"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/1167", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "트리의 지름이란, 트리에서 임의의 두 점 사이의 거리 중 가장 긴 것을 말한다. 트리의 지름을 구하는 프로그램을 작성하시오." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "트리가 입력으로 주어진다. 먼저 첫 번째 줄에서는 트리의 정점의 개수 V가 주어지고 (2 ≤ V ≤ 100,000)둘째 줄부터 V개의 줄에 걸쳐 간선의 정보가 다음과 같이 주어진다. 정점 번호는 1부터 V까지 매겨져 있다." }), "\n", _jsx(_components.p, { children: "먼저 정점 번호가 주어지고, 이어서 연결된 간선의 정보를 의미하는 정수가 두 개씩 주어지는데, 하나는 정점번호, 다른 하나는 그 정점까지의 거리이다. 예를 들어 네 번째 줄의 경우 정점 3은 정점 1과 거리가 2인 간선으로 연결되어 있고, 정점 4와는 거리가 3인 간선으로 연결되어 있는 것을 보여준다. 각 줄의 마지막에는 -1이 입력으로 주어진다. 주어지는 거리는 모두 10,000 이하의 자연수이다." }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 트리의 지름을 출력한다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsx(_components.p, { children: "트리의 지름은 임의의 한 정점에서 가장 먼 정점을 찾고, 그 정점에서 다시 가장 먼 정점을 찾으면 구할 수 있다. 트리에는 사이클이 없기 때문에 이 두 번의 DFS만으로 지름의 한 끝과 전체 길이를 정확히 얻을 수 있다." }), "\n", _jsxs(_components.p, { children: ["코드에서는 먼저 ", _jsx(_components.code, { children: "1" }), "번 정점에서 DFS를 시작해 가장 멀리 있는 정점 ", _jsx(_components.code, { children: "maxNode" }), "를 찾는다. 그다음 방문 배열을 초기화하고 ", _jsx(_components.code, { children: "maxNode" }), "에서 다시 DFS를 돌려 가장 멀리 도달한 거리 ", _jsx(_components.code, { children: "ans" }), "를 구한다. 이 두 번째 DFS의 최대 거리가 곧 트리의 지름이다."] }), "\n", 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";" })] }), "\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: ", _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: "V" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "O(V)" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: 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children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "O(V)" })] }) }) }), _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: "0.2222em" }, children: "V" }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] })] }), "\n"] }), "\n", _jsx(_components.h2, { children: "마무리" }), "\n", _jsx(_components.p, { children: "트리 지름의 정석은 역시 두 번의 DFS다. 한 번은 지름의 끝점을 찾고, 한 번은 그 끝에서 실제 길이를 재는 과정이라고 보면 된다." }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-1167/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 1167 - 트리의 지름