"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/17396", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "유섭이는 무척이나 게으르다. 오늘도 할 일을 모두 미뤄둔 채 열심히 롤을 하던 유섭이는 오늘까지 문제를 내야 한다는 사실을 깨달았다. 그러나 게임은 시작되었고 지는 걸 무척이나 싫어하는 유섭이는 어쩔 수 없이 백도어를 해 게임을 최대한 빠르게 끝내기로 결심하였다." }), "\n", _jsx(_components.p, { children: "최대한 빨리 게임을 끝내고 문제를 출제해야 하기 때문에 유섭이는 최대한 빨리 넥서스가 있는 곳으로 달려가려고 한다. 유섭이의 챔피언은 총 N개의 분기점에 위치할 수 있다. 0번째 분기점은 현재 유섭이의 챔피언이 있는 곳을, N-1 번째 분기점은 상대편 넥서스를 의미하며 나머지 1, 2, ..., N-2번째 분기점은 중간 거점들이다. 그러나 유섭이의 챔피언이 모든 분기점을 지나칠 수 있는 것은 아니다. 백도어의 핵심은 안 들키고 살금살금 가는 것이기 때문에 적 챔피언 혹은 적 와드(시야를 밝혀주는 토템), 미니언, 포탑 등 상대의 시야에 걸리는 곳은 지나칠 수 없다." }), "\n", _jsx(_components.p, { children: "입력으로 각 분기점을 지나칠 수 있는지에 대한 여부와 각 분기점에서 다른 분기점으로 가는데 걸리는 시간이 주어졌을 때, 유섭이가 현재 위치에서 넥서스까지 갈 수 있는 최소 시간을 구하여라." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫 번째 줄에 분기점의 수와 분기점들을 잇는 길의 수를 의미하는 두 자연수 N과 M이 공백으로 구분되어 주어진다.(1 <= N <= 100,000, 1 <= M <= 300,000)" }), "\n", _jsx(_components.p, { children: "두 번째 줄에 각 분기점이 적의 시야에 보이는지를 의미하는 N개의 정수 a₀, a₁, ..., aₙ₋₁가 공백으로 구분되어 주어진다. aᵢ가 0이면 i번째 분기점이 상대의 시야에 보이지 않는다는 뜻이며, 1이면 보인다는 뜻이다. 추가적으로 a₀ = 0, aₙ₋₁ = 1이다. N-1번째 분기점은 상대 넥서스이기 때문에 어쩔 수 없이 상대의 시야에 보이게 되며, 또 유일하게 상대 시야에 보이면서 갈 수 있는 곳이다." }), "\n", _jsxs(_components.p, { children: ["다음 M개의 줄에 걸쳐 세 정수 ", _jsx(_components.code, { children: "a" }), ", ", _jsx(_components.code, { children: "b" }), ", ", _jsx(_components.code, { children: "t" }), "가 공백으로 구분되어 주어진다. 이는 ", _jsx(_components.code, { children: "a" }), "번과 ", _jsx(_components.code, { children: "b" }), "번 분기점을 연결하는 양방향 길을 지나가는 데 ", _jsx(_components.code, { children: "t" }), "만큼의 시간이 걸린다는 뜻이다."] }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsx(_components.p, { children: "그래프 자체는 일반 최단 경로 문제지만, 시야에 걸리는 정점은 중간에 지나갈 수 없다는 조건이 있다. 그래서 애초에 그런 정점으로 들어가는 간선을 그래프에 넣지 않는 방식이 편하다." }), "\n", _jsxs(_components.p, { children: ["코드에서는 ", _jsx(_components.code, { children: "vision[i] == 1" }), "인 정점은 목적지가 아닌 이상 그래프에서 제외한 것처럼 처리한다. 이후에는 남은 그래프에 대해 다익스트라를 그대로 수행하면 된다."] }), "\n", _jsxs(_components.p, { children: ["가중치 합이 커질 수 있어서 거리 배열과 우선순위 큐의 비용은 ", _jsx(_components.code, { children: "long" }), "으로 관리한다."] }), "\n", _jsxs(_components.p, { children: ["중요한 예외는 마지막 정점이다. 도착 지점은 시야에 보이더라도 반드시 들어가야 하므로, 코드에서도 ", _jsx(_components.code, { children: "vision[N - 1] = 0" }), "으로 강제로 바꿔 놓고 그래프를 만든다. 이 처리를 빼면 도착 자체가 막혀 버릴 수 있다."] }), "\n", _jsx(_components.p, { children: "결국 핵심은 \"못 가는 정점을 탐색 중에 걸러내는 것\"이 아니라 \"그래프를 만들 때부터 제거하는 것\"이다. 그렇게 전처리해 두면 이후 로직은 평범한 다익스트라와 다르지 않다." }), "\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" }), 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BOJ 17396 - 백도어