"use strict"; const {Fragment: _Fragment, jsx: _jsx, jsxs: _jsxs} = arguments[0]; const {useMDXComponents: _provideComponents} = arguments[0]; function _createMdxContent(props) { const _components = { a: "a", annotation: "annotation", code: "code", figure: "figure", h2: "h2", img: "img", li: "li", math: "math", mi: "mi", mn: "mn", mo: "mo", mrow: "mrow", msup: "msup", p: "p", pre: "pre", semantics: "semantics", span: "span", ul: "ul", ..._provideComponents(), ...props.components }; return _jsxs(_Fragment, { children: [_jsx(_components.p, { children: _jsx(_components.a, { href: "https://www.acmicpc.net/problem/14502", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "인체에 치명적인 바이러스를 연구하던 연구소에서 바이러스가 유출되었다. 다행히 바이러스는 아직 퍼지지 않았고, 바이러스의 확산을 막기 위해서 연구소에 벽을 세우려고 한다." }), "\n", _jsx(_components.p, { children: "연구소는 크기가 N×M인 직사각형으로 나타낼 수 있으며, 직사각형은 1×1 크기의 정사각형으로 나누어져 있다. 연구소는 빈 칸, 벽으로 이루어져 있으며, 벽은 칸 하나를 가득 차지한다." }), "\n", _jsx(_components.p, { children: "일부 칸은 바이러스가 존재하며, 이 바이러스는 상하좌우로 인접한 빈 칸으로 모두 퍼져나갈 수 있다. 새로 세울 수 있는 벽의 개수는 3개이며, 꼭 3개를 세워야 한다." }), "\n", _jsx(_components.p, { children: "예를 들어, 아래와 같이 연구소가 생긴 경우를 살펴보자." }), "\n", _jsx(_components.figure, { "data-rehype-pretty-code-figure": "", children: _jsx(_components.pre, { style: { backgroundColor: "#2e3440ff", color: "#d8dee9ff" }, tabIndex: "0", "data-language": "text", "data-theme": "nord", children: _jsxs(_components.code, { "data-language": "text", "data-theme": "nord", style: { display: "grid" }, children: [_jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "2 0 0 0 1 1 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 0 1 0 1 2 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 1 0 1 0 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 0 0 0 0 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 0 0 0 0 1 1" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 0 0 0 0 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 0 0 0 0 0" }) })] }) }) }), "\n", _jsx(_components.p, { children: "이때, 0은 빈 칸, 1은 벽, 2는 바이러스가 있는 곳이다. 아무런 벽을 세우지 않는다면, 바이러스는 모든 빈 칸으로 퍼져나갈 수 있다." }), "\n", _jsx(_components.p, { children: "2행 1열, 1행 2열, 4행 6열에 벽을 세운다면 지도의 모양은 아래와 같아지게 된다." }), "\n", _jsx(_components.figure, { "data-rehype-pretty-code-figure": "", children: _jsx(_components.pre, { style: { backgroundColor: "#2e3440ff", color: "#d8dee9ff" }, tabIndex: "0", "data-language": "text", "data-theme": "nord", children: _jsxs(_components.code, { "data-language": "text", "data-theme": "nord", style: { display: "grid" }, children: [_jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "2 1 0 0 1 1 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "1 0 1 0 1 2 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 1 0 1 0 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 0 0 0 1 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 0 0 0 0 1 1" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 0 0 0 0 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 0 0 0 0 0" }) })] }) }) }), "\n", _jsx(_components.p, { children: "바이러스가 퍼진 뒤의 모습은 아래와 같아진다." }), "\n", _jsx(_components.figure, { "data-rehype-pretty-code-figure": "", children: _jsx(_components.pre, { style: { backgroundColor: "#2e3440ff", color: "#d8dee9ff" }, tabIndex: "0", "data-language": "text", "data-theme": "nord", children: _jsxs(_components.code, { "data-language": "text", "data-theme": "nord", style: { display: "grid" }, children: [_jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "2 1 0 0 1 1 2" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "1 0 1 0 1 2 2" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 1 0 1 2 2" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 0 0 0 1 2" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 0 0 0 0 1 1" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 0 0 0 0 0" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { children: "0 1 0 0 0 0 0" }) })] }) }) }), "\n", _jsx(_components.p, { children: "벽을 3개 세운 뒤, 바이러스가 퍼질 수 없는 곳을 안전 영역이라고 한다. 위의 지도에서 안전 영역의 크기는 27이다." }), "\n", _jsx(_components.p, { children: "연구소의 지도가 주어졌을 때 얻을 수 있는 안전 영역 크기의 최댓값을 구하는 프로그램을 작성하시오." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 지도의 세로 크기 N과 가로 크기 M이 주어진다. (3 ≤ N, M ≤ 8)" }), "\n", _jsx(_components.p, { children: "둘째 줄부터 N개의 줄에 지도의 모양이 주어진다. 0은 빈 칸, 1은 벽, 2는 바이러스가 있는 위치이다. 2의 개수는 2보다 크거나 같고, 10보다 작거나 같은 자연수이다." }), "\n", _jsx(_components.p, { children: "빈 칸의 개수는 3개 이상이다." }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 얻을 수 있는 안전 영역의 최대 크기를 출력한다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsx(_components.p, { children: "세 개의 벽을 어디에 세울지만 정하면, 이후 바이러스 확산 결과는 BFS로 바로 계산할 수 있다. 그래서 빈 칸 중 3곳을 고르는 조합 완전탐색과 확산 시뮬레이션을 합치면 된다." }), "\n", _jsx(_components.p, { children: "코드에서는 세 벽 조합을 하나 고를 때마다 복사한 지도에 벽을 세우고, 초기 바이러스 위치들에서 BFS를 돌려 퍼진 영역을 표시한다. 마지막에 남은 안전 구역 크기를 세어 최댓값을 갱신하면 된다." }), "\n", _jsx(_components.p, { children: "벽 선택은 브루트포스, 전염은 BFS라고 보면 구조가 선명해진다." }), "\n", _jsx(_components.h2, { children: "코드" }), "\n", _jsx(_components.figure, { "data-rehype-pretty-code-figure": "", children: _jsx(_components.pre, { style: { backgroundColor: "#2e3440ff", color: "#d8dee9ff" }, tabIndex: 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color: "#D8DEE9FF" }, children: " ny" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "))" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " }" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " }" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " }" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " }" }) }), "\n", _jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " ans " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "=" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " Math" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "." }), _jsx(_components.span, { style: { color: "#88C0D0" }, children: "max" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "(" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "ans" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "," }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " safeZone" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " }" }) }), "\n", _jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "}" }) })] }) }) }), "\n", _jsx(_components.h2, { children: "복잡도" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["시간 복잡도: 빈 칸 수를 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "E" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "E" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0576em" }, children: "E" })] }) })] }), "라 하면 벽 3개 조합마다 BFS를 수행하므로 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "O" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "E" }), _jsx(_components.mn, { children: "3" })] }), _jsx(_components.mi, { children: "N" }), _jsx(_components.mi, { children: "M" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "O(E^3NM)" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "O" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0576em" }, children: "E" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "3" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.109em" }, children: "N" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.109em" }, children: "M" }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] }), "이다."] }), "\n", _jsxs(_components.li, { children: ["공간 복잡도: 지도 복사와 큐, 방문 상태를 사용하므로 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "O" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "N" }), _jsx(_components.mi, { children: "M" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "O(NM)" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "O" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.109em" }, children: "N" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.109em" }, children: "M" }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] }), "이다."] }), "\n"] }), "\n", _jsx(_components.h2, { children: "마무리" }), "\n", _jsx(_components.p, { children: "연구소 문제는 결국 어디를 막을지만 정하면 된다. 벽 배치 조합과 바이러스 BFS를 분리해서 보면 흐름이 단순해진다." }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-14502/assets/1.png", alt: "" }) })] }); } function MDXContent(props = {}) { const {wrapper: MDXLayout} = { ..._provideComponents(), ...props.components }; return MDXLayout ? _jsx(MDXLayout, { ...props, children: _jsx(_createMdxContent, { ...props }) }) : _createMdxContent(props); } return { default: MDXContent };

BOJ 14502 - 연구소