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
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<pre>172
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<p>Okay, this is actually kind of embarrassing. Why am I even zipping when I have the month right there in my function. Problem is, that my weekday generator starts with Monday, but Monday was the start in 1900 not in 1901. Let's try to do better. 1.1.1901 was a Tuesday, so we drop Monday from the generator.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">wds</span> <span class="o">=</span> <span class="n">weekday_generator_function</span><span class="p">()</span>
<span class="nb">next</span><span class="p">(</span><span class="n">wds</span><span class="p">)</span> <span class="c1"># get rid of first Monday</span>
<span class="n">ds</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="n">wds</span><span class="p">,</span> <span class="n">day_of_month_generator_function</span><span class="p">())</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">len</span><span class="p">([</span><span class="mi">1</span> <span class="k">for</span> <span class="n">weekday</span><span class="p">,</span> <span class="n">date</span> <span class="ow">in</span> <span class="n">ds</span> <span class="k">if</span> <span class="n">weekday</span> <span class="o">==</span> <span class="s2">&quot;Sunday&quot;</span> <span class="ow">and</span> <span class="n">date</span> <span class="o">==</span> <span class="mi">1</span><span class="p">])</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">len</span><span class="p">([</span><span class="mi">1</span> <span class="k">for</span> <span class="n">weekday</span><span class="p">,</span> <span class="n">date</span> <span class="ow">in</span> <span class="n">ds</span> <span class="k">if</span> <span class="n">weekday</span> <span class="o">==</span> <span class="s2">"Sunday"</span> <span class="ow">and</span> <span class="n">date</span> <span class="o">==</span> <span class="mi">1</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
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<pre>171
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<p>And finally, here we go. Actually not a dummy exercise and shows how imporessive the shortcut from the beginning is. Raw power is not always the best solution if we can also use brain.</p>
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