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<time class="post-time" datetime="2015-07-03T17:40:00+03:00" pubdate>
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Пт. 03 Июль 2015
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<a href="../../posts/eshche-odno-vychislenie-vyrazhenii/" rel="bookmark"><h1>Еще одно вычисление выражений</h1></a>
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<a href="../../posts/eshchio-odno-vychislenie-vyrazhenii/" rel="bookmark"><h1>Ещё одно вычисление выражений</h1></a>
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<title> Моё решение задачи 60
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<time class="post-time" datetime="2015-07-17T17:40:00+03:00" pubdate>
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Пт. 17 Июль 2015
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<a href="../../posts/moio-reshenie-zadachi-60/" rel="bookmark"><h1>Моё решение задачи 60</h1></a>
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<p>Необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число. Здесь под процедурой “склеивания” чисел <span class="math">\(a\)</span> и <span class="math">\(b\)</span> подразумевается получения из <span class="math">\(a = \overline{a_1 a_2 \ldots a_n}\)</span> и <span class="math">\(b = \overline{b_1 b_2 \ldots b_m}\)</span> некоторого <span class="math">\(c\)</span> так, что <span class="math">\(c = \overline{a_1 a_2 \ldots a_n b_1 b_2 \ldots b_m}\)</span>.</p>
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<p>Полное условие можно найти <a href="https://projecteuler.net/problem=60">тут</a></p>
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<p>Для начала, можно понять, что непосредственный перебор “в лоб” слишком медленный и нужного результата не даст. Поэтому хочется уйти от, как мне кажется, не самого формализуемого условия к чему-то более простого, с чем проще работать. Давайте сначала поймём, какие вообще числа могут быть в одном множестве. Для этого достаточно перебрать все разбиения на два подчисла всех простых чисел. Это достаточно быстро, порядка <span class="math">\(O\left( N \right)\)</span> операций. Важно не забыть, что мы можем разбивать число <span class="math">\(p\)</span> только на <span class="math">\(\overline{p_1 p_2}\)</span>, между числами не может быть нулей! То есть если число 37 разбивается на 3 и 7, то 307 нет.</p>
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<p>Пусть мы получили набор таких разбиений, то есть набор пар вида <span class="math">\(\left( p, q \right)\)</span>. Давайте составим из них граф, где вершинки это простые числа, а ориентированное ребро из <span class="math">\(p\)</span> в <span class="math">\(q\)</span> означает, что есть пара <span class="math">\(\left( p, q \right)\)</span>. Из того, что порядок склеивания чисел произвольный сразу следует, что рассматриваемый граф должен быть неориентированным. Таким образом, все пары <span class="math">\(\left( p, q \right)\)</span> для которых нет пары <span class="math">\(\left( q, p \right)\)</span> необходимо выкинуть, а из оставшихся построить граф.</p>
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<p>Теперь задача стало гораздо понятнее: достаточно выбрать клику размера 5, что сумма значений её вершин минимальна. В общем случае, это достаточно ресурсоёмкая(как мне кажется) задача, но в реальном графе количество рёбер не слишком большое. В худшем случае, по теореме Турана, количество рёбер в графе лишь с одной такой кликой примерно на 10% меньше числа рёбер в полном графе.</p>
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<p>Непосредственно сам поиск такой клики можно реализовать тривиально. Ниже мой код на C++11 с использованием библиотеки Boost Graph Library (<span class="caps">BGL</span>).</p>
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<div class="highlight"><pre><span class="code-line"><span class="cp">#include <iostream></span></span>
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<span class="code-line"><span class="cp">#include <algorithm></span></span>
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<span class="code-line"><span class="cp">#include <vector></span></span>
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<span class="code-line"><span class="cp">#include <set></span></span>
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<span class="code-line"><span class="cp">#include <map></span></span>
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<span class="code-line"><span class="cp">#include <cstdint></span></span>
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<span class="code-line"></span>
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<span class="code-line"><span class="cp">#include <boost/graph/adjacency_list.hpp></span></span>
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<span class="code-line"><span class="cp">#include "primesieve.hpp"</span></span>
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<span class="code-line"></span>
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<span class="code-line"><span class="k">using</span> <span class="k">namespace</span> <span class="n">std</span><span class="p">;</span></span>
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<span class="code-line"><span class="k">using</span> <span class="k">namespace</span> <span class="n">boost</span><span class="p">;</span></span>
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<span class="code-line"></span>
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<span class="code-line"><span class="k">typedef</span> <span class="n">adjacency_list</span><span class="o"><</span><span class="n">listS</span><span class="p">,</span> <span class="n">vecS</span><span class="p">,</span> <span class="n">undirectedS</span><span class="o">></span> <span class="n">Graph</span><span class="p">;</span></span>
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<span class="code-line"></span>
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<span class="code-line"><span class="k">template</span> <span class="o"><</span><span class="k">class</span> <span class="nc">T</span><span class="o">></span> </span>
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<span class="code-line"><span class="n">vector</span><span class="o"><</span> <span class="n">T</span> <span class="o">></span> <span class="n">getDigs</span><span class="p">(</span><span class="n">T</span> <span class="n">num</span><span class="p">)</span> <span class="p">{</span></span>
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<span class="code-line"> <span class="n">vector</span><span class="o"><</span> <span class="n">T</span> <span class="o">></span> <span class="n">res</span><span class="p">;</span></span>
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<span class="code-line"> <span class="k">while</span> <span class="p">(</span> <span class="n">num</span> <span class="o">!=</span> <span class="mi">0</span> <span class="p">)</span> <span class="p">{</span></span>
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<span class="code-line"> <span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">num</span> <span class="o">%</span> <span class="mi">10</span><span class="p">);</span></span>
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<span class="code-line"> <span class="n">num</span> <span class="o">=</span> <span class="n">num</span> <span class="o">/</span> <span class="mi">10</span><span class="p">;</span></span>
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<span class="code-line"> <span class="p">}</span></span>
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<span class="code-line"> <span class="n">reverse</span><span class="p">(</span><span class="n">res</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="n">res</span><span class="p">.</span><span class="n">end</span><span class="p">());</span></span>
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<span class="code-line"> <span class="k">return</span> <span class="n">res</span><span class="p">;</span></span>
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<span class="code-line"><span class="p">}</span></span>
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<span class="code-line"></span>
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<span class="code-line"><span class="k">template</span> <span class="o"><</span><span class="k">class</span> <span class="nc">T</span><span class="o">></span></span>
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<span class="code-line"><span class="n">T</span> <span class="n">getNum</span><span class="p">(</span><span class="k">const</span> <span class="n">vector</span><span class="o"><</span><span class="n">T</span><span class="o">></span> <span class="o">&</span><span class="n">digs</span><span class="p">){</span></span>
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<span class="code-line"> <span class="n">T</span> <span class="n">res</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span></span>
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<span class="code-line"> <span class="n">T</span> <span class="nf">cur_mult</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span></span>
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<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">it</span> <span class="o">=</span> <span class="n">digs</span><span class="p">.</span><span class="n">rbegin</span><span class="p">();</span> <span class="n">it</span> <span class="o">!=</span> <span class="n">digs</span><span class="p">.</span><span class="n">rend</span><span class="p">();</span> <span class="o">++</span><span class="n">it</span><span class="p">){</span></span>
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<span class="code-line"> <span class="n">res</span> <span class="o">+=</span> <span class="o">*</span><span class="n">it</span> <span class="o">*</span> <span class="n">cur_mult</span><span class="p">;</span></span>
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<span class="code-line"> <span class="n">cur_mult</span> <span class="o">*=</span> <span class="n">T</span><span class="p">(</span><span class="mi">10</span><span class="p">);</span></span>
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<span class="code-line"> <span class="p">}</span></span>
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<span class="code-line"> <span class="k">return</span> <span class="n">res</span><span class="p">;</span></span>
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<span class="code-line"><span class="p">}</span></span>
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<span class="code-line"></span>
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<span class="code-line"><span class="k">template</span> <span class="o"><</span><span class="k">class</span> <span class="nc">T</span><span class="o">></span></span>
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<span class="code-line"><span class="n">vector</span><span class="o"><</span> <span class="n">pair</span><span class="o"><</span><span class="n">T</span><span class="p">,</span><span class="n">T</span><span class="o">></span> <span class="o">></span> <span class="n">getPrimePairs</span><span class="p">(</span><span class="n">T</span> <span class="n">prime</span><span class="p">,</span> <span class="n">set</span><span class="o"><</span><span class="n">T</span><span class="o">></span> <span class="o">&</span><span class="n">primes</span><span class="p">)</span> <span class="p">{</span></span>
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<span class="code-line"> <span class="n">vector</span><span class="o"><</span> <span class="n">pair</span><span class="o"><</span><span class="n">T</span><span class="p">,</span><span class="n">T</span><span class="o">></span> <span class="o">></span> <span class="n">res</span><span class="p">;</span></span>
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<span class="code-line"> <span class="k">auto</span> <span class="n">digs</span> <span class="o">=</span> <span class="n">getDigs</span><span class="o"><</span><span class="n">T</span><span class="o">></span><span class="p">(</span><span class="n">prime</span><span class="p">);</span></span>
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<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="kt">size_t</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span> <span class="n">i</span> <span class="o"><=</span> <span class="n">digs</span><span class="p">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">;</span> <span class="o">++</span><span class="n">i</span><span class="p">){</span></span>
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<span class="code-line"> <span class="n">T</span> <span class="n">q1</span> <span class="o">=</span> <span class="n">getNum</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">T</span><span class="o">></span><span class="p">(</span><span class="n">digs</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span> <span class="n">digs</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span> <span class="o">+</span> <span class="n">i</span><span class="p">));</span></span>
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<span class="code-line"> <span class="n">T</span> <span class="n">q2</span> <span class="o">=</span> <span class="n">getNum</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">T</span><span class="o">></span><span class="p">(</span><span class="n">digs</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span> <span class="o">+</span> <span class="n">i</span><span class="p">,</span> <span class="n">digs</span><span class="p">.</span><span class="n">end</span><span class="p">()));</span></span>
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<span class="code-line"></span>
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||||
<span class="code-line"> <span class="k">if</span> <span class="p">(</span> <span class="p">(</span><span class="n">primes</span><span class="p">.</span><span class="n">find</span><span class="p">(</span><span class="n">q1</span><span class="p">)</span> <span class="o">!=</span> <span class="n">primes</span><span class="p">.</span><span class="n">end</span><span class="p">())</span></span>
|
||||
<span class="code-line"> <span class="o">&&</span> <span class="p">(</span><span class="n">primes</span><span class="p">.</span><span class="n">find</span><span class="p">(</span><span class="n">q2</span><span class="p">)</span> <span class="o">!=</span> <span class="n">primes</span><span class="p">.</span><span class="n">end</span><span class="p">())</span> <span class="o">&&</span> <span class="p">(</span><span class="n">digs</span><span class="p">.</span><span class="n">at</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">)</span> <span class="p">){</span></span>
|
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<span class="code-line"> <span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">make_pair</span><span class="p">(</span><span class="n">q1</span><span class="p">,</span><span class="n">q2</span><span class="p">));</span></span>
|
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<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="k">return</span> <span class="n">res</span><span class="p">;</span></span>
|
||||
<span class="code-line"><span class="p">}</span></span>
|
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<span class="code-line"></span>
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<span class="code-line"><span class="c1">// removes all (p,q) that (p,q) in edges but (q,p) is not</span></span>
|
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<span class="code-line"><span class="k">template</span> <span class="o"><</span><span class="k">class</span> <span class="nc">T</span><span class="o">></span></span>
|
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<span class="code-line"><span class="kt">void</span> <span class="n">delBadEdges</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span> <span class="n">pair</span><span class="o"><</span><span class="n">T</span><span class="p">,</span><span class="n">T</span><span class="o">></span> <span class="o">></span> <span class="o">&</span><span class="n">edges</span><span class="p">){</span></span>
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<span class="code-line"> <span class="n">map</span><span class="o"><</span> <span class="kt">int64_t</span><span class="p">,</span> <span class="kt">int</span> <span class="o">></span> <span class="n">mults</span><span class="p">;</span> <span class="c1">// contains counts of p * q</span></span>
|
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<span class="code-line"></span>
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<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">p</span><span class="o">:</span> <span class="n">edges</span><span class="p">)</span> <span class="p">{</span></span>
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<span class="code-line"> <span class="kt">int64_t</span> <span class="n">key</span> <span class="o">=</span> <span class="n">p</span><span class="p">.</span><span class="n">first</span> <span class="o">*</span> <span class="n">p</span><span class="p">.</span><span class="n">second</span><span class="p">;</span></span>
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||||
<span class="code-line"> <span class="k">if</span> <span class="p">(</span> <span class="n">mults</span><span class="p">.</span><span class="n">find</span><span class="p">(</span><span class="n">key</span><span class="p">)</span> <span class="o">!=</span> <span class="n">mults</span><span class="p">.</span><span class="n">end</span><span class="p">()</span> <span class="p">)</span></span>
|
||||
<span class="code-line"> <span class="n">mults</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span><span class="p">;</span></span>
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<span class="code-line"> <span class="k">else</span></span>
|
||||
<span class="code-line"> <span class="n">mults</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="n">vector</span><span class="o"><</span> <span class="n">pair</span><span class="o"><</span><span class="n">T</span><span class="p">,</span><span class="n">T</span><span class="o">></span> <span class="o">></span> <span class="n">res</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">p</span><span class="o">:</span> <span class="n">edges</span><span class="p">)</span> <span class="p">{</span></span>
|
||||
<span class="code-line"> <span class="kt">int64_t</span> <span class="n">key</span> <span class="o">=</span> <span class="n">p</span><span class="p">.</span><span class="n">first</span> <span class="o">*</span> <span class="n">p</span><span class="p">.</span><span class="n">second</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="k">if</span> <span class="p">(</span> <span class="n">mults</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">==</span> <span class="mi">2</span> <span class="p">){</span></span>
|
||||
<span class="code-line"> <span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">p</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="c1">// edge (p,q) is already exists</span></span>
|
||||
<span class="code-line"> <span class="n">mults</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="n">swap</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="n">edges</span><span class="p">);</span></span>
|
||||
<span class="code-line"><span class="p">}</span></span>
|
||||
<span class="code-line"></span>
|
||||
<span class="code-line"><span class="k">template</span> <span class="o"><</span><span class="k">class</span> <span class="nc">T</span><span class="o">></span> </span>
|
||||
<span class="code-line"><span class="n">set</span><span class="o"><</span><span class="n">T</span><span class="o">></span> <span class="n">getUniqNums</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span> <span class="n">pair</span><span class="o"><</span><span class="n">T</span><span class="p">,</span><span class="n">T</span><span class="o">></span> <span class="o">></span> <span class="o">&</span><span class="n">edges</span><span class="p">){</span></span>
|
||||
<span class="code-line"> <span class="n">set</span><span class="o"><</span><span class="n">T</span><span class="o">></span> <span class="n">res</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">p</span><span class="o">:</span> <span class="n">edges</span><span class="p">)</span> <span class="p">{</span></span>
|
||||
<span class="code-line"> <span class="n">res</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">p</span><span class="p">.</span><span class="n">first</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="n">res</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">p</span><span class="p">.</span><span class="n">second</span><span class="p">);</span> </span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="k">return</span> <span class="n">res</span><span class="p">;</span></span>
|
||||
<span class="code-line"><span class="p">}</span></span>
|
||||
<span class="code-line"></span>
|
||||
<span class="code-line"><span class="k">template</span> <span class="o"><</span><span class="k">class</span> <span class="nc">T</span><span class="o">></span></span>
|
||||
<span class="code-line"><span class="kt">void</span> <span class="n">getNeedSet</span><span class="p">(</span><span class="n">Graph</span> <span class="o">&</span><span class="n">g</span><span class="p">,</span> <span class="n">Graph</span><span class="o">::</span><span class="n">vertex_descriptor</span> <span class="n">st</span><span class="p">,</span><span class="kt">int</span> <span class="n">depth</span><span class="p">,</span> </span>
|
||||
<span class="code-line"> <span class="n">set</span><span class="o"><</span><span class="n">Graph</span><span class="o">::</span><span class="n">vertex_descriptor</span><span class="o">></span> <span class="n">cur_set</span><span class="p">,</span> <span class="k">const</span> <span class="n">map</span><span class="o"><</span><span class="n">Graph</span><span class="o">::</span><span class="n">vertex_descriptor</span><span class="p">,</span> <span class="n">T</span><span class="o">></span> <span class="o">&</span><span class="n">vert_prime</span><span class="p">,</span></span>
|
||||
<span class="code-line"> <span class="n">vector</span><span class="o"><</span> <span class="n">set</span><span class="o"><</span><span class="n">Graph</span><span class="o">::</span><span class="n">vertex_descriptor</span><span class="o">></span> <span class="o">></span> <span class="o">&</span><span class="n">v_out</span><span class="p">){</span></span>
|
||||
<span class="code-line"> <span class="k">auto</span> <span class="n">edges</span> <span class="o">=</span> <span class="n">out_edges</span><span class="p">(</span><span class="n">st</span><span class="p">,</span> <span class="n">g</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="n">vector</span><span class="o"><</span> <span class="n">Graph</span><span class="o">::</span><span class="n">vertex_descriptor</span> <span class="o">></span> <span class="n">adj_verts</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">e_it</span> <span class="o">=</span> <span class="n">edges</span><span class="p">.</span><span class="n">first</span><span class="p">;</span> <span class="n">e_it</span> <span class="o">!=</span> <span class="n">edges</span><span class="p">.</span><span class="n">second</span><span class="p">;</span> <span class="o">++</span><span class="n">e_it</span><span class="p">)</span></span>
|
||||
<span class="code-line"> <span class="n">adj_verts</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">target</span><span class="p">(</span><span class="o">*</span><span class="n">e_it</span><span class="p">,</span><span class="n">g</span><span class="p">));</span></span>
|
||||
<span class="code-line"></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">prev_v</span><span class="o">:</span> <span class="n">cur_set</span><span class="p">)</span></span>
|
||||
<span class="code-line"> <span class="k">if</span> <span class="p">(</span> <span class="n">find</span><span class="p">(</span><span class="n">adj_verts</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span> <span class="n">adj_verts</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span> <span class="n">prev_v</span><span class="p">)</span> <span class="o">==</span> <span class="n">adj_verts</span><span class="p">.</span><span class="n">end</span><span class="p">()</span> <span class="p">)</span></span>
|
||||
<span class="code-line"> <span class="k">return</span><span class="p">;</span></span>
|
||||
<span class="code-line"></span>
|
||||
<span class="code-line"> <span class="n">cur_set</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">st</span><span class="p">);</span></span>
|
||||
<span class="code-line"></span>
|
||||
<span class="code-line"> <span class="k">if</span> <span class="p">(</span> <span class="n">depth</span> <span class="o">==</span> <span class="mi">1</span> <span class="p">){</span></span>
|
||||
<span class="code-line"> <span class="n">v_out</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">cur_set</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="k">return</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">v</span><span class="o">:</span> <span class="n">adj_verts</span><span class="p">){</span></span>
|
||||
<span class="code-line"> <span class="k">if</span> <span class="p">(</span> <span class="p">(</span><span class="n">vert_prime</span><span class="p">.</span><span class="n">at</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="o"><</span> <span class="n">vert_prime</span><span class="p">.</span><span class="n">at</span><span class="p">(</span><span class="n">st</span><span class="p">))</span> <span class="p">)</span></span>
|
||||
<span class="code-line"> <span class="k">continue</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="n">getNeedSet</span><span class="p">(</span><span class="n">g</span><span class="p">,</span><span class="n">v</span><span class="p">,</span><span class="n">depth</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">cur_set</span><span class="p">,</span> <span class="n">vert_prime</span><span class="p">,</span> <span class="n">v_out</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"><span class="p">}</span></span>
|
||||
<span class="code-line"></span>
|
||||
<span class="code-line"><span class="kt">int</span> <span class="n">main</span><span class="p">(</span><span class="kt">int</span> <span class="n">argc</span><span class="p">,</span> <span class="kt">char</span> <span class="o">**</span><span class="n">argv</span><span class="p">)</span> <span class="p">{</span></span>
|
||||
<span class="code-line"> <span class="k">const</span> <span class="kt">int</span> <span class="n">MAX_VAL</span> <span class="o">=</span> <span class="mi">100000000</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="n">vector</span><span class="o"><</span> <span class="kt">long</span> <span class="o">></span> <span class="n">v_primes</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="n">primesieve</span><span class="o">::</span><span class="n">generate_primes</span><span class="p">(</span><span class="n">MAX_VAL</span><span class="p">,</span> <span class="o">&</span><span class="n">v_primes</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="n">set</span><span class="o"><</span> <span class="kt">long</span> <span class="o">></span> <span class="n">s_primes</span><span class="p">(</span><span class="n">v_primes</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span> <span class="n">v_primes</span><span class="p">.</span><span class="n">end</span><span class="p">());</span></span>
|
||||
<span class="code-line"></span>
|
||||
<span class="code-line"> <span class="n">cout</span> <span class="o"><<</span> <span class="s">"Number of primes is "</span> <span class="o"><<</span> <span class="n">v_primes</span><span class="p">.</span><span class="n">size</span><span class="p">()</span> <span class="o"><<</span> <span class="n">endl</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="n">v_primes</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span></span>
|
||||
<span class="code-line"></span>
|
||||
<span class="code-line"> <span class="n">vector</span><span class="o"><</span> <span class="n">pair</span><span class="o"><</span> <span class="kt">long</span><span class="p">,</span><span class="kt">long</span> <span class="o">></span> <span class="o">></span> <span class="n">all_edges</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">pr</span><span class="o">:</span> <span class="n">s_primes</span><span class="p">){</span></span>
|
||||
<span class="code-line"> <span class="k">auto</span> <span class="n">t_v</span> <span class="o">=</span> <span class="n">getPrimePairs</span><span class="p">(</span><span class="n">pr</span><span class="p">,</span> <span class="n">s_primes</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="n">copy</span><span class="p">(</span><span class="n">t_v</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="n">t_v</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="n">back_inserter</span><span class="p">(</span><span class="n">all_edges</span><span class="p">));</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="n">cout</span> <span class="o"><<</span> <span class="s">"There are "</span> <span class="o"><<</span> <span class="n">all_edges</span><span class="p">.</span><span class="n">size</span><span class="p">()</span> <span class="o"><<</span> <span class="s">" edges"</span> <span class="o"><<</span> <span class="n">endl</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="n">delBadEdges</span><span class="p">(</span><span class="n">all_edges</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="n">cout</span> <span class="o"><<</span> <span class="s">"After deleting bad edges: "</span> <span class="o"><<</span> <span class="n">all_edges</span><span class="p">.</span><span class="n">size</span><span class="p">()</span> <span class="o"><<</span> <span class="s">" edges"</span> <span class="o"><<</span> <span class="n">endl</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="c1">// We only need this primes</span></span>
|
||||
<span class="code-line"> <span class="n">s_primes</span> <span class="o">=</span> <span class="n">getUniqNums</span><span class="p">(</span><span class="n">all_edges</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="n">map</span><span class="o"><</span> <span class="n">Graph</span><span class="o">::</span><span class="n">vertex_descriptor</span><span class="p">,</span> <span class="kt">long</span> <span class="o">></span> <span class="n">vert_prime</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="n">map</span><span class="o"><</span> <span class="kt">long</span><span class="p">,</span> <span class="n">Graph</span><span class="o">::</span><span class="n">vertex_descriptor</span> <span class="o">></span> <span class="n">prime_vert</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="n">Graph</span> <span class="n">g</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">pr</span><span class="o">:</span> <span class="n">s_primes</span><span class="p">){</span></span>
|
||||
<span class="code-line"> <span class="n">vert_prime</span><span class="p">[</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">g</span><span class="p">)]</span> <span class="o">=</span> <span class="n">pr</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">v</span><span class="o">:</span> <span class="n">vert_prime</span><span class="p">){</span></span>
|
||||
<span class="code-line"> <span class="n">prime_vert</span><span class="p">[</span><span class="n">v</span><span class="p">.</span><span class="n">second</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span><span class="p">.</span><span class="n">first</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">p</span><span class="o">:</span> <span class="n">all_edges</span><span class="p">)</span></span>
|
||||
<span class="code-line"> <span class="n">add_edge</span><span class="p">(</span><span class="n">prime_vert</span><span class="p">.</span><span class="n">at</span><span class="p">(</span><span class="n">p</span><span class="p">.</span><span class="n">first</span><span class="p">),</span><span class="n">prime_vert</span><span class="p">.</span><span class="n">at</span><span class="p">(</span><span class="n">p</span><span class="p">.</span><span class="n">second</span><span class="p">),</span><span class="n">g</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="k">auto</span> <span class="n">all_vertices</span> <span class="o">=</span> <span class="n">vertices</span><span class="p">(</span><span class="n">g</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="n">vector</span><span class="o"><</span> <span class="n">set</span><span class="o"><</span><span class="n">Graph</span><span class="o">::</span><span class="n">vertex_descriptor</span><span class="o">></span> <span class="o">></span> <span class="n">goods</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">v_it</span> <span class="o">=</span> <span class="n">all_vertices</span><span class="p">.</span><span class="n">first</span><span class="p">;</span> <span class="n">v_it</span> <span class="o">!=</span> <span class="n">all_vertices</span><span class="p">.</span><span class="n">second</span><span class="p">;</span> <span class="o">++</span><span class="n">v_it</span><span class="p">){</span></span>
|
||||
<span class="code-line"> <span class="n">getNeedSet</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="o">*</span><span class="n">v_it</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span> <span class="n">set</span><span class="o"><</span><span class="n">Graph</span><span class="o">::</span><span class="n">vertex_descriptor</span><span class="o">></span><span class="p">(),</span> <span class="n">vert_prime</span><span class="p">,</span> <span class="n">goods</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="n">vector</span><span class="o"><</span> <span class="n">pair</span><span class="o"><</span><span class="kt">size_t</span><span class="p">,</span> <span class="kt">size_t</span><span class="o">></span> <span class="o">></span> <span class="n">good_sums</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="kt">size_t</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">i</span> <span class="o"><</span> <span class="n">goods</span><span class="p">.</span><span class="n">size</span><span class="p">();</span> <span class="o">++</span><span class="n">i</span><span class="p">){</span></span>
|
||||
<span class="code-line"> <span class="n">cout</span> <span class="o"><<</span> <span class="s">"Good set #"</span> <span class="o"><<</span> <span class="n">i</span><span class="o">+</span><span class="mi">1</span> <span class="o"><<</span> <span class="s">": "</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="kt">size_t</span> <span class="n">cur_sum</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="k">for</span> <span class="p">(</span><span class="k">auto</span> <span class="n">el</span><span class="o">:</span> <span class="n">goods</span><span class="p">[</span><span class="n">i</span><span class="p">]){</span></span>
|
||||
<span class="code-line"> <span class="n">el</span> <span class="o">=</span> <span class="n">vert_prime</span><span class="p">.</span><span class="n">at</span><span class="p">(</span><span class="n">el</span><span class="p">);</span></span>
|
||||
<span class="code-line"> <span class="n">cur_sum</span> <span class="o">+=</span> <span class="n">el</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="n">cout</span> <span class="o"><<</span> <span class="n">el</span> <span class="o"><<</span> <span class="s">" "</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="n">cout</span> <span class="o"><<</span> <span class="n">endl</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="n">good_sums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">make_pair</span><span class="p">(</span><span class="n">cur_sum</span><span class="p">,</span> <span class="n">i</span><span class="p">));</span></span>
|
||||
<span class="code-line"> <span class="p">}</span></span>
|
||||
<span class="code-line"> <span class="k">if</span> <span class="p">(</span> <span class="o">!</span><span class="n">good_sums</span><span class="p">.</span><span class="n">empty</span><span class="p">()</span> <span class="p">)</span></span>
|
||||
<span class="code-line"> <span class="n">cout</span> <span class="o"><<</span> <span class="s">"Result is "</span> <span class="o"><<</span> <span class="n">min_element</span><span class="p">(</span><span class="n">good_sums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="n">good_sums</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span> <span class="p">[](</span><span class="n">pair</span><span class="o"><</span><span class="kt">size_t</span><span class="p">,</span> <span class="kt">size_t</span><span class="o">></span> <span class="n">a</span><span class="p">,</span> <span class="n">pair</span><span class="o"><</span><span class="kt">size_t</span><span class="p">,</span> <span class="kt">size_t</span><span class="o">></span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="p">.</span><span class="n">first</span> <span class="o"><</span> <span class="n">b</span><span class="p">.</span><span class="n">first</span><span class="p">;})</span><span class="o">-></span><span class="n">first</span> <span class="o"><<</span> <span class="n">endl</span><span class="p">;</span></span>
|
||||
<span class="code-line"> <span class="k">return</span> <span class="mi">0</span><span class="p">;</span></span>
|
||||
<span class="code-line"><span class="p">}</span></span>
|
||||
</pre></div>
|
||||
|
||||
|
||||
<p>Ответ: <strong>26033</strong></p>
|
||||
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||||
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mathjaxscript.type = 'text/javascript';
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mathjaxscript.src = '//cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML';
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