"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", ol: "ol", 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/2610", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "KOI 준비를 위해 회의를 개최하려 한다. 주최측에서는 회의에 참석하는 사람의 수와 참석자들 사이의 관계를 따져 하나 이상의 위원회를 구성하려고 한다. 위원회를 구성하는 방식은 다음과 같다." }), "\n", _jsxs(_components.ol, { children: ["\n", _jsx(_components.li, { children: "서로 알고 있는 사람은 반드시 같은 위원회에 속해야 한다." }), "\n", _jsx(_components.li, { children: "효율적인 회의 진행을 위해 위원회의 수는 최대가 되어야 한다." }), "\n"] }), "\n", _jsx(_components.p, { children: "이런 방식으로 위원회를 구성한 후에 각 위원회의 대표를 한 명씩 뽑아야 한다. 각 위원회의 대표만이 회의 시간 중 발언권을 가지며, 따라서 회의 참석자들이 자신의 의견을 말하기 위해서는 자신이 속한 위원회의 대표에게 자신의 의견을 전달해야 한다. 그런데 각 참석자는 자신이 알고 있는 사람에게만 의견을 전달할 수 있어 대표에게 의견을 전달하기 위해서는 때로 여러 사람을 거쳐야 한다. 대표에게 의견을 전달하는 경로가 여러 개 있을 경우에는 가장 적은 사람을 거치는 경로로 의견을 전달하며 이때 거치는 사람의 수를 참석자의 의사전달시간이라고 한다." }), "\n", _jsx(_components.p, { children: "위원회에서 모든 참석자들의 의사전달시간 중 최댓값이 최소가 되도록 대표를 정하는 프로그램을 작성하시오." }), "\n", _jsx(_components.p, { children: "예를 들어 1번, 2번, 3번 세 사람으로 구성되어 있는 위원회에서 1번과 2번, 2번과 3번이 서로 알고 있다고 하자. 1번이 대표가 되면 3번이 대표인 1번에게 의견을 전달하기 위해서 2번을 거쳐야만 한다. 반대로 3번이 대표가 되어도 1번이 대표인 3번에게 의견을 전달하려면 2번을 거쳐야만 한다. 하지만 2번이 대표가 되면 1번과 3번 둘 다 아무도 거치지 않고 대표에게 직접 의견을 전달 할 수 있다. 따라서 이와 같은 경우 2번이 대표가 되어야 한다." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 회의에 참석하는 사람의 수 N이 주어진다. 참석자들은 1부터 N까지의 자연수로 표현되며 회의에 참석하는 인원은 100 이하이다. 둘째 줄에는 서로 알고 있는 관계의 수 M이 주어진다. 이어 M개의 각 줄에는 서로 아는 사이인 참석자를 나타내는 두개의 자연수가 주어진다." }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "첫째 줄에는 구성되는 위원회의 수 K를 출력한다. 다음 K줄에는 각 위원회의 대표 번호를 작은 수부터 차례로 한 줄에 하나씩 출력한다. 한 위원회의 대표가 될 수 있는 사람이 둘 이상일 경우 그중 한 명만 출력하면 된다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsxs(_components.p, { children: ["먼저 각 사람 사이의 최단 거리를 모두 알아야 한다. ", _jsx(_components.code, { children: "N" }), "이 크지 않아서 플로이드-워셜로 전체 최단 거리를 구할 수 있다."] }), "\n", _jsxs(_components.p, { children: ["이후 연결 요소별로 사람들을 묶고, 각 후보 ", _jsx(_components.code, { children: "candidate" }), "에 대해 같은 그룹 사람들까지의 최장 거리 ", _jsx(_components.code, { children: "maxDist" }), "를 계산한다. 이 값이 가장 작은 사람이 그 그룹의 대표가 된다."] }), "\n", _jsx(_components.p, { children: "여기서 대표를 고르는 기준은 \"그 사람이 소식을 전달하기 시작했을 때, 같은 위원회 전체에 전달되기까지 걸리는 최대 시간\"을 최소화하는 것이다. 즉 그룹 안에서의 eccentricity가 가장 작은 정점을 찾는 문제라고 보면 된다." }), "\n", _jsxs(_components.p, { children: ["코드에서는 아직 방문하지 않은 사람 하나를 기준으로 ", _jsx(_components.code, { children: "dist[i][j] != INF" }), "인 정점들을 같은 그룹으로 모은다. 그리고 그 그룹 안의 모든 후보를 돌면서 가장 멀리 있는 사람까지의 거리를 계산해 최솟값을 찾는다. 마지막에는 대표 번호들을 정렬해서 출력하면 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": 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children: "\t\tdist" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "u" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "][" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "v" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "]" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " =" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " dist" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "v" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "][" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "u" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "]" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " =" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 1" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "\t}" }) }), "\n", _jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#88C0D0" }, children: "\tsolve" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "(" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "N" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\treturn" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 0" }), _jsx(_components.span, { style: { color: "#81A1C1" }, 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: ", _jsx(_components.code, { children: "O(N^3)" })] }), "\n", _jsxs(_components.li, { children: ["공간 복잡도: ", _jsx(_components.code, { children: "O(N^2)" })] }), "\n"] }), "\n", _jsx(_components.h2, { children: "마무리" }), "\n", _jsx(_components.p, { children: "그룹만 나누는 것으로 끝나지 않고, 그룹 안에서 가장 중심적인 사람까지 골라야 한다. 최단 거리 배열을 만들어 두면 이 판단이 쉬워진다." }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-2610/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 2610 - 회의준비