Solved 44 and 45.
This commit is contained in:
@@ -11778,6 +11778,7 @@ div#notebook {
|
||||
</div>
|
||||
<div class="inner_cell">
|
||||
<div class="text_cell_render border-box-sizing rendered_html">
|
||||
<p><a href="https://projecteuler.net/problem=43">https://projecteuler.net/problem=43</a></p>
|
||||
<p>The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.</p>
|
||||
<p>Let $d_1$ be the 1st digit, $d_2$ be the 2nd digit, and so on. In this way, we note the following:</p>
|
||||
<p>$d_2d_3d_4$=406 is divisible by 2</p>
|
||||
@@ -11791,6 +11792,116 @@ div#notebook {
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
|
||||
</div>
|
||||
<div class="inner_cell">
|
||||
<div class="text_cell_render border-box-sizing rendered_html">
|
||||
<p>We write a function that tests for the sub-string divisibility property. Then we simply brute force.</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [14]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">is_sub_string_divisible</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>
|
||||
<span class="n">s</span> <span class="o">=</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">if</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">4</span><span class="p">])</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="kc">False</span>
|
||||
<span class="k">if</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">5</span><span class="p">])</span> <span class="o">%</span> <span class="mi">3</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="kc">False</span>
|
||||
<span class="k">if</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">3</span><span class="p">:</span><span class="mi">6</span><span class="p">])</span> <span class="o">%</span> <span class="mi">5</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="kc">False</span>
|
||||
<span class="k">if</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">4</span><span class="p">:</span><span class="mi">7</span><span class="p">])</span> <span class="o">%</span> <span class="mi">7</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="kc">False</span>
|
||||
<span class="k">if</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">5</span><span class="p">:</span><span class="mi">8</span><span class="p">])</span> <span class="o">%</span> <span class="mi">11</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="kc">False</span>
|
||||
<span class="k">if</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">6</span><span class="p">:</span><span class="mi">9</span><span class="p">])</span> <span class="o">%</span> <span class="mi">13</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="kc">False</span>
|
||||
<span class="k">if</span> <span class="nb">int</span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="mi">7</span><span class="p">:</span><span class="mi">10</span><span class="p">])</span> <span class="o">%</span> <span class="mi">17</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="kc">False</span>
|
||||
<span class="k">return</span> <span class="kc">True</span>
|
||||
|
||||
<span class="k">assert</span><span class="p">(</span><span class="n">is_sub_string_divisible</span><span class="p">(</span><span class="s2">"1406357289"</span><span class="p">))</span>
|
||||
<span class="k">assert</span><span class="p">(</span><span class="n">is_sub_string_divisible</span><span class="p">(</span><span class="s2">"1406357298"</span><span class="p">)</span> <span class="o">==</span> <span class="kc">False</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [15]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">itertools</span>
|
||||
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</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">p</span><span class="p">))</span> <span class="k">for</span> <span class="n">p</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">"0123456789"</span><span class="p">)</span> <span class="k">if</span> <span class="n">is_sub_string_divisible</span><span class="p">(</span><span class="n">p</span><span class="p">)])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [17]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<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>
|
||||
<span class="k">assert</span><span class="p">(</span><span class="n">s</span> <span class="o">==</span> <span class="mi">16695334890</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="prompt"></div>
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>16695334890
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
|
||||
</div>
|
||||
<div class="inner_cell">
|
||||
<div class="text_cell_render border-box-sizing rendered_html">
|
||||
<p>I just want to write my own permutations functions to see that I am able to do it quickly. We pick each element once and combine it with the permutations for the remaining items:</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [32]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">permutations</span><span class="p">(</span><span class="n">items</span><span class="p">):</span>
|
||||
<span class="n">items</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">items</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">items</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="p">[[]]</span>
|
||||
<span class="n">perms</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">items</span><span class="p">:</span>
|
||||
<span class="n">items_new</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">items</span><span class="p">)</span>
|
||||
<span class="n">items_new</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>
|
||||
<span class="n">permutations_new</span> <span class="o">=</span> <span class="n">permutations</span><span class="p">(</span><span class="n">items_new</span><span class="p">)</span>
|
||||
<span class="k">for</span> <span class="n">perm</span> <span class="ow">in</span> <span class="n">permutations_new</span><span class="p">:</span>
|
||||
<span class="n">perms</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">item</span><span class="p">]</span> <span class="o">+</span> <span class="n">perm</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">perms</span>
|
||||
|
||||
|
||||
<span class="k">assert</span><span class="p">(</span><span class="n">permutations</span><span class="p">([])</span> <span class="o">==</span> <span class="p">[[]])</span>
|
||||
<span class="k">assert</span><span class="p">(</span><span class="n">permutations</span><span class="p">([</span><span class="mi">1</span><span class="p">])</span> <span class="o">==</span> <span class="p">[[</span><span class="mi">1</span><span class="p">]])</span>
|
||||
<span class="k">assert</span><span class="p">(</span><span class="n">permutations</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">])</span> <span class="o">==</span> <span class="p">[[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">]])</span>
|
||||
<span class="k">assert</span><span class="p">(</span><span class="n">permutations</span><span class="p">([</span><span class="mi">1</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="o">==</span> <span class="p">[[</span><span class="mi">1</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="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">],</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">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">]])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [ ]:</div>
|
||||
|
||||
11891
ipython/html/EulerProblem044.html
Normal file
11891
ipython/html/EulerProblem044.html
Normal file
File diff suppressed because it is too large
Load Diff
11874
ipython/html/EulerProblem045.html
Normal file
11874
ipython/html/EulerProblem045.html
Normal file
File diff suppressed because it is too large
Load Diff
@@ -677,16 +677,50 @@
|
||||
</tr>
|
||||
|
||||
|
||||
<tr class="table-warning">
|
||||
<tr>
|
||||
|
||||
<td><a href="EulerProblem043.html">Problem 043</a></td>
|
||||
<td></td>
|
||||
<td>Fri, 21 Dec 2018, 16:28</td>
|
||||
<td>
|
||||
|
||||
<kbd>pandigital</kbd>
|
||||
|
||||
<kbd>divisibility</kbd>
|
||||
|
||||
<kbd>permutations</kbd>
|
||||
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
<tr>
|
||||
|
||||
<td><a href="EulerProblem044.html">Problem 044</a></td>
|
||||
<td>Sat, 22 Dec 2018, 22:57</td>
|
||||
<td>
|
||||
|
||||
<kbd>pentagonal</kbd>
|
||||
|
||||
<kbd>brute force</kbd>
|
||||
|
||||
<kbd>improve</kbd>
|
||||
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
<tr>
|
||||
|
||||
<td><a href="EulerProblem045.html">Problem 045</a></td>
|
||||
<td>Sat, 22 Dec 2018, 23:17</td>
|
||||
<td>
|
||||
|
||||
<kbd>triangular</kbd>
|
||||
|
||||
<kbd>pentagona</kbd>
|
||||
|
||||
<kbd>hexagonal</kbd>
|
||||
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
Reference in New Issue
Block a user