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CodeObject/storage/zeta/_static/28311.html
2026-04-27 09:44:16 +09:00

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<!DOCTYPE html>
<html lang="ko">
<head>
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>BOJ 28311 - Offline</title>
<style>
:root {
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--code-bg: #f4f6fb;
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body {
margin: 0;
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radial-gradient(circle at 15% 0%, #f0efe9 0%, transparent 42%),
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pre {
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font-size: 1.35rem;
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opacity: 0.7;
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blockquote > :first-child { margin-top: 0; }
blockquote > :last-child { margin-bottom: 0; }
q {
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font-size: 1em;
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</style>
</head>
<body>
<main>
<header class="header">
<h1>벽의 가치</h1>
</header>
<article class="section">
<h2>문제</h2>
<p>Albert는 혼자서도 할 수 있는 보드 게임을 즐겨한다. 이 게임을 플레이 하기 위해 우선 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>R</mi></mrow></math></span><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi></mrow></math></span>열 크기의 격자 보드 게임판을 준비한 후 임의의 칸에 벽을 설치한다. 이후, <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math></span>개의 서로 다른 빈칸에 (즉, 벽이 없는 칸) 게임말을 하나씩 놓고, 마지막으로 남아있는 빈칸 중 한 곳을 골라 각 게임말이 도달해야하는 목적지를 정한다 - 목적지 칸의 위치를 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">&#x00028;</mo><mi>r</mi><mo>&#x0002C;</mo><mi>c</mi><mo stretchy="false">&#x00029;</mo></mrow></math></span>라 하자 (<span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>r</mi></mrow></math></span><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>c</mi></mrow></math></span>열). 편의상 게임말에는 1번부터 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math></span>번까지 번호가 붙어있다고 하고, <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>i</mi></mrow></math></span> 번째 말이 놓인 칸을 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">&#x00028;</mo><msub><mi>X</mi><mi>i</mi></msub><mo>&#x0002C;</mo><msub><mi>Y</mi><mi>i</mi></msub><mo stretchy="false">&#x00029;</mo></mrow></math></span>라 하자.</p>
<p>예를 들어 아래 그림의 좌측은 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>R</mi><mo>&#x0003D;</mo><mi>C</mi><mo>&#x0003D;</mo><mn>4</mn></mrow></math></span> 인 게임 보드판의 모습을 나타내고 <span class="marker">&#39;W&#39;</span> 로 표시된 칸은 벽을 나타낸다. 나머지 <span class="marker">&#39;.&#39;</span> 로 표시된 칸은 빈칸을 나타낸다. 편의상 이 문제에서 문자열 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>A</mi><mi>i</mi></msub></mrow></math></span><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>i</mi></mrow></math></span>번째 행의 게임 보드판의 모습을 나타내는 길이가 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi></mrow></math></span>인 문자열이라 하면, 이 예제의 게임 보드판은 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>A</mi><mo>&#x0003D;</mo><mo stretchy="false">[</mo></mrow></math></span><code>&quot;.WW.&quot;</code>, <code>&quot;..W.&quot;</code>, <code>&quot;.WW.&quot;</code>, <code>&quot;....&quot;</code><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">]</mo></mrow></math></span> 로 나타낼 수 있다. 우측 그림은 이후 Albert가 총 3개의 게임말을 놓은 칸과 목적지 칸을 나타내는데, <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo>&#x0003D;</mo><mo stretchy="false">[</mo><mn>1</mn><mo>&#x0002C;</mo><mn>1</mn><mo>&#x0002C;</mo><mn>4</mn><mo stretchy="false">]</mo></mrow></math></span>, <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Y</mi><mo>&#x0003D;</mo><mo stretchy="false">[</mo><mn>1</mn><mo>&#x0002C;</mo><mn>4</mn><mo>&#x0002C;</mo><mn>4</mn></mrow></math></span>], 그리고 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">&#x00028;</mo><mi>r</mi><mo>&#x0002C;</mo><mi>c</mi><mo stretchy="false">&#x00029;</mo><mo>&#x0003D;</mo><mo stretchy="false">&#x00028;</mo><mn>2</mn><mo>&#x0002C;</mo><mn>2</mn><mo stretchy="false">&#x00029;</mo></mrow></math></span> 이다.</p>
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" style="height: 132px; width: 320px;" /></p>
<p>이 때 각 말이 목적지에 도달하려면 벽이 없는 빈칸을 통해 상/하/좌/우로 이동할 수 있는데, <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>i</mi></mrow></math></span>번째 말이 목적지까지 이동해야하는 최소 거리를 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>d</mi><mi>i</mi></msub></mrow></math></span>라 하자. 위 예제에서 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>d</mi><mn>1</mn></msub><mo>&#x0003D;</mo><mn>2</mn></mrow></math></span> (하 -&gt; 우 로 이동하면 된다), <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>d</mi><mn>2</mn></msub><mo>&#x0003D;</mo><mn>9</mn></mrow></math></span>, 그리고 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>d</mi><mn>3</mn></msub><mo>&#x0003D;</mo><mn>6</mn></mrow></math></span> 임을 쉽게 알 수 있다. 모든 말이 이동해야하는 최소 거리의 총 합을 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mo>&#x0003D;</mo><msub><mo>&#x02211;</mo><mrow><mn>1</mn><mo>&#x02264;</mo><mi>i</mi><mo>&#x02264;</mo><mi>N</mi></mrow></msub><msub><mi>d</mi><mi>i</mi></msub></mrow></math></span> 라 하고, 이는 게임의 점수가 된다 - 이 예제의 게임 점수는 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>&#x0002B;</mo><mn>9</mn><mo>&#x0002B;</mo><mn>6</mn><mo>&#x0003D;</mo><mn>17</mn></mrow></math></span> 점이다.</p>
<p>이 놀이가 너무 심심하다고 느낀 Albet는 게임을 약간 변형해보기로 했다. 우선, 맨 처음의 보드 게임 상태를 유지한채로 벽을 하나 없애보기로 했다. 벽을 없애면 새로운 길이 생길 수 있으므로 게임의 점수는 같거나 낮아질텐데, 이 점수의 차이를 없어진 &quot;벽의 가치&quot;라 정의하자. 위 예제에서는 벽이 총 5칸 있으므로, 아래 그림 처럼 5가지 다른 방법으로 벽을 딱 하나 없앨 수 있다 - 벽이 없어진 칸은 알아보기 쉽도록 그림에서 <span class="marker">&#39;X&#39;</span>로 표시했지만 빈칸이므로 게임말이 지나갈 수 있다.</p>
<p style="text-align: center;"><img alt="" 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style="height: 134px; width: 900px;" /></p>
<p>위 다섯가지의 새로운 게임 보드에서 점수를 구한 후 기존 게임의 점수 (앞서 구한 17점) 과의 차이를 구하면 없앤 벽의 가치가 된다. 왼쪽 부터 순서대로 이를 구해보면:</p>
<ul>
<li>가장 좌측 게임의 점수는 17점으로 기존 게임의 점수와 동일하므로 (1, 2) 칸에 놓인 벽의 가치는 0이다.</li>
<li>좌측에서 두 번째 게임의 점수도 17점이고 (1, 3) 칸에 놓인 벽의 가치도 0이다.</li>
<li>좌측에서 세 번째 게임의 점수는 9점이고 (2, 3번 말의 최소 거리가 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>d</mi><mn>2</mn></msub><mo>&#x0003D;</mo><mn>3</mn></mrow></math></span>, <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>d</mi><mn>3</mn></msub><mo>&#x0003D;</mo><mn>4</mn></mrow></math></span>로 낮아지기 때문), 따라서 (2, 3) 칸에 놓인 벽의 가치는 8이다.</li>
<li>좌측에서 네 번째 게임의 점수는 13점이고 (2, 3번 말의 최소 거리가 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>d</mi><mn>2</mn></msub><mo>&#x0003D;</mo><mn>7</mn></mrow></math></span>, <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>d</mi><mn>3</mn></msub><mo>&#x0003D;</mo><mn>4</mn></mrow></math></span>로 낮아지기 때문), 따라서 (3, 2) 칸에 놓인 벽의 가치는 4이다.</li>
<li>좌측에서 다섯 번째 게임의 점수는 17점이고 따라서 (3, 3) 칸에 놓인 벽의 가치는 0점이다.</li>
<li>이렇게 다섯 개의 벽의 가치를 모두 구한 후 더해보면 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0</mn><mo>&#x0002B;</mo><mn>0</mn><mo>&#x0002B;</mo><mn>8</mn><mo>&#x0002B;</mo><mn>4</mn><mo>&#x0002B;</mo><mn>0</mn><mo>&#x0003D;</mo><mn>12</mn></mrow></math></span>가 된다 -- 이를 벽의 가치 총합이라 하자.</li>
</ul>
<p>게임 보드의 상태가 주어졌을 때, 기존 게임의 점수 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi></mrow></math></span>를 구하고 모든 벽의 가치 총합도 구해보자.</p>
</article>
<article class="section">
<h2>입력</h2>
<p>입력 첫 줄에 테스트 케이스의 수 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi></mrow></math></span> 가 주어진다.</p>
<p>각 테스트 케이스의 첫 줄에는 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>R</mi><mo>&#x0002C;</mo><mi>C</mi><mo>&#x0002C;</mo><mi>N</mi><mo>&#x0002C;</mo><mi>r</mi><mo>&#x0002C;</mo><mi>c</mi></mrow></math></span>가 공백으로 구분되어 주어진다. 다음 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math></span>줄에 걸쳐 각 줄에 한 쌍의 정수가 공백으로 구분되어 주어지는데 이는 순서대로 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>i</mi></mrow></math></span>번째 게임 말의 위치인 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>X</mi><mi>i</mi></msub><mo>&#x0002C;</mo><msub><mi>Y</mi><mi>i</mi></msub></mrow></math></span>를 나타낸다. 다음 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>R</mi></mrow></math></span>줄에 걸쳐 각 줄에 길이가 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi></mrow></math></span>인 문자열이 공백없이 주어지는데 이는 순서대로 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>i</mi></mrow></math></span>번째 행의 보드 게임판을 나타내는 문자열 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>A</mi><mi>i</mi></msub></mrow></math></span> 이며, 벽이 있는 칸은 <span class="marker">&#39;W&#39;</span>가 주어지고 없는 칸은 <span class="marker">&#39;.&#39;</span>가 주어진다.</p>
</article>
<article class="section">
<h2>출력</h2>
<p>각 테스트 케이스의 정답인 한 쌍의 정수를 공백으로 구분하여 각 줄에 출력한다. 첫 정수는 기존 게임의 점수인 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi></mrow></math></span>를 출력하고 두 번째 정수는 모든 벽의 가치 총합을 나타낸다.</p>
</article>
<article class="section">
<h2>제한</h2>
<ul>
<li><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>&#x02264;</mo><mi>T</mi><mo>&#x02264;</mo><mn>5</mn></mrow></math></span></li>
<li><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>&#x02264;</mo><mi>R</mi><mo>&#x0002C;</mo><mi>C</mi><mo>&#x02264;</mo><mn>200</mn></mrow></math></span></li>
<li><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>&#x02264;</mo><mi>N</mi><mo>&#x02264;</mo><mn>50</mn></mrow></math></span></li>
<li><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>&#x02264;</mo><mi>r</mi><mo>&#x02264;</mo><mi>R</mi></mrow></math></span> 그리고 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>&#x02264;</mo><mi>c</mi><mo>&#x02264;</mo><mi>C</mi></mrow></math></span></li>
<li><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>&#x02264;</mo><mi>i</mi><mo>&#x02264;</mo><mi>N</mi></mrow></math></span><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>i</mi></mrow></math></span>에 대하여:
<ul>
<li><span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>&#x02264;</mo><msub><mi>X</mi><mi>i</mi></msub><mo>&#x02264;</mo><mi>R</mi></mrow></math></span> 그리고 <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>&#x02264;</mo><msub><mi>Y</mi><mi>i</mi></msub><mo>&#x02264;</mo><mi>C</mi></mrow></math></span></li>
</ul>
</li>
<li>각 테스트 케이스 내에서 게임 말의 위치와 목적지의 위치는 고유하다 - 즉 같은 칸에 두 개의 게임 말이 있거나 게임 말과 목적지가 함께 있는 경우는 없다.</li>
<li>게임 말의 위치와 목적지의 위치는 벽이 없는 칸임이 보장된다.</li>
<li>벽을 하나도 부수지 않아도 각 게임말에서 상/하/좌/우로 이동하며 빈칸만 이용하여 목적지에 도달하는 것이 가능한 테스트 케이스만 입력으로 주어진다.</li>
<li>벽은 적어도 1개 주어진다.</li>
</ul>
</article>
<article class="section">
<h2>예제 입력 1 복사</h2>
<pre class="sampledata" id="sample-input-1">3
4 4 3 2 2
1 1
1 4
4 4
.WW.
..W.
.WW.
....
5 7 3 2 4
2 1
4 3
3 7
.W..W..
.WW.WWW
.W..W..
....W..
.......
5 7 3 2 4
2 1
4 3
3 7
.W.....
.WW.WW.
.W..W..
....W..
....W..
</pre>
</article>
<article class="section">
<h2>예제 출력 1 복사</h2>
<pre class="sampledata" id="sample-output-1">17 12
18 10
16 6
</pre>
</article>
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