214 lines
7.5 KiB
HTML
214 lines
7.5 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 13193 - 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>Router 2</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>Henry and Hetty were recently hired by a networking company from Piatra Neamț. Their first project is to create a new type of router, the revolutionary Connect Ethernet Operating Interface 2016, comprised of:</p>
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<ul>
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<li>N input nodes, numbered from 1 to N;</li>
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<li>N output nodes, numbered from N+1 to 2×N;</li>
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<li>K internal nodes, numbered from 2×N+1 to 2×N+K;</li>
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<li>M unidirectional direct connections between pairs of distinct nodes.</li>
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</ul>
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<p>A node X can send data to a node Y (and hence Y can receive data from X) if:</p>
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<ul>
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<li>X = Y, or</li>
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<li>there exists a node Z such that X can send data to Z and there is a direct connection from node Z to node Y.</li>
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</ul>
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<p>If a node X can send data to a node Y, and X ≠ Y, then we define a data path from X to Y as a set of direct connections {(A<sub>1</sub>, A<sub>2</sub>), (A<sub>2</sub>, A<sub>3</sub>), … (A<sub>L-1</sub>, A<sub>L</sub>)} for some L ≥ 2, such that A<sub>1</sub> = X and A<sub>L</sub> = Y.</p>
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<p>A router works properly if:</p>
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<ul>
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<li>Each input node can send data to each output node;</li>
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<li>Each input node can receive data only from itself;</li>
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<li>Each output node can send data only to itself;</li>
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<li>For any two nodes X and Y, if X ≠ Y and X can send data to Y, then Y cannot send data to X;</li>
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<li>For any two nodes X and Y, if X ≠ Y and X can send data to Y, then the data path from X to Y is unique. In particular, any two nodes X and Y should be connected by at most 1 direct connection.</li>
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</ul>
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<p>Like any other electronic device, a router needs electricity to work. Let's define the power needed to operate a node X as P<sub>X</sub> = IN<sub>X</sub> × OUT<sub>X</sub>, where IN<sub>X</sub> is the number of input nodes that can send data to X, and OUT<sub>X</sub> is the number of output nodes that can receive data from X. Let's define the maximum power used by the router as P<sub>max</sub> = max(P<sub>1</sub>, P<sub>2</sub>, … P<sub>2×N+K</sub>).</p>
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<p>The project manager has given Henry and Hetty the technical specifications for building a few test routers, listed in the table below. For each of these specifications, the manager wants a router which:</p>
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<ul>
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<li>has exactly N input nodes and N output nodes;</li>
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<li>uses at most M<sub>lim</sub> direct connections;</li>
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<li>uses a maximum power which is at most Plim;</li>
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<li>uses at most 500 000 nodes overall (Total nodes = N<sub>tot</sub> = 2×N + K ≤ 500 000).</li>
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</ul>
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</article>
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<article class="section">
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<h2>입력</h2>
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<p>On the first and only line, three integers: N, the number of input and output nodes; M<sub>lim</sub>, the maximum number of direct connections allowed; and P<sub>lim</sub>, the maximum power the router uses.</p>
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<p>N = 223, M<sub>lim</sub> = 1 000 000, P<sub>lim</sub> =1 000 000</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>You will output two integer numbers separated by a space: N<sub>tot</sub> = 2×N + K, representing the total number of nodes used to build the router; and M, representing the total number of direct connections used. On each of the following M lines you should output a pair of integers X and Y, meaning a direct connection from node X to node Y was built.</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">3 100 200
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</pre>
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</article>
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<article class="section">
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<h2>예제 입력 2 복사</h2>
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<pre class="sampledata" id="sample-input-2">3 100 200
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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">9 8
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1 7
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2 7
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3 8
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7 8
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8 4
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8 9
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9 5
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9 6
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</pre>
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</article>
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<article class="section">
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<h2>예제 출력 2 복사</h2>
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<pre class="sampledata" id="sample-output-2">6 9
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1 4
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1 5
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1 6
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2 4
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2 5
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2 6
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3 4
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3 5
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3 6
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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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