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<!DOCTYPE html><!--[if lt IE 7]> <html class="no-js lt-ie9 lt-ie8 lt-ie7"> <![endif]--><!--[if IE 7]> <html class="no-js lt-ie9 lt-ie8"> <![endif]--><!--[if IE 8]> <html class="no-js lt-ie9"> <![endif]--><!--[if gt IE 8]><!--><html class=no-js> <!--<![endif]--> <head><meta charset=utf-8><meta http-equiv=X-UA-Compatible content="IE=edge,chrome=1"><title>Моё решение задачи 60</title><meta name=description content><meta name=viewport content="width=device-width"><link rel=stylesheet href=../../theme/css/normalize.css><link href="https://fonts.googleapis.com/css?family=Forum|Oswald|PT+Sans|Philosopher|Ubuntu+Mono" rel=stylesheet><link rel=stylesheet href=../../theme/css/font-awesome.min.css><link rel=stylesheet href=../../theme/css/main.css><link rel=stylesheet href=../../theme/css/blog.css><link rel=stylesheet href=../../theme/css/github.css><link href=https://likemath.ru/feeds/all.atom.xml type=application/atom+xml rel=alternate title="Блог 529 Atom Feed"><link href=https://likemath.ru/feeds/all.rss.xml type=application/rss+xml rel=alternate title="Блог 529 RSS Feed"><script src=../../theme/js/vendor/modernizr-2.6.2.min.js></script></head> <body> <!--[if lt IE 7]>
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<![endif]--> <div id=wrapper> <header id=sidebar class=side-shadow> <hgroup id=site-header> <a id=site-title href=../..><h2><i class=icon-pencil></i> Блог 529</h2></a> <p id=site-desc> Project Euler и остальное </p> </hgroup> <nav> <ul id=nav-links> <li><a href=../../ >Главная</a></li> <li><a href=../../pages/projects.html>Мои проекты</a></li> <li><a href=../../pages/about.html>Об авторе</a></li> <li><a href=../../feeds/feed.atom.xml>Atom feed</a></li> </ul> </nav> <footer id=site-info> <p> Powered by Pelican. </p> </footer></header> <div id=post-container> <ol id=post-list> <li> <article class=post-entry> <header class=entry-header> <time class=post-time datetime=2015-07-17T17:40:00+03:00 pubdate> Пт 17 июля 2015 </time> <a href=../../posts/moio-reshenie-zadachi-60/ rel=bookmark><h1>Моё решение задачи&nbsp;60</h1></a> </header> <section class=post-content> <p>Необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после &#8220;склеивания&#8221; в любом порядке любых двух чисел из него тоже будет простое число. Здесь под процедурой &#8220;склеивания&#8221; 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> <p>Полное условие можно найти <a href="https://projecteuler.net/problem=60">тут</a></p> <p>Для начала, можно понять, что непосредственный перебор &#8220;в лоб&#8221; 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&nbsp;нет.</p> <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&nbsp;граф.</p> <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&nbsp;графе.</p> <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> <div class=highlight><pre><span class=code-line><span></span><span class=cp>#include</span> <span class=cpf>&lt;iostream&gt;</span><span class=cp></span></span>
<span class=code-line><span class=cp>#include</span> <span class=cpf>&lt;algorithm&gt;</span><span class=cp></span></span>
<span class=code-line><span class=cp>#include</span> <span class=cpf>&lt;vector&gt;</span><span class=cp></span></span>
<span class=code-line><span class=cp>#include</span> <span class=cpf>&lt;set&gt;</span><span class=cp></span></span>
<span class=code-line><span class=cp>#include</span> <span class=cpf>&lt;map&gt;</span><span class=cp></span></span>
<span class=code-line><span class=cp>#include</span> <span class=cpf>&lt;cstdint&gt;</span><span class=cp></span></span>
<span class=code-line></span>
<span class=code-line><span class=cp>#include</span> <span class=cpf>&lt;boost/graph/adjacency_list.hpp&gt;</span><span class=cp></span></span>
<span class=code-line><span class=cp>#include</span> <span class=cpf>&quot;primesieve.hpp&quot;</span><span class=cp></span></span>
<span class=code-line></span>
<span class=code-line><span class=k>using</span> <span class=k>namespace</span> <span class=n>std</span><span class=p>;</span></span>
<span class=code-line><span class=k>using</span> <span class=k>namespace</span> <span class=n>boost</span><span class=p>;</span></span>
<span class=code-line></span>
<span class=code-line><span class=k>typedef</span> <span class=n>adjacency_list</span><span class=o>&lt;</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>&gt;</span> <span class=n>Graph</span><span class=p>;</span></span>
<span class=code-line></span>
<span class=code-line><span class=k>template</span> <span class=o>&lt;</span><span class=k>class</span> <span class=nc>T</span><span class=o>&gt;</span> </span>
<span class=code-line><span class=n>vector</span><span class=o>&lt;</span> <span class=n>T</span> <span class=o>&gt;</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>
<span class=code-line> <span class=n>vector</span><span class=o>&lt;</span> <span class=n>T</span> <span class=o>&gt;</span> <span class=n>res</span><span class=p>;</span></span>
<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>
<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>
<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>
<span class=code-line> <span class=p>}</span></span>
<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>
<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>&lt;</span><span class=k>class</span> <span class=nc>T</span><span class=o>&gt;</span></span>
<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>&lt;</span><span class=n>T</span><span class=o>&gt;</span> <span class=o>&amp;</span><span class=n>digs</span><span class=p>){</span></span>
<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>
<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>
<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>
<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>
<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>
<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>&lt;</span><span class=k>class</span> <span class=nc>T</span><span class=o>&gt;</span></span>
<span class=code-line><span class=n>vector</span><span class=o>&lt;</span> <span class=n>pair</span><span class=o>&lt;</span><span class=n>T</span><span class=p>,</span><span class=n>T</span><span class=o>&gt;</span> <span class=o>&gt;</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>&lt;</span><span class=n>T</span><span class=o>&gt;</span> <span class=o>&amp;</span><span class=n>primes</span><span class=p>)</span> <span class=p>{</span></span>
<span class=code-line> <span class=n>vector</span><span class=o>&lt;</span> <span class=n>pair</span><span class=o>&lt;</span><span class=n>T</span><span class=p>,</span><span class=n>T</span><span class=o>&gt;</span> <span class=o>&gt;</span> <span class=n>res</span><span class=p>;</span></span>
<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>&lt;</span><span class=n>T</span><span class=o>&gt;</span><span class=p>(</span><span class=n>prime</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>1</span><span class=p>;</span> <span class=n>i</span> <span class=o>&lt;=</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>
<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>&lt;</span><span class=n>T</span><span class=o>&gt;</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>
<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>&lt;</span><span class=n>T</span><span class=o>&gt;</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>
<span class=code-line></span>
<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>&amp;&amp;</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>&amp;&amp;</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>
<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>
<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>
<span class=code-line></span>
<span class=code-line><span class=c1>// removes all (p,q) that (p,q) in edges but (q,p) is not</span></span>
<span class=code-line><span class=k>template</span> <span class=o>&lt;</span><span class=k>class</span> <span class=nc>T</span><span class=o>&gt;</span></span>
<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>&lt;</span> <span class=n>pair</span><span class=o>&lt;</span><span class=n>T</span><span class=p>,</span><span class=n>T</span><span class=o>&gt;</span> <span class=o>&gt;</span> <span class=o>&amp;</span><span class=n>edges</span><span class=p>){</span></span>
<span class=code-line> <span class=n>map</span><span class=o>&lt;</span> <span class=kt>int64_t</span><span class=p>,</span> <span class=kt>int</span> <span class=o>&gt;</span> <span class=n>mults</span><span class=p>;</span> <span class=c1>// contains counts of p * q</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=nl>p</span><span class=p>:</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>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>
<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>&lt;</span> <span class=n>pair</span><span class=o>&lt;</span><span class=n>T</span><span class=p>,</span><span class=n>T</span><span class=o>&gt;</span> <span class=o>&gt;</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=nl>p</span><span class=p>:</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>&lt;</span><span class=k>class</span> <span class=nc>T</span><span class=o>&gt;</span> </span>
<span class=code-line><span class=n>set</span><span class=o>&lt;</span><span class=n>T</span><span class=o>&gt;</span> <span class=n>getUniqNums</span><span class=p>(</span><span class=n>vector</span><span class=o>&lt;</span> <span class=n>pair</span><span class=o>&lt;</span><span class=n>T</span><span class=p>,</span><span class=n>T</span><span class=o>&gt;</span> <span class=o>&gt;</span> <span class=o>&amp;</span><span class=n>edges</span><span class=p>){</span></span>
<span class=code-line> <span class=n>set</span><span class=o>&lt;</span><span class=n>T</span><span class=o>&gt;</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=nl>p</span><span class=p>:</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>&lt;</span><span class=k>class</span> <span class=nc>T</span><span class=o>&gt;</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>&amp;</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>&lt;</span><span class=n>Graph</span><span class=o>::</span><span class=n>vertex_descriptor</span><span class=o>&gt;</span> <span class=n>cur_set</span><span class=p>,</span> <span class=k>const</span> <span class=n>map</span><span class=o>&lt;</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>&gt;</span> <span class=o>&amp;</span><span class=n>vert_prime</span><span class=p>,</span></span>
<span class=code-line> <span class=n>vector</span><span class=o>&lt;</span> <span class=n>set</span><span class=o>&lt;</span><span class=n>Graph</span><span class=o>::</span><span class=n>vertex_descriptor</span><span class=o>&gt;</span> <span class=o>&gt;</span> <span class=o>&amp;</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>&lt;</span> <span class=n>Graph</span><span class=o>::</span><span class=n>vertex_descriptor</span> <span class=o>&gt;</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=nl>prev_v</span><span class=p>:</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=nl>v</span><span class=p>:</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>&lt;</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>&lt;</span> <span class=kt>long</span> <span class=o>&gt;</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>&amp;</span><span class=n>v_primes</span><span class=p>);</span></span>
<span class=code-line> <span class=n>set</span><span class=o>&lt;</span> <span class=kt>long</span> <span class=o>&gt;</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>&lt;&lt;</span> <span class=s>&quot;Number of primes is &quot;</span> <span class=o>&lt;&lt;</span> <span class=n>v_primes</span><span class=p>.</span><span class=n>size</span><span class=p>()</span> <span class=o>&lt;&lt;</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>&lt;</span> <span class=n>pair</span><span class=o>&lt;</span> <span class=kt>long</span><span class=p>,</span><span class=kt>long</span> <span class=o>&gt;</span> <span class=o>&gt;</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=nl>pr</span><span class=p>:</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>&lt;&lt;</span> <span class=s>&quot;There are &quot;</span> <span class=o>&lt;&lt;</span> <span class=n>all_edges</span><span class=p>.</span><span class=n>size</span><span class=p>()</span> <span class=o>&lt;&lt;</span> <span class=s>&quot; edges&quot;</span> <span class=o>&lt;&lt;</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>&lt;&lt;</span> <span class=s>&quot;After deleting bad edges: &quot;</span> <span class=o>&lt;&lt;</span> <span class=n>all_edges</span><span class=p>.</span><span class=n>size</span><span class=p>()</span> <span class=o>&lt;&lt;</span> <span class=s>&quot; edges&quot;</span> <span class=o>&lt;&lt;</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>&lt;</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>&gt;</span> <span class=n>vert_prime</span><span class=p>;</span></span>
<span class=code-line> <span class=n>map</span><span class=o>&lt;</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>&gt;</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=nl>pr</span><span class=p>:</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=nl>v</span><span class=p>:</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=nl>p</span><span class=p>:</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>&lt;</span> <span class=n>set</span><span class=o>&lt;</span><span class=n>Graph</span><span class=o>::</span><span class=n>vertex_descriptor</span><span class=o>&gt;</span> <span class=o>&gt;</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>&lt;</span><span class=n>Graph</span><span class=o>::</span><span class=n>vertex_descriptor</span><span class=o>&gt;</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>&lt;</span> <span class=n>pair</span><span class=o>&lt;</span><span class=kt>size_t</span><span class=p>,</span> <span class=kt>size_t</span><span class=o>&gt;</span> <span class=o>&gt;</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>&lt;</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>&lt;&lt;</span> <span class=s>&quot;Good set #&quot;</span> <span class=o>&lt;&lt;</span> <span class=n>i</span><span class=o>+</span><span class=mi>1</span> <span class=o>&lt;&lt;</span> <span class=s>&quot;: &quot;</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=nl>el</span><span class=p>:</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>&lt;&lt;</span> <span class=n>el</span> <span class=o>&lt;&lt;</span> <span class=s>&quot; &quot;</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>&lt;&lt;</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>&lt;&lt;</span> <span class=s>&quot;Result is &quot;</span> <span class=o>&lt;&lt;</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>&lt;</span><span class=kt>size_t</span><span class=p>,</span> <span class=kt>size_t</span><span class=o>&gt;</span> <span class=n>a</span><span class=p>,</span> <span class=n>pair</span><span class=o>&lt;</span><span class=kt>size_t</span><span class=p>,</span> <span class=kt>size_t</span><span class=o>&gt;</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>&lt;</span> <span class=n>b</span><span class=p>.</span><span class=n>first</span><span class=p>;})</span><span class=o>-&gt;</span><span class=n>first</span> <span class=o>&lt;&lt;</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> <p><strong><span class=caps>UPD</span>.</strong> Кажется, <code>getNeedSet</code> можно было реализовать гораздо проще, использую <span class=caps>BGL</span> посетителей (Visitors). Но, к сожалению, на этапе написания кода я про это&nbsp;забыл.</p> <script type=text/javascript>if (!document.getElementById('mathjaxscript_pelican_#%@#$@#')) {
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