"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", 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/2096", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "N줄에 0 이상 9 이하의 숫자가 세 개씩 적혀 있다. 내려가기 게임을 하고 있는데, 이 게임은 첫 줄에서 시작해서 마지막 줄에서 끝나게 되는 놀이이다." }), "\n", _jsx(_components.p, { children: "먼저 처음에 적혀 있는 세 개의 숫자 중에서 하나를 골라서 시작하게 된다. 그리고 다음 줄로 내려가는데, 다음 줄로 내려갈 때에는 다음과 같은 제약 조건이 있다. 바로 아래의 수로 넘어가거나, 아니면 바로 아래의 수와 붙어 있는 수로만 이동할 수 있다는 것이다. 이 제약 조건을 그림으로 나타내어 보면 다음과 같다." }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-2096/assets/img1.png", alt: "" }) }), "\n", _jsx(_components.p, { children: "별표는 현재 위치이고, 그 아랫 줄의 파란 동그라미는 원룡이가 다음 줄로 내려갈 수 있는 위치이며, 빨간 가위표는 원룡이가 내려갈 수 없는 위치가 된다. 숫자표가 주어져 있을 때, 얻을 수 있는 최대 점수, 최소 점수를 구하는 프로그램을 작성하시오. 점수는 원룡이가 위치한 곳의 수의 합이다." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 N(1 ≤ N ≤ 100,000)이 주어진다. 다음 N개의 줄에는 숫자가 세 개씩 주어진다. 숫자는 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 중의 하나가 된다." }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 얻을 수 있는 최대 점수와 최소 점수를 띄어서 출력한다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsx(_components.p, { children: "현재 문제를 더 작은 부분 문제로 나눌 수 있으므로 다이나믹 프로그래밍으로 보는 것이 자연스럽다. 필요한 상태를 정하고, 이미 계산한 값을 재사용하는 점화식을 세우면 된다." }), "\n", _jsx(_components.p, { children: "코드에서는 배열이나 메모이제이션으로 상태 값을 저장하고, 더 작은 범위나 이전 위치에서 현재 상태로 넘어오는 값을 이용해 갱신한다. 특히 구간 DP, 비트마스크 DP, 1차원/2차원 DP처럼 상태 형태를 먼저 분류해 보면 점화식이 훨씬 선명해진다." }), "\n", _jsx(_components.p, { children: "결국 중요한 것은 무엇을 기억해야 중복 계산이 사라지는지 찾는 일이다. 상태 정의가 맞으면 전이 자체는 비교적 자연스럽게 따라오는 경우가 많다." }), "\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": "cpp", "data-theme": "nord", children: _jsxs(_components.code, { "data-language": "cpp", "data-theme": "nord", style: { display: "grid" }, children: [_jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#5E81AC", fontWeight: "bold" }, children: "#" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "include" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " <" }), _jsx(_components.span, { style: { color: "#A3BE8C" }, children: "iostream" }), _jsx(_components.span, { 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color: "#D8DEE9FF" }, children: " ios_base" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "::" }), _jsx(_components.span, { style: { color: "#88C0D0" }, children: "sync_with_stdio" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "(" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "false" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9" }, children: " cin" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "." }), _jsx(_components.span, { style: { color: "#88C0D0" }, children: "tie" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "(" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "NULL" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9" }, children: " cout" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "." }), _jsx(_components.span, { style: { color: "#88C0D0" }, children: "tie" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "(" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "NULL" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#88C0D0" }, children: " solve" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "()" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: " return" }), _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: "#ECEFF4" }, children: "}" }) })] }) }) }), "\n", _jsx(_components.h2, { children: "복잡도" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["시간 복잡도: 각 행의 세 칸 상태를 한 번씩 갱신하므로 ", _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", style: { marginRight: "0.109em" }, children: "N" }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] }), "이다."] }), "\n", _jsxs(_components.li, { children: ["공간 복잡도: 이전 행의 최댓값/최솟값만 유지하므로 ", _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.mn, { children: "1" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "O(1)" })] }) }) }), _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", children: "1" }), 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BOJ 2096 - 내려가기