"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/1753", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "방향그래프가 주어지면 주어진 시작점에서 다른 모든 정점으로의 최단 경로를 구하는 프로그램을 작성하시오. 단, 모든 간선의 가중치는 10 이하의 자연수이다." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 정점의 개수 V와 간선의 개수 E가 주어진다. (1 ≤ V ≤ 20,000, 1 ≤ E ≤ 300,000) 모든 정점에는 1부터 V까지 번호가 매겨져 있다고 가정한다. 둘째 줄에는 시작 정점의 번호 K(1 ≤ K ≤ V)가 주어진다. 셋째 줄부터 E개의 줄에 걸쳐 각 간선을 나타내는 세 개의 정수 (u, v, w)가 순서대로 주어진다. 이는 u에서 v로 가는 가중치 w인 간선이 존재한다는 뜻이다. u와 v는 서로 다르며 w는 10 이하의 자연수이다. 서로 다른 두 정점 사이에 여러 개의 간선이 존재할 수도 있음에 유의한다." }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "첫째 줄부터 V개의 줄에 걸쳐, i번째 줄에 i번 정점으로의 최단 경로의 경로값을 출력한다. 시작점 자신은 0으로 출력하고, 경로가 존재하지 않는 경우에는 INF를 출력하면 된다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsx(_components.p, { children: "방향 그래프에서 시작점 하나가 주어지고, 모든 정점까지의 최단 거리를 구해야 하므로 전형적인 다익스트라 문제다. 간선 가중치가 모두 양수이기 때문에 우선순위 큐를 이용한 거리 확정 방식이 그대로 통한다." }), "\n", _jsx(_components.p, { children: "코드에서는 시작 정점 K의 거리를 0으로 두고 우선순위 큐에 넣는다. 이후 가장 비용이 작은 정점을 꺼내고, 그 값이 dist 배열에 기록된 값보다 크면 오래된 정보이므로 건너뛴다. 아니라면 인접 정점들에 대해 더 짧은 경로가 나오는지 확인하며 거리 완화를 수행한다." }), "\n", _jsx(_components.p, { children: "또한 도달할 수 없는 정점은 끝까지 INF로 남기 때문에, 마지막 출력에서 그대로 구분할 수 있다. 핵심은 방문 배열 없이도 dist 기준으로 오래된 큐 원소를 버리면 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default: MDXContent };

BOJ 1753 - 최단경로