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Solved problem 41.

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Felix Martin
2018-12-19 15:58:46 -05:00
parent 1444f7cc7e
commit ab4840204c
3 changed files with 144 additions and 8 deletions
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@@ -11778,6 +11778,7 @@ div#notebook {
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<p>[<a href="https://projecteuler.net/problem=41">https://projecteuler.net/problem=41</a>]</p>
<p>We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.</p>
<p>What is the largest n-digit pandigital prime that exists?</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">expmod</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">exp</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
<span class="k">if</span> <span class="n">exp</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">return</span> <span class="mi">1</span>
<span class="k">if</span> <span class="p">(</span><span class="n">exp</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="n">expmod</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">exp</span> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="n">m</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">%</span> <span class="n">m</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span><span class="n">base</span> <span class="o">*</span> <span class="n">expmod</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">exp</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">)</span> <span class="o">%</span> <span class="n">m</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">expmod_naiv</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">exp</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
<span class="k">return</span> <span class="n">base</span> <span class="o">**</span> <span class="n">exp</span> <span class="o">%</span> <span class="n">m</span>
<span class="k">def</span> <span class="nf">fermat_test</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">3</span>
<span class="k">return</span> <span class="n">expmod</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span> <span class="o">==</span> <span class="n">a</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">assert</span><span class="p">(</span><span class="n">expmod</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">100000</span><span class="p">,</span> <span class="mi">2143</span><span class="p">)</span> <span class="o">==</span> <span class="n">expmod_naiv</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">100000</span><span class="p">,</span> <span class="mi">2143</span><span class="p">))</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">assert</span><span class="p">(</span><span class="n">fermat_test</span><span class="p">(</span><span class="mi">2143</span><span class="p">))</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">itertools</span>
<span class="k">for</span> <span class="n">pandigital</span> <span class="ow">in</span> <span class="n">itertools</span><span class="o">.</span><span class="n">permutations</span><span class="p">(</span><span class="s2">"7654321"</span><span class="p">):</span>
<span class="n">p</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">pandigital</span><span class="p">))</span>
<span class="k">if</span> <span class="n">fermat_test</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">p</span>
<span class="k">break</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">7652413</span><span class="p">)</span>
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<pre>7652413
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