"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", mo: "mo", mrow: "mrow", 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/6209", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "GSHS에서는 체력측정에서 제자리 멀리뛰기가 가장 중요하다. GSHS의 체육선생님께서는 학생들의 제자리 멀리뛰기 실력을 키워주게 하기 위해서 특수 훈련을 준비중이다." }), "\n", _jsx(_components.p, { children: "특수 훈련장소는 GSHS특수 트레이닝 센터로 이 곳은 끓는 용암으로 가득 차 있다. 체육선생님께서는 이 용암으로 가득찬 방의 가운데 있는 돌섬에 학생들을 가두고 학생들이 탈출해 나오기를 기대하고 있다. 탈출할 수 있는 방법은 단 한가지 이다. 돌섬에서 탈출구까지 띄엄 띄엄 존재하는 작은 돌섬들로 점프하여 탈출구까지 가는 것이다." }), "\n", _jsx(_components.p, { children: "돌섬에서 탈출구 사이에는 총 n개의 작은 돌섬이 있다. 선생님은 이 n개의 작은 돌섬들 중 m개를 제거하여 학생들이 최대한 멀리뛰기 연습의 효율을 높이기 위해서 학생들이 각 돌섬을 점프한 거리의 최솟값을 최대한 크게 하려고 한다. 물론 학생들은 체력이 좋기 때문에 두 돌섬이 아무리 멀더라도 점프할 수 있다. 즉, 빠지는 일은 없다." }), "\n", _jsx(_components.p, { children: "그리고 학생들은 탈출 시 n-m개의 모든 돌섬을 밟으면서 탈출해야 한다." }), "\n", _jsx(_components.p, { children: "학 생들이 갇힌 돌섬으로부터 탈출구까지의 거리 d가 주어지고, 각 n개의 작은 돌섬의 위치(갇힌 돌섬으로 부터의 거리)가 주어지며, 제거할 수 있는 작은 돌섬의 수 m이 주어질 때, m개를 제거한 후 학생들이 점프하는 최소거리의 최댓값을 구하는 프로그램을 작성하시오." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫 번째 줄에는 갇힌 돌섬으로부터 탈출구까지의 거리 d(1 <= d <= 1,000,000,000), 작은 돌섬의 수 n(0 <= n <= 50,000), 제거할 수 있는 작은 돌섬의 수 m (0 <= m <= n)이 공백으로 구분되어 주어진다." }), "\n", _jsx(_components.p, { children: "두 번째 줄부터 n줄에 걸쳐서 갇힌섬으로부터 각 작은 돌섬이 얼마나 떨어져 있는지를 나타내는 하나의 정수가 한 줄에 하나씩 주어진다. (단, 두 돌섬은 같은 위치에 있을 수 없다.)" }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "m개의 작은섬을 제거한 뒤 학생들이 점프할 수 있는 최소거리의 최댓값을 출력한다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsxs(_components.p, { children: ["전형적인 매개 변수 탐색 문제다. \"최소 점프 거리를 ", _jsx(_components.code, { children: "mid" }), " 이상으로 만들 수 있는가?\"를 판정하면 된다."] }), "\n", _jsxs(_components.p, { children: ["돌을 왼쪽부터 보면서 직전으로 남겨 둔 돌과의 거리가 ", _jsx(_components.code, { children: "mid" }), "보다 작으면 그 돌은 제거해야 하고, ", _jsx(_components.code, { children: "mid" }), " 이상이면 남긴다. 이렇게 해서 제거한 돌의 개수가 ", _jsx(_components.code, { children: "m" }), " 이하면 ", _jsx(_components.code, { children: "mid" }), "는 가능한 값이다."] }), "\n", _jsx(_components.p, { children: "가능하면 더 큰 최소 거리를 탐색하고, 불가능하면 줄이는 이분 탐색으로 답을 찾는다." }), "\n", _jsxs(_components.p, { children: ["판정이 그리디로 되는 이유는, 최소 점프 거리를 ", _jsx(_components.code, { children: "mid" }), " 이상으로 유지하려면 현재 돌을 남길 수 있을 때 굳이 제거할 이유가 없기 때문이다. 반대로 거리가 ", _jsx(_components.code, { children: "mid" }), "보다 작다면 둘 중 하나는 반드시 없어져야 하므로, 현재 돌을 제거하는 선택이 자연스럽다."] }), "\n", _jsxs(_components.p, { children: ["코드에서는 마지막 도착점 ", _jsx(_components.code, { children: "d" }), "를 배열에 넣지 않고도 같은 논리로 이분 탐색을 진행한다. 남겨진 돌들 사이의 최소 간격을 최대화하는 문제를 \"이 간격이 가능한가?\"라는 판정 문제로 바꾸는 것이 핵심이다."] }), "\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: "0", "data-language": "java", "data-theme": "nord", children: _jsxs(_components.code, { "data-language": "java", "data-theme": "nord", style: { display: "grid" }, children: [_jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "import" }), _jsx(_components.span, { style: { color: "#8FBCBB" }, children: " java" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "." }), _jsx(_components.span, { style: { 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"#81A1C1" }, children: " =" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 0" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\tint" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " left" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " =" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 0" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\tint" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " right" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " =" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " d" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t\t" }) }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\twhile" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " (" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "left " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "<=" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " right" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " {" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\t\tint" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " mid" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " =" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " (" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "left " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "+" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " right" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " /" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 2" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\t\tint" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " idx" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " =" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 0" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\t\tint" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " cnt" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " =" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 0" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t\t\t" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#616E88" }, children: "\t\t\t// 최소거리 찾기" }) }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\t\tfor" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " (" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "int" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " i" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " =" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 1" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " i " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "<=" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " n" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " i" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "++" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " {" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#616E88" }, children: "\t\t\t\t// 돌섬 제거하면서 계산" }) }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\t\t\tif" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " (" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "mid " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "<=" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " rocks" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "i" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "]" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " -" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " rocks" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "idx" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "])" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t\t\t\t\tidx " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "=" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " i" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\t\t\telse" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " " })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t\t\t\t\tcnt" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "++;" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "\t\t\t}" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t\t\t" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#616E88" }, children: "\t\t\t// cnt가 m을 넘어서면 최소거리가 아님" }) }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\t\tif" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " (" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "cnt " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ">" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " m" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t\t\t\tright " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "=" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " mid " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "-" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 1" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\t\telse" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " {" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t\t\t\tans " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "=" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " mid" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t\t\t\tleft " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "=" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " mid " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "+" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 1" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "\t\t\t}" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "\t\t}" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t\t" }) }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\treturn" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " ans" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "\t}" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t" }) }), "\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: ", _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: "log" }), _jsx(_components.mo, { children: "⁡" }), _jsx(_components.mi, { children: "d" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "O(n \\log d)" })] }) }) }), _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", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mop", children: ["lo", _jsx(_components.span, { style: { marginRight: "0.0139em" }, children: "g" })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "d" }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] })] }), "\n", _jsxs(_components.li, { children: ["공간 복잡도: ", _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.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "O(n)" })] }) }) }), _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", children: "n" }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] })] }), "\n"] }), "\n", _jsx(_components.h2, { children: "마무리" }), "\n", _jsx(_components.p, { children: "어떤 최소 점프 거리가 가능한지만 판정해 보면 구조가 단순해진다. 돌 제거 문제는 이런 식의 이분 탐색으로 자주 바뀐다." }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-6209/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 6209 - 제자리 멀리뛰기