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<h2 class="fw-bold">1613번 - 역사</h2>
<h4 id="-">분류 : 그래프 이론, 자료구조, 플로이드-워셜</h4>
<h4 id="-">제약조건</h4>
<ul>
<li><p>사건의 일어나 순서에 대해 전후관계가 입력으로 주어진다.</p>
</li>
<li><p>이 입력들을 기반으로 s개의 a,b 사건 쌍이 주어졌을 때 사건이 발생한 순서가 a가 먼저이면 -1을 b가 먼저이면 1을 알 수 없으면 0을 출력</p>
</li>
</ul>
<h4 id="-">설계</h4>
<ol>
<li><p>처음에는 위상 정렬을 사용하려 풀려 했지만 위상 정렬로는 임의의 두 사건이 주어졌을 때 해당 사건이 동위상인지 아닌지 판별할 방법이 없어서 기각했다.</p>
</li>
<li><p>두 번째로 생각한 방법은 bfs로 임의의 사건 t 마다 확실하게 t보다 위상이 뒤인 사건들을 Iterable한 자료 구조에 담아 <code>Map<Integer,Iterable<>></code> 의 타입으로 저장하는 것을 생각했다.</p>
<ul>
<li>임의의 사건 k가 t를 key로 하는 Iterable 자료구조에 포함된다면 t가 k보다 먼저 발생했다는 것을 알 수 있다.</li>
</ul>
</li>
<li><p>이 때 Iterable한 자료 구조 중 처음엔 List를 생각했지만 List에 element가 포함되어 있는 지 판별하는 데에는 O(n)의 시간복잡도가 소모되기 때문에 사건 쌍의 최대 개수가 50000개 인 것을 생각해보았을 때 O(1)로 접근이 가능한 Map으로 구현하였다.</p>
<ul>
<li>최종 bfs로 저장된 Map은 <code>Map<Integer,Map<Integer,Boolean>></code>으로 정했다.</li>
</ul>
</li>
<li>compare메서드를 구현해 int a,b가 매개변수로 들어왔을 때 a를 key로 한 <code>Map<Integer,Boolean></code> 자료구조에 b가 포함되는 지 containsKey() 메서드로 판별하고 그렇다면 -1을 return b를 key로 한 <code>Map<Integer,Boolean></code> 자료구조에 a가 포함된다면 1를 return 그렇지 않다면 0을 return하게 구현하였다.</li>
</ol>
<div class="sourceCode" id="cb1"><pre
class="sourceCode java"><code class="sourceCode java"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">import</span> <span class="im">java</span><span class="op">.</span><span class="im">io</span><span class="op">.</span><span class="im">BufferedReader</span><span class="op">;</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="kw">import</span> <span class="im">java</span><span class="op">.</span><span class="im">io</span><span class="op">.</span><span class="im">IOException</span><span class="op">;</span></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="kw">import</span> <span class="im">java</span><span class="op">.</span><span class="im">io</span><span class="op">.</span><span class="im">InputStreamReader</span><span class="op">;</span></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="kw">import</span> <span class="im">java</span><span class="op">.</span><span class="im">util</span><span class="op">.*;</span></span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="kw">public</span> <span class="kw">class</span> Main <span class="op">{</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a> <span class="dt">static</span> <span class="bu">Map</span><span class="op"><</span><span class="bu">Integer</span><span class="op">,</span><span class="bu">Map</span><span class="op"><</span><span class="bu">Integer</span><span class="op">,</span><span class="bu">Boolean</span><span class="op">>></span> isIncludeMap<span class="op">;</span></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a> <span class="dt">static</span> <span class="bu">List</span><span class="op"><</span><span class="bu">Integer</span><span class="op">>[]</span> orderArr<span class="op">;</span></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a> <span class="kw">public</span> <span class="dt">static</span> <span class="dt">void</span> <span class="fu">main</span><span class="op">(</span><span class="bu">String</span><span class="op">[]</span> args<span class="op">)</span> <span class="kw">throws</span> <span class="bu">IOException</span> <span class="op">{</span></span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a> <span class="bu">BufferedReader</span> bf <span class="op">=</span> <span class="kw">new</span> <span class="bu">BufferedReader</span><span class="op">(</span><span class="kw">new</span> <span class="bu">InputStreamReader</span><span class="op">(</span><span class="bu">System</span><span class="op">.</span><span class="fu">in</span><span class="op">));</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a> <span class="bu">String</span><span class="op">[]</span> s <span class="op">=</span> bf<span class="op">.</span><span class="fu">readLine</span><span class="op">().</span><span class="fu">split</span><span class="op">(</span><span class="st">" "</span><span class="op">);</span></span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> n <span class="op">=</span> <span class="bu">Integer</span><span class="op">.</span><span class="fu">parseInt</span><span class="op">(</span>s<span class="op">[</span><span class="dv">0</span><span class="op">]);</span></span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> k <span class="op">=</span> <span class="bu">Integer</span><span class="op">.</span><span class="fu">parseInt</span><span class="op">(</span>s<span class="op">[</span><span class="dv">1</span><span class="op">]);</span></span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a> orderArr <span class="op">=</span> <span class="kw">new</span> <span class="bu">List</span><span class="op">[</span>n<span class="op">+</span><span class="dv">1</span><span class="op">];</span></span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> <span class="op">(</span><span class="dt">int</span> i <span class="op">=</span> <span class="dv">1</span><span class="op">;</span> i <span class="op"><</span> n<span class="op">+</span><span class="dv">1</span><span class="op">;</span> i<span class="op">++)</span></span>
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a> orderArr<span class="op">[</span>i<span class="op">]</span> <span class="op">=</span> <span class="kw">new</span> <span class="bu">ArrayList</span><span class="op"><>();</span></span>
<span id="cb1-19"><a href="#cb1-19" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-20"><a href="#cb1-20" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> <span class="op">(</span><span class="dt">int</span> i <span class="op">=</span> <span class="dv">0</span><span class="op">;</span> i <span class="op"><</span> k<span class="op">;</span> i<span class="op">++)</span> <span class="op">{</span></span>
<span id="cb1-21"><a href="#cb1-21" aria-hidden="true" tabindex="-1"></a> <span class="bu">String</span><span class="op">[]</span> tmp <span class="op">=</span> bf<span class="op">.</span><span class="fu">readLine</span><span class="op">().</span><span class="fu">split</span><span class="op">(</span><span class="st">" "</span><span class="op">);</span></span>
<span id="cb1-22"><a href="#cb1-22" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> a <span class="op">=</span> <span class="bu">Integer</span><span class="op">.</span><span class="fu">parseInt</span><span class="op">(</span>tmp<span class="op">[</span><span class="dv">0</span><span class="op">]);</span></span>
<span id="cb1-23"><a href="#cb1-23" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> b <span class="op">=</span> <span class="bu">Integer</span><span class="op">.</span><span class="fu">parseInt</span><span class="op">(</span>tmp<span class="op">[</span><span class="dv">1</span><span class="op">]);</span></span>
<span id="cb1-24"><a href="#cb1-24" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-25"><a href="#cb1-25" aria-hidden="true" tabindex="-1"></a> orderArr<span class="op">[</span>a<span class="op">].</span><span class="fu">add</span><span class="op">(</span>b<span class="op">);</span></span>
<span id="cb1-26"><a href="#cb1-26" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-27"><a href="#cb1-27" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-28"><a href="#cb1-28" aria-hidden="true" tabindex="-1"></a> <span class="fu">isIncludeMapping</span><span class="op">();</span></span>
<span id="cb1-29"><a href="#cb1-29" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-30"><a href="#cb1-30" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> t <span class="op">=</span> <span class="bu">Integer</span><span class="op">.</span><span class="fu">parseInt</span><span class="op">(</span>bf<span class="op">.</span><span class="fu">readLine</span><span class="op">().</span><span class="fu">split</span><span class="op">(</span><span class="st">" "</span><span class="op">)[</span><span class="dv">0</span><span class="op">]);</span></span>
<span id="cb1-31"><a href="#cb1-31" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> <span class="op">(</span><span class="dt">int</span> i <span class="op">=</span> <span class="dv">0</span><span class="op">;</span> i <span class="op"><</span> t<span class="op">;</span> i<span class="op">++)</span> <span class="op">{</span></span>
<span id="cb1-32"><a href="#cb1-32" aria-hidden="true" tabindex="-1"></a> <span class="bu">String</span><span class="op">[]</span> tmp <span class="op">=</span> bf<span class="op">.</span><span class="fu">readLine</span><span class="op">().</span><span class="fu">split</span><span class="op">(</span><span class="st">" "</span><span class="op">);</span></span>
<span id="cb1-33"><a href="#cb1-33" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> a <span class="op">=</span> <span class="bu">Integer</span><span class="op">.</span><span class="fu">parseInt</span><span class="op">(</span>tmp<span class="op">[</span><span class="dv">0</span><span class="op">]);</span></span>
<span id="cb1-34"><a href="#cb1-34" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> b <span class="op">=</span> <span class="bu">Integer</span><span class="op">.</span><span class="fu">parseInt</span><span class="op">(</span>tmp<span class="op">[</span><span class="dv">1</span><span class="op">]);</span></span>
<span id="cb1-35"><a href="#cb1-35" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-36"><a href="#cb1-36" aria-hidden="true" tabindex="-1"></a> <span class="bu">System</span><span class="op">.</span><span class="fu">out</span><span class="op">.</span><span class="fu">println</span><span class="op">(</span><span class="fu">compare</span><span class="op">(</span>a<span class="op">,</span>b<span class="op">));</span></span>
<span id="cb1-37"><a href="#cb1-37" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-38"><a href="#cb1-38" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-39"><a href="#cb1-39" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-40"><a href="#cb1-40" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-41"><a href="#cb1-41" aria-hidden="true" tabindex="-1"></a> <span class="dt">static</span> <span class="dt">void</span> <span class="fu">isIncludeMapping</span><span class="op">()</span> <span class="op">{</span></span>
<span id="cb1-42"><a href="#cb1-42" aria-hidden="true" tabindex="-1"></a> isIncludeMap <span class="op">=</span> <span class="kw">new</span> <span class="bu">HashMap</span><span class="op"><>();</span></span>
<span id="cb1-43"><a href="#cb1-43" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> <span class="op">(</span><span class="dt">int</span> i <span class="op">=</span> <span class="dv">1</span><span class="op">;</span> i <span class="op"><</span> orderArr<span class="op">.</span><span class="fu">length</span><span class="op">;</span> i<span class="op">++)</span></span>
<span id="cb1-44"><a href="#cb1-44" aria-hidden="true" tabindex="-1"></a> isIncludeMap<span class="op">.</span><span class="fu">put</span><span class="op">(</span>i<span class="op">,</span><span class="fu">bfs</span><span class="op">(</span>i<span class="op">));</span></span>
<span id="cb1-45"><a href="#cb1-45" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-46"><a href="#cb1-46" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-47"><a href="#cb1-47" aria-hidden="true" tabindex="-1"></a> <span class="dt">static</span> <span class="bu">Map</span><span class="op"><</span><span class="bu">Integer</span><span class="op">,</span><span class="bu">Boolean</span><span class="op">></span> <span class="fu">bfs</span><span class="op">(</span><span class="dt">int</span> start<span class="op">)</span> <span class="op">{</span></span>
<span id="cb1-48"><a href="#cb1-48" aria-hidden="true" tabindex="-1"></a> <span class="bu">Queue</span><span class="op"><</span><span class="bu">Integer</span><span class="op">></span> queue <span class="op">=</span> <span class="kw">new</span> <span class="bu">LinkedList</span><span class="op"><>();</span></span>
<span id="cb1-49"><a href="#cb1-49" aria-hidden="true" tabindex="-1"></a> <span class="bu">Map</span><span class="op"><</span><span class="bu">Integer</span><span class="op">,</span><span class="bu">Boolean</span><span class="op">></span> res <span class="op">=</span> <span class="kw">new</span> <span class="bu">HashMap</span><span class="op"><>();</span></span>
<span id="cb1-50"><a href="#cb1-50" aria-hidden="true" tabindex="-1"></a> <span class="dt">boolean</span><span class="op">[]</span> visit <span class="op">=</span> <span class="kw">new</span> <span class="dt">boolean</span><span class="op">[</span>orderArr<span class="op">.</span><span class="fu">length</span><span class="op">];</span></span>
<span id="cb1-51"><a href="#cb1-51" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-52"><a href="#cb1-52" aria-hidden="true" tabindex="-1"></a> queue<span class="op">.</span><span class="fu">add</span><span class="op">(</span>start<span class="op">);</span></span>
<span id="cb1-53"><a href="#cb1-53" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-54"><a href="#cb1-54" aria-hidden="true" tabindex="-1"></a> <span class="cf">while</span> <span class="op">(</span>queue<span class="op">.</span><span class="fu">size</span><span class="op">()</span> <span class="op">></span> <span class="dv">0</span><span class="op">)</span> <span class="op">{</span></span>
<span id="cb1-55"><a href="#cb1-55" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> node <span class="op">=</span> queue<span class="op">.</span><span class="fu">poll</span><span class="op">();</span></span>
<span id="cb1-56"><a href="#cb1-56" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> <span class="op">(</span><span class="dt">int</span> num <span class="op">:</span> orderArr<span class="op">[</span>node<span class="op">])</span></span>
<span id="cb1-57"><a href="#cb1-57" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> <span class="op">(!</span>visit<span class="op">[</span>num<span class="op">])</span> <span class="op">{</span></span>
<span id="cb1-58"><a href="#cb1-58" aria-hidden="true" tabindex="-1"></a> visit<span class="op">[</span>num<span class="op">]</span> <span class="op">=</span> <span class="kw">true</span><span class="op">;</span></span>
<span id="cb1-59"><a href="#cb1-59" aria-hidden="true" tabindex="-1"></a> res<span class="op">.</span><span class="fu">put</span><span class="op">(</span>num<span class="op">,</span><span class="kw">true</span><span class="op">);</span></span>
<span id="cb1-60"><a href="#cb1-60" aria-hidden="true" tabindex="-1"></a> queue<span class="op">.</span><span class="fu">add</span><span class="op">(</span>num<span class="op">);</span></span>
<span id="cb1-61"><a href="#cb1-61" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-62"><a href="#cb1-62" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-63"><a href="#cb1-63" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> res<span class="op">;</span></span>
<span id="cb1-64"><a href="#cb1-64" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-65"><a href="#cb1-65" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-66"><a href="#cb1-66" aria-hidden="true" tabindex="-1"></a> <span class="dt">static</span> <span class="dt">int</span> <span class="fu">compare</span><span class="op">(</span><span class="dt">int</span> a<span class="op">,</span> <span class="dt">int</span> b<span class="op">)</span> <span class="op">{</span></span>
<span id="cb1-67"><a href="#cb1-67" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> <span class="op">(</span>isIncludeMap<span class="op">.</span><span class="fu">get</span><span class="op">(</span>a<span class="op">).</span><span class="fu">containsKey</span><span class="op">(</span>b<span class="op">))</span> <span class="cf">return</span> <span class="op">-</span><span class="dv">1</span><span class="op">;</span></span>
<span id="cb1-68"><a href="#cb1-68" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> <span class="op">(</span>isIncludeMap<span class="op">.</span><span class="fu">get</span><span class="op">(</span>b<span class="op">).</span><span class="fu">containsKey</span><span class="op">(</span>a<span class="op">))</span> <span class="cf">return</span> <span class="dv">1</span><span class="op">;</span></span>
<span id="cb1-69"><a href="#cb1-69" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> <span class="dv">0</span><span class="op">;</span></span>
<span id="cb1-70"><a href="#cb1-70" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-71"><a href="#cb1-71" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
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