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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>EulerProblem040</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
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<h1 id="Champernowne's-constant-(Euler-Problem-40)">Champernowne's constant (Euler Problem 40)<a class="anchor-link" href="#Champernowne's-constant-(Euler-Problem-40)">&#182;</a></h1><p><a href="https://projecteuler.net/problem=40">https://projecteuler.net/problem=40</a></p>
<h1 id="Champernowne's-constant-(Euler-Problem-40)">Champernowne's constant (Euler Problem 40)<a class="anchor-link" href="#Champernowne's-constant-(Euler-Problem-40)"></a></h1><p><a href="/euler">Back to overview.</a></p><p><a href="https://projecteuler.net/problem=40">https://projecteuler.net/problem=40</a></p>
<p>An irrational decimal fraction is created by concatenating the positive integers:</p>
<pre><code>0.123456789101112131415161718192021...
</code></pre>
<p>It can be seen that the 12th digit of the fractional part is 1.</p>
<p>If dn represents the nth digit of the fractional part, find the value of the following expression.</p>
<p>$d_{1} × d_{10} × d_{100} × d_{1000} × d_{10000} × d_{100000} × d_{1000000}$</p>
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<p>I do not see why we cannot hold $8 bytes \times 10^{6} = 8 MB$ in memory.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">get_irrational_fraction</span><span class="p">(</span><span class="n">digits_max</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">1</span>
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<span class="n">s</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">n</span><span class="p">))</span>
<span class="n">digits</span> <span class="o">+=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">n</span><span class="p">))</span>
<span class="n">n</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="s2">&quot;&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="k">return</span> <span class="s2">""</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="k">assert</span><span class="p">(</span><span class="n">get_irrational_fraction</span><span class="p">(</span><span class="mi">20</span><span class="p">)[</span><span class="mi">12</span><span class="p">]</span> <span class="o">==</span> <span class="s2">&quot;1&quot;</span><span class="p">)</span>
<span class="k">assert</span><span class="p">(</span><span class="n">get_irrational_fraction</span><span class="p">(</span><span class="mi">20</span><span class="p">)[</span><span class="mi">12</span><span class="p">]</span> <span class="o">==</span> <span class="s2">"1"</span><span class="p">)</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">get_irrational_fraction</span><span class="p">(</span><span class="mi">1000001</span><span class="p">)</span>
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<p>Okay, we got the fractional. No we get the digits at the different positions and calculate the product. For that purpose we reuse our poduct function from problem 8.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">product</span><span class="p">(</span><span class="n">xs</span><span class="p">):</span>
<span class="kn">from</span> <span class="nn">operator</span> <span class="k">import</span> <span class="n">mul</span>
<span class="kn">from</span> <span class="nn">functools</span> <span class="k">import</span> <span class="n">reduce</span>
<span class="k">return</span> <span class="n">reduce</span><span class="p">(</span><span class="n">mul</span><span class="p">,</span> <span class="n">xs</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">s</span> <span class="o">=</span> <span class="n">product</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="p">[</span><span class="n">f</span><span class="p">[</span><span class="mi">10</span><span class="o">**</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</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">7</span><span class="p">)]))</span>
<span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="k">assert</span><span class="p">(</span><span class="n">s</span> <span class="o">==</span> <span class="mi">210</span><span class="p">)</span>
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<pre>210
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