"use strict"; const {Fragment: _Fragment, jsx: _jsx, jsxs: _jsxs} = arguments[0]; const {useMDXComponents: _provideComponents} = arguments[0]; function _createMdxContent(props) { const _components = { a: "a", code: "code", figure: "figure", h2: "h2", img: "img", li: "li", p: "p", pre: "pre", span: "span", ul: "ul", ..._provideComponents(), ...props.components }; return _jsxs(_Fragment, { children: [_jsx(_components.p, { children: _jsx(_components.a, { href: "https://www.acmicpc.net/problem/1562", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "45656이란 수를 보자." }), "\n", _jsx(_components.p, { children: "이 수는 인접한 모든 자리의 차이가 1이다. 이런 수를 계단 수라고 한다." }), "\n", _jsx(_components.p, { children: "N이 주어질 때, 길이가 N이면서 0부터 9까지 숫자가 모두 등장하는 계단 수가 총 몇 개 있는지 구하는 프로그램을 작성하시오. 0으로 시작하는 수는 계단수가 아니다." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 N이 주어진다. N은 1보다 크거나 같고, 100보다 작거나 같은 자연수이다." }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 정답을 1,000,000,000으로 나눈 나머지를 출력한다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsx(_components.p, { children: "모든 숫자를 한 번 이상 사용해야 하므로, 현재 마지막 숫자뿐 아니라 지금까지 어떤 숫자를 사용했는지도 함께 상태로 가져가야 한다. 그래서 길이, 마지막 숫자, 사용한 숫자 비트마스크를 상태로 두는 DP가 필요하다." }), "\n", _jsx(_components.p, { children: "한 자리씩 늘릴 때는 현재 마지막 숫자에서 -1 또는 +1로만 이동할 수 있다. 다음 숫자를 붙이면서 비트마스크에 해당 숫자를 켜 주면, 길이가 N이 되었을 때 모든 숫자가 켜진 상태만 정답 후보가 된다." }), "\n", _jsx(_components.p, { children: "단순 계단 수 DP에 모든 숫자를 사용했는가라는 조건이 하나 더 붙은 형태라고 보면 된다." }), "\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", 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}, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "N" }), _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: "#D8DEE9FF" }, children: "MAX_VISIT" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "])" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " %" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " MOD" }), _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: "#D8DEE9FF" }, children: " ans" }), _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: 상태 수 기준 ", _jsx(_components.code, { children: "O(N * 10 * 2^10)" })] }), "\n", _jsx(_components.li, { children: "공간 복잡도: DP 배열 크기만큼" }), "\n"] }), "\n", _jsx(_components.h2, { children: "마무리" }), "\n", _jsx(_components.p, { children: "계단 수 자체는 익숙하지만, 이번에는 어떤 숫자를 썼는지도 기억해야 한다. 마지막 숫자와 사용 집합을 함께 들고 가면 조건이 자연스럽게 녹아든다." }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-1562/assets/1.png", alt: "" }) })] }); } 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BOJ 1562 - 계단 수