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<h2 class="fw-bold">4485번 - 녹색 옷을 입은 애가 젤다지?</h2>
<h4 id="-">분류 : 다익스트라</h4>
<h4 id="-">문제</h4>
<p>젤다의 전설 게임에서 화폐의 단위는 루피(rupee)다. 그런데 간혹 '도둑루피'라 불리는 검정색 루피도 존재하는데, 이걸 획득하면 오히려 소지한 루피가 감소하게 된다!</p>
<p>젤다의 전설 시리즈의 주인공, 링크는 지금 도둑루피만 가득한 N x N 크기의 동굴의 제일 왼쪽 위에 있다. [0][0]번 칸이기도 하다. 왜 이런 곳에 들어왔냐고 묻는다면 밖에서 사람들이 자꾸 "젤다의 전설에 나오는 녹색 애가 젤다지?"라고 물어봤기 때문이다. 링크가 녹색 옷을 입은 주인공이고 젤다는 그냥 잡혀있는 공주인데, 게임 타이틀에 젤다가 나와있다고 자꾸 사람들이 이렇게 착각하니까 정신병에 걸릴 위기에 놓인 것이다.</p>
<p>하여튼 젤다...아니 링크는 이 동굴의 반대편 출구, 제일 오른쪽 아래 칸인 [N-1][N-1]까지 이동해야 한다. 동굴의 각 칸마다 도둑루피가 있는데, 이 칸을 지나면 해당 도둑루피의 크기만큼 소지금을 잃게 된다. 링크는 잃는 금액을 최소로 하여 동굴 건너편까지 이동해야 하며, 한 번에 상하좌우 인접한 곳으로 1칸씩 이동할 수 있다.</p>
<p>링크가 잃을 수밖에 없는 최소 금액은 얼마일까?</p>
<h4 id="-">풀이</h4>
<p>한 지점에서 목표 지점으로 가는 데에 들어가는 비용을 구하는 문제이다.</p>
<p>비용이 없는 간선이라면 bfs를 사용하는 것이 적합하겠지만 비용이 있는 간선이기 때문에 다익스트라를 이용해서 풀이하였다.</p>
<p>비용과 목적지를 멤버변수로 갖는 Node 클래스를 정의하고 Comparable 인터페이스의 compareTo 메서드를 재정의하면서 코스트가 가장 낮은 노드가 우선순위 큐에서 뽑히도록 설계하였다.</p>
<p>dp를 이용하여 각 노드에 도착했을 때마다 비용을 갱신해주고 우선순위 큐에서 뽑은 노드의 비용이 dp의 값보다 크면 continue 해주었다.</p>
<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">util</span><span class="op">.</span><span class="im">Arrays</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">util</span><span class="op">.</span><span class="im">PriorityQueue</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">util</span><span class="op">.</span><span class="im">Scanner</span><span class="op">;</span></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="kw">class</span> <span class="bu">Node</span> <span class="kw">implements</span> <span class="bu">Comparable</span><span class="op"><</span><span class="bu">Node</span><span class="op">>{</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> x<span class="op">,</span>y<span class="op">,</span>cost<span class="op">;</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a> <span class="kw">public</span> <span class="bu">Node</span><span class="op">(</span><span class="dt">int</span> x<span class="op">,</span> <span class="dt">int</span> y<span class="op">,</span> <span class="dt">int</span> cost<span class="op">)</span> <span class="op">{</span></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a> <span class="kw">this</span><span class="op">.</span><span class="fu">x</span> <span class="op">=</span> x<span class="op">;</span></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a> <span class="kw">this</span><span class="op">.</span><span class="fu">y</span> <span class="op">=</span> y<span class="op">;</span></span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a> <span class="kw">this</span><span class="op">.</span><span class="fu">cost</span> <span class="op">=</span> cost<span class="op">;</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a> <span class="at">@Override</span></span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a> <span class="kw">public</span> <span class="dt">int</span> <span class="fu">compareTo</span><span class="op">(</span><span class="bu">Node</span> o<span class="op">)</span> <span class="op">{</span></span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> <span class="kw">this</span><span class="op">.</span><span class="fu">cost</span> <span class="op">-</span> o<span class="op">.</span><span class="fu">cost</span><span class="op">;</span></span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a><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="kw">public</span> <span class="kw">class</span> Main <span class="op">{</span></span>
<span id="cb1-21"><a href="#cb1-21" aria-hidden="true" tabindex="-1"></a> <span class="dt">static</span> <span class="dt">int</span><span class="op">[][]</span> arr<span class="op">,</span>dp<span class="op">;</span></span>
<span id="cb1-22"><a href="#cb1-22" aria-hidden="true" tabindex="-1"></a> <span class="dt">static</span> <span class="dt">int</span><span class="op">[]</span> dx <span class="op">=</span> <span class="op">{</span><span class="dv">1</span><span class="op">,-</span><span class="dv">1</span><span class="op">,</span><span class="dv">0</span><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">static</span> <span class="dt">int</span><span class="op">[]</span> dy <span class="op">=</span> <span class="op">{</span><span class="dv">0</span><span class="op">,</span><span class="dv">0</span><span class="op">,</span><span class="dv">1</span><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 class="dt">static</span> <span class="dt">int</span> n<span class="op">;</span></span>
<span id="cb1-25"><a href="#cb1-25" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-26"><a href="#cb1-26" 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="op">{</span></span>
<span id="cb1-27"><a href="#cb1-27" aria-hidden="true" tabindex="-1"></a> <span class="bu">Scanner</span> sc <span class="op">=</span> <span class="kw">new</span> <span class="bu">Scanner</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="cb1-28"><a href="#cb1-28" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> cnt <span class="op">=</span> <span class="dv">1</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="cf">while</span> <span class="op">(</span><span class="kw">true</span><span class="op">)</span> <span class="op">{</span></span>
<span id="cb1-31"><a href="#cb1-31" aria-hidden="true" tabindex="-1"></a> n <span class="op">=</span> sc<span class="op">.</span><span class="fu">nextInt</span><span class="op">();</span></span>
<span id="cb1-32"><a href="#cb1-32" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> <span class="op">(</span>n <span class="op">==</span> <span class="dv">0</span><span class="op">)</span> <span class="cf">break</span><span class="op">;</span></span>
<span id="cb1-33"><a href="#cb1-33" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-34"><a href="#cb1-34" aria-hidden="true" tabindex="-1"></a> arr <span class="op">=</span> <span class="kw">new</span> <span class="dt">int</span><span class="op">[</span>n<span class="op">][</span>n<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="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> n<span class="op">;</span> i<span class="op">++)</span></span>
<span id="cb1-37"><a href="#cb1-37" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> <span class="op">(</span><span class="dt">int</span> j <span class="op">=</span> <span class="dv">0</span><span class="op">;</span> j <span class="op"><</span> n<span class="op">;</span> j<span class="op">++)</span></span>
<span id="cb1-38"><a href="#cb1-38" aria-hidden="true" tabindex="-1"></a> arr<span class="op">[</span>i<span class="op">][</span>j<span class="op">]</span> <span class="op">=</span> sc<span class="op">.</span><span class="fu">nextInt</span><span class="op">();</span></span>
<span id="cb1-39"><a href="#cb1-39" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-40"><a href="#cb1-40" 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">printf</span><span class="op">(</span><span class="st">"Problem </span><span class="sc">%d</span><span class="st">: </span><span class="sc">%d\n</span><span class="st">"</span><span class="op">,</span>cnt<span class="op">,</span><span class="fu">game</span><span class="op">());</span></span>
<span id="cb1-41"><a href="#cb1-41" aria-hidden="true" tabindex="-1"></a> cnt<span class="op">++;</span></span>
<span id="cb1-42"><a href="#cb1-42" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-43"><a href="#cb1-43" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-44"><a href="#cb1-44" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-45"><a href="#cb1-45" aria-hidden="true" tabindex="-1"></a> <span class="dt">static</span> <span class="dt">int</span> <span class="fu">game</span><span class="op">()</span> <span class="op">{</span></span>
<span id="cb1-46"><a href="#cb1-46" aria-hidden="true" tabindex="-1"></a> <span class="bu">PriorityQueue</span><span class="op"><</span><span class="bu">Node</span><span class="op">></span> queue <span class="op">=</span> <span class="kw">new</span> <span class="bu">PriorityQueue</span><span class="op"><>();</span></span>
<span id="cb1-47"><a href="#cb1-47" aria-hidden="true" tabindex="-1"></a> queue<span class="op">.</span><span class="fu">add</span><span class="op">(</span><span class="kw">new</span> <span class="bu">Node</span><span class="op">(</span><span class="dv">0</span><span class="op">,</span><span class="dv">0</span><span class="op">,</span>arr<span class="op">[</span><span class="dv">0</span><span class="op">][</span><span class="dv">0</span><span class="op">]));</span></span>
<span id="cb1-48"><a href="#cb1-48" aria-hidden="true" tabindex="-1"></a> dp <span class="op">=</span> <span class="kw">new</span> <span class="dt">int</span><span class="op">[</span>n<span class="op">][</span>n<span class="op">];</span></span>
<span id="cb1-49"><a href="#cb1-49" 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> n<span class="op">;</span> i<span class="op">++)</span></span>
<span id="cb1-50"><a href="#cb1-50" aria-hidden="true" tabindex="-1"></a> <span class="bu">Arrays</span><span class="op">.</span><span class="fu">fill</span><span class="op">(</span>dp<span class="op">[</span>i<span class="op">],(</span><span class="dt">int</span><span class="op">)</span><span class="fl">1e9</span><span class="op">);</span></span>
<span id="cb1-51"><a href="#cb1-51" aria-hidden="true" tabindex="-1"></a> dp<span class="op">[</span><span class="dv">0</span><span class="op">][</span><span class="dv">0</span><span class="op">]</span> <span class="op">=</span> arr<span class="op">[</span><span class="dv">0</span><span class="op">][</span><span class="dv">0</span><span class="op">];</span></span>
<span id="cb1-52"><a href="#cb1-52" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-53"><a href="#cb1-53" 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="cb1-54"><a href="#cb1-54" aria-hidden="true" tabindex="-1"></a> <span class="bu">Node</span> node <span class="op">=</span> queue<span class="op">.</span><span class="fu">poll</span><span class="op">();</span></span>
<span id="cb1-55"><a href="#cb1-55" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> <span class="op">(</span>node<span class="op">.</span><span class="fu">x</span> <span class="op">==</span> n<span class="op">-</span><span class="dv">1</span> <span class="op">&&</span> node<span class="op">.</span><span class="fu">y</span> <span class="op">==</span> n<span class="op">-</span><span class="dv">1</span><span class="op">)</span></span>
<span id="cb1-56"><a href="#cb1-56" aria-hidden="true" tabindex="-1"></a> <span class="cf">break</span><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>node<span class="op">.</span><span class="fu">cost</span> <span class="op">></span> dp<span class="op">[</span>node<span class="op">.</span><span class="fu">x</span><span class="op">][</span>node<span class="op">.</span><span class="fu">y</span><span class="op">])</span></span>
<span id="cb1-58"><a href="#cb1-58" aria-hidden="true" tabindex="-1"></a> <span class="cf">continue</span><span class="op">;</span></span>
<span id="cb1-59"><a href="#cb1-59" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> <span class="op">(</span><span class="dt">int</span> t <span class="op">=</span> <span class="dv">0</span><span class="op">;</span> t <span class="op"><</span> <span class="dv">4</span><span class="op">;</span> t<span class="op">++)</span> <span class="op">{</span></span>
<span id="cb1-60"><a href="#cb1-60" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> nx <span class="op">=</span> node<span class="op">.</span><span class="fu">x</span> <span class="op">+</span> dx<span class="op">[</span>t<span class="op">];</span></span>
<span id="cb1-61"><a href="#cb1-61" aria-hidden="true" tabindex="-1"></a> <span class="dt">int</span> ny <span class="op">=</span> node<span class="op">.</span><span class="fu">y</span> <span class="op">+</span> dy<span class="op">[</span>t<span class="op">];</span></span>
<span id="cb1-62"><a href="#cb1-62" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-63"><a href="#cb1-63" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> <span class="op">(</span><span class="dv">0</span> <span class="op"><=</span> nx <span class="op">&&</span> nx <span class="op"><</span> n <span class="op">&&</span> <span class="dv">0</span> <span class="op"><=</span> ny <span class="op">&&</span> ny <span class="op"><</span> n<span class="op">)</span> <span class="op">{</span></span>
<span id="cb1-64"><a href="#cb1-64" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> <span class="op">(</span>node<span class="op">.</span><span class="fu">cost</span> <span class="op">+</span> arr<span class="op">[</span>nx<span class="op">][</span>ny<span class="op">]</span> <span class="op"><</span> dp<span class="op">[</span>nx<span class="op">][</span>ny<span class="op">])</span> <span class="op">{</span></span>
<span id="cb1-65"><a href="#cb1-65" aria-hidden="true" tabindex="-1"></a> dp<span class="op">[</span>nx<span class="op">][</span>ny<span class="op">]</span> <span class="op">=</span> node<span class="op">.</span><span class="fu">cost</span> <span class="op">+</span> arr<span class="op">[</span>nx<span class="op">][</span>ny<span class="op">];</span></span>
<span id="cb1-66"><a href="#cb1-66" aria-hidden="true" tabindex="-1"></a> queue<span class="op">.</span><span class="fu">add</span><span class="op">(</span><span class="kw">new</span> <span class="bu">Node</span><span class="op">(</span>nx<span class="op">,</span> ny<span class="op">,</span> node<span class="op">.</span><span class="fu">cost</span> <span class="op">+</span> arr<span class="op">[</span>nx<span class="op">][</span>ny<span class="op">]));</span></span>
<span id="cb1-67"><a href="#cb1-67" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-68"><a href="#cb1-68" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-69"><a href="#cb1-69" aria-hidden="true" tabindex="-1"></a> <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>
<span id="cb1-72"><a href="#cb1-72" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> dp<span class="op">[</span>n<span class="op">-</span><span class="dv">1</span><span class="op">][</span>n<span class="op">-</span><span class="dv">1</span><span class="op">];</span></span>
<span id="cb1-73"><a href="#cb1-73" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb1-74"><a href="#cb1-74" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
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