"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/16940", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "BOJ에서 정답이 여러가지인 경우에는 스페셜 저지를 사용한다. 스페셜 저지는 유저가 출력한 답을 검증하는 코드를 통해서 정답 유무를 결정하는 방식이다. 오늘은 스페셜 저지 코드를 하나 만들어보려고 한다." }), "\n", _jsx(_components.p, { children: "정점의 개수가 N이고, 정점에 1부터 N까지 번호가 매겨져있는 양방향 그래프가 있을 때, BFS 알고리즘은 다음과 같은 형태로 이루어져 있다." }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["\n", _jsx(_components.p, { children: "큐에 시작 정점을 넣는다. 이 문제에서 시작 정점은 1이다. 1을 방문했다고 처리한다." }), "\n"] }), "\n", _jsxs(_components.li, { children: ["\n", _jsx(_components.p, { children: "큐가 비어 있지 않은 동안 다음을 반복한다." }), "\n"] }), "\n", _jsxs(_components.li, { children: ["\n", _jsx(_components.p, { children: "큐에 들어있는 첫 정점을 큐에서 꺼낸다. 이 정점을 x라고 하자." }), "\n"] }), "\n", _jsxs(_components.li, { children: ["\n", _jsx(_components.p, { children: "x와 연결되어 있으면, 아직 방문하지 않은 정점 y를 모두 큐에 넣는다. 모든 y를 방문했다고 처리한다." }), "\n"] }), "\n"] }), "\n", _jsx(_components.p, { children: "2-2 단계에서 방문하지 않은 정점을 방문하는 순서는 중요하지 않다. 따라서, BFS의 결과는 여러가지가 나올 수 있다." }), "\n", _jsx(_components.p, { children: "트리가 주어졌을 때, 올바른 BFS 방문 순서인지 구해보자." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 정점의 수 N(2 ≤ N ≤ 100,000)이 주어진다. 둘째 줄부터 N-1개의 줄에는 트리의 간선 정보가 주어진다. 마지막 줄에는 BFS 방문 순서가 주어진다. BFS 방문 순서는 항상 N개의 정수로 이루어져 있으며, 1부터 N까지 자연수가 한 번씩 등장한다." }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "입력으로 주어진 BFS 방문 순서가 올바른 순서면 1, 아니면 0을 출력한다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsx(_components.p, { children: "주어진 방문 순서가 BFS로 가능한지 판정하려면, 그 순서를 기준으로 인접 리스트를 정렬한 뒤 실제 BFS를 한 번 돌려 보면 된다. BFS는 같은 레벨 안에서의 순서가 자유롭기 때문에, 원하는 순서를 우선순위로 넣어 주는 방식이다." }), "\n", _jsx(_components.p, { children: "코드에서는 입력으로 받은 방문 순서의 위치를 pos에 저장하고, 각 정점의 인접 정점을 그 순서대로 정렬한다. 그 상태에서 BFS를 돌렸을 때 실제 탐색 순서가 입력 순서와 같다면 가능한 BFS 순서다." }), "\n", _jsx(_components.p, { children: "임의의 BFS 순서 검증 문제를 정렬 후 비교 문제로 바꾼 것이다." }), "\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: " <" }), 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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: 정렬 포함 ", _jsx(_components.code, { children: "O(N log N)" }), " 수준"] }), "\n", _jsxs(_components.li, { children: ["공간 복잡도: ", _jsx(_components.code, { children: "O(N)" })] }), "\n"] }), "\n", _jsx(_components.h2, { children: "마무리" }), "\n", _jsx(_components.p, { children: "가능한 BFS 순서를 직접 정의하려 하지 말고, 입력 순서를 우선하도록 인접 리스트를 정렬해 보면 된다. 그 결과가 그대로 나오면 정답이다." }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-16940/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 16940 - BFS 스페셜 저지