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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>EulerProblem024</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-24">Euler Problem 24<a class="anchor-link" href="#Euler-Problem-24">&#182;</a></h1><p>A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:</p>
<h1 id="Euler-Problem-24">Euler Problem 24<a class="anchor-link" href="#Euler-Problem-24"></a></h1><p><a href="/euler">Back to overview.</a></p><p>A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:</p>
<p>012 021 102 120 201 210</p>
<p>What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?</p>
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<p>I tried to solve this by thinking and failed to be hones. So we implement a generator and get the millionth element.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="k">import</span> <span class="n">deque</span>
<span class="k">def</span> <span class="nf">permutation_generator</span><span class="p">(</span><span class="n">xs</span><span class="p">):</span>
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<span class="k">yield</span> <span class="n">y</span>
<span class="k">raise</span> <span class="ne">StopIteration</span>
<span class="k">assert</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">s</span><span class="p">:</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="n">permutation_generator</span><span class="p">(</span><span class="s2">&quot;012&quot;</span><span class="p">)))</span> <span class="o">==</span> <span class="p">[</span><span class="s1">&#39;012&#39;</span><span class="p">,</span> <span class="s1">&#39;021&#39;</span><span class="p">,</span> <span class="s1">&#39;102&#39;</span><span class="p">,</span> <span class="s1">&#39;120&#39;</span><span class="p">,</span> <span class="s1">&#39;201&#39;</span><span class="p">,</span> <span class="s1">&#39;210&#39;</span><span class="p">])</span>
<span class="k">assert</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">s</span><span class="p">:</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="n">permutation_generator</span><span class="p">(</span><span class="s2">"012"</span><span class="p">)))</span> <span class="o">==</span> <span class="p">[</span><span class="s1">'012'</span><span class="p">,</span> <span class="s1">'021'</span><span class="p">,</span> <span class="s1">'102'</span><span class="p">,</span> <span class="s1">'120'</span><span class="p">,</span> <span class="s1">'201'</span><span class="p">,</span> <span class="s1">'210'</span><span class="p">])</span>
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<p>All right, now we reuse the function to get the nth element from problem 7 and give ourselves a solution.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">get_nth</span><span class="p">(</span><span class="n">generator</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="kn">import</span> <span class="nn">itertools</span>
<span class="k">return</span> <span class="nb">next</span><span class="p">(</span><span class="n">itertools</span><span class="o">.</span><span class="n">islice</span><span class="p">(</span><span class="n">generator</span><span class="p">,</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">))</span>
<span class="n">ps</span> <span class="o">=</span> <span class="n">permutation_generator</span><span class="p">(</span><span class="s2">&quot;0123456789&quot;</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="s2">&quot;&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">get_nth</span><span class="p">(</span><span class="n">ps</span><span class="p">,</span> <span class="mi">1000000</span><span class="p">)))</span>
<span class="n">ps</span> <span class="o">=</span> <span class="n">permutation_generator</span><span class="p">(</span><span class="s2">"0123456789"</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="s2">""</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">get_nth</span><span class="p">(</span><span class="n">ps</span><span class="p">,</span> <span class="mi">1000000</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">2783915460</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>2783915460
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