162 lines
8.2 KiB
HTML
162 lines
8.2 KiB
HTML
<!DOCTYPE html>
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<html lang="ko">
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<head>
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<meta charset="UTF-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1.0" />
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<title>BOJ 31159 - Offline</title>
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<style>
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:root {
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--bg: #fafaf8;
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--paper: #ffffff;
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--ink: #1e1f24;
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--muted: #6a6d75;
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--line: #d8dce3;
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--accent: #0d6e6e;
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--code-bg: #f4f6fb;
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}
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* { box-sizing: border-box; }
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body {
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margin: 0;
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background:
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radial-gradient(circle at 15% 0%, #f0efe9 0%, transparent 42%),
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radial-gradient(circle at 85% 20%, #e7f1f2 0%, transparent 38%),
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var(--bg);
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color: var(--ink);
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font-family: "Noto Sans KR", "Pretendard", "Apple SD Gothic Neo", sans-serif;
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line-height: 1.65;
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}
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main {
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max-width: 980px;
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margin: 0 auto;
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padding: 24px 16px 56px;
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}
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.header {
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background: var(--paper);
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border: 1px solid var(--line);
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border-radius: 14px;
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padding: 18px 20px;
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margin-bottom: 18px;
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}
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.header h1 { margin: 0 0 6px; font-size: 1.5rem; }
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.header p { margin: 0; color: var(--muted); font-size: 0.95rem; }
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.header a { color: var(--accent); text-decoration: none; }
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.section {
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background: var(--paper);
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border: 1px solid var(--line);
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border-radius: 14px;
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padding: 16px 18px;
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margin-bottom: 14px;
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overflow-x: auto;
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}
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h2 {
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margin: 0 0 10px;
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font-size: 1.05rem;
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color: var(--accent);
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border-bottom: 1px solid var(--line);
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padding-bottom: 8px;
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}
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pre, code {
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font-family: "JetBrains Mono", "Fira Code", monospace;
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background: var(--code-bg);
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}
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pre {
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padding: 12px;
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border-radius: 10px;
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border: 1px solid #e7ebf2;
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overflow: auto;
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}
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blockquote {
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margin: 14px 0;
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padding: 16px 16px 14px 22px;
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border-left: 4px solid var(--accent);
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border-radius: 10px;
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background: linear-gradient(90deg, #eef8f8 0%, #f9fdfd 100%);
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color: #24313a;
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font-weight: 600;
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position: relative;
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}
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blockquote::before {
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content: "“";
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position: absolute;
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left: 8px;
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top: 2px;
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font-size: 1.35rem;
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line-height: 1;
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color: #0b5f5f;
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opacity: 0.7;
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}
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blockquote > :first-child { margin-top: 0; }
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blockquote > :last-child { margin-bottom: 0; }
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q {
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color: #114f50;
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font-weight: 700;
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background: #edf8f8;
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border-radius: 6px;
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padding: 0 4px;
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}
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.math-inline math {
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font-size: 1em;
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vertical-align: middle;
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}
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.math-block {
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margin: 10px 0;
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padding: 8px 10px;
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overflow-x: auto;
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background: #f8fbff;
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border: 1px solid #e2ecf8;
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border-radius: 8px;
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}
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.math-block math {
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font-size: 1.04em;
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display: block;
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}
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table { border-collapse: collapse; width: 100%; }
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th, td { border: 1px solid var(--line); padding: 6px 8px; }
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img { max-width: 100%; height: auto; }
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</style>
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</head>
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<body>
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<main>
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<header class="header">
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<h1>Max Pair Matching</h1>
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</header>
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<article class="section">
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<h2>문제</h2>
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<p>You are given <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>n</mi></mrow></math></span> pairs <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><msub><mi>a</mi><mi>i</mi></msub><mo>,</mo><msub><mi>b</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow></math></span> of integers. Consider a complete graph on <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>n</mi></mrow></math></span> vertices and define the weight of the edge <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi>i</mi><mi>j</mi><mo stretchy="false">)</mo></mrow></math></span> to be <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>w</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mo stretchy="false">|</mo><msub><mi>a</mi><mi>i</mi></msub><mo>−</mo><msub><mi>a</mi><mi>j</mi></msub><mo stretchy="false">|</mo><mo>,</mo><mo stretchy="false">|</mo><msub><mi>a</mi><mi>i</mi></msub><mo>−</mo><msub><mi>b</mi><mi>j</mi></msub><mo stretchy="false">|</mo><mo>,</mo><mo stretchy="false">|</mo><msub><mi>b</mi><mi>i</mi></msub><mo>−</mo><msub><mi>a</mi><mi>j</mi></msub><mo stretchy="false">|</mo><mo>,</mo><mo stretchy="false">|</mo><msub><mi>b</mi><mi>i</mi></msub><mo>−</mo><msub><mi>b</mi><mi>j</mi></msub><mo stretchy="false">|</mo><mo stretchy="false">)</mo></mrow></math></span>. </p>
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<p>Determine the maximum weight of the matching in this graph.</p>
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<p>In other words, consider all ways to select <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi></mrow></math></span> edges of this graph such that no two chosen edges have a common endpoint. What is the maximum possible total weight of these edges?</p>
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</article>
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<article class="section">
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<h2>입력</h2>
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<p>The first line of the input contains a single integer <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi></mrow></math></span> (<span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>≤</mo><mi>n</mi><mo>≤</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></math></span>).</p>
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<p>The <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>i</mi></mrow></math></span>-th of the next <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>n</mi></mrow></math></span> lines contain two integers <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> and <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>b</mi><mi>i</mi></msub></mrow></math></span> (<span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0</mn><mo>≤</mo><msub><mi>a</mi><mi>i</mi></msub><mo>,</mo><msub><mi>b</mi><mi>i</mi></msub><mo>≤</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></math></span>).</p>
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</article>
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<article class="section">
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<h2>출력</h2>
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<p>Print a single integer --- the maximum weight of the matching in this graph.</p>
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</article>
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<article class="section">
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<h2>힌트</h2>
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<p>Adjacency matrix: <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>7</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>15</mn></mtd></mtr><mtr><mtd><mn>7</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>8</mn></mtd></mtr><mtr><mtd><mn>9</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>11</mn></mtd></mtr><mtr><mtd><mn>15</mn></mtd><mtd><mn>8</mn></mtd><mtd><mn>11</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mrow></math></span></p>
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</article>
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<article class="section">
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<h2>예제 입력 1 복사</h2>
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<pre class="sampledata" id="sample-input-1">2
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0 10
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7 7
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9 4
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2 15
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</pre>
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</article>
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<article class="section">
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<h2>예제 출력 1 복사</h2>
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<pre class="sampledata" id="sample-output-1">18
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</pre>
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</article>
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</main>
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</body>
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</html>
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