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<p>We start by writing a function that takes a number and returns all possible replacements.</p>
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<p>For example 13 will return ["x3", "1x"].</p>
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<p>I actually had a version that simply replace even digits at first, but that does not work for 56333 for example, because you want to get 56xx3 and not 56xxx. So basically, we have to search for all combinations for each digit. I should probably document what each list comprehension does or I will never understand it again. Haha.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="k">import</span> <span class="n">combinations</span>
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<span class="k">def</span> <span class="nf">get_replacements</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<span class="n">n</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
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<span class="n">xss</span><span class="o">=</span> <span class="p">[[</span><span class="n">i</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">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">n</span><span class="p">))</span> <span class="k">if</span> <span class="n">n</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">d</span><span class="p">]</span>
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<span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="s2">"0123456789"</span><span class="p">]</span>
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<span class="n">xss</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span>
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<span class="k">for</span> <span class="n">xs</span> <span class="ow">in</span> <span class="n">xss</span> <span class="k">if</span> <span class="n">xs</span>
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<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="nb">len</span><span class="p">(</span><span class="n">xs</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
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<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">combinations</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">i</span><span class="p">)]</span>
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<span class="n">xss</span> <span class="o">=</span> <span class="p">[</span><span class="s2">""</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="s1">'x'</span> <span class="k">if</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">xs</span> <span class="k">else</span> <span class="n">d</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">n</span><span class="p">)])</span>
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<span class="k">for</span> <span class="n">xs</span> <span class="ow">in</span> <span class="n">xss</span><span class="p">]</span>
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<span class="k">return</span> <span class="n">xss</span>
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<span class="c1">#assert(get_replacements(13) == ["x3", "1x"])</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">get_replacements</span><span class="p">(</span><span class="mi">13</span><span class="p">))</span>
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<pre>['x3', '1x']
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<p>We will use our good old prime generator.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">is_prime</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">smaller_primes</span><span class="p">):</span>
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<span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">smaller_primes</span><span class="p">:</span>
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<span class="k">if</span> <span class="n">n</span> <span class="o">%</span> <span class="n">s</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
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<span class="k">return</span> <span class="kc">False</span>
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<span class="k">if</span> <span class="n">s</span> <span class="o">*</span> <span class="n">s</span> <span class="o">></span> <span class="n">n</span><span class="p">:</span>
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<span class="k">return</span> <span class="kc">True</span>
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<span class="k">return</span> <span class="kc">True</span>
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<span class="k">def</span> <span class="nf">prime_generator_function</span><span class="p">():</span>
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<span class="n">primes</span> <span class="o">=</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">]</span>
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<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">primes</span><span class="p">:</span>
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<span class="k">yield</span> <span class="n">p</span>
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<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
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<span class="n">p</span> <span class="o">+=</span> <span class="mi">2</span>
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<span class="k">if</span> <span class="n">is_prime</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">primes</span><span class="p">):</span>
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<span class="n">primes</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
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<span class="k">yield</span> <span class="n">p</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">replacements</span> <span class="o">=</span> <span class="p">{}</span>
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<span class="n">ps</span> <span class="o">=</span> <span class="n">prime_generator_function</span><span class="p">()</span>
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<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">ps</span><span class="p">:</span>
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<span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">get_replacements</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
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<span class="k">try</span><span class="p">:</span>
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<span class="n">replacements</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
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<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">replacements</span><span class="p">[</span><span class="n">r</span><span class="p">])</span> <span class="o">==</span> <span class="mi">8</span><span class="p">:</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">replacements</span><span class="p">[</span><span class="n">r</span><span class="p">])</span>
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<span class="n">s</span> <span class="o">=</span> <span class="n">replacements</span><span class="p">[</span><span class="n">r</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
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<span class="n">p</span> <span class="o">=</span> <span class="mi">100000000000</span> <span class="c1"># We have found a solution so we go home</span>
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<span class="k">except</span> <span class="ne">KeyError</span><span class="p">:</span>
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<span class="n">replacements</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="n">p</span><span class="p">]</span>
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<span class="k">if</span> <span class="n">p</span> <span class="o">></span> <span class="mi">1000000</span><span class="p">:</span>
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<span class="k">break</span>
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<pre>[121313, 222323, 323333, 424343, 525353, 626363, 828383, 929393]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">s</span> <span class="o">==</span> <span class="mi">121313</span><span class="p">)</span>
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<pre>121313
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11900
ipython/html/EulerProblem052.html
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@@ -809,12 +809,32 @@
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<td><a href="EulerProblem051.html">Problem 051</a></td>
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<td></td>
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<td>Sun, 23 Dec 2018, 23:47</td>
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<td>
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<kbd>prime</kbd>
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<kbd>combinations</kbd>
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<kbd>replacement</kbd>
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</td>
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<tr>
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<td><a href="EulerProblem052.html">Problem 052</a></td>
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<td>Mon, 24 Dec 2018, 02:32</td>
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<td>
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<kbd>digits</kbd>
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<kbd>permutations</kbd>
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</tr>
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