"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/10423", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "세계에서 GDP가 가장 높은 서강 나라는 소프트웨어와 하드웨어 기술이 모두 최고라서 IT강국이라 불리고, 2015년부터 세상에서 가장 살기 좋은 나라 1등으로 꼽히고 있다." }), "\n", _jsx(_components.p, { children: "살기 좋은 나라 1등으로 꼽힌 이후 외국인 방문객들이 많아졌고, 그에 따라 전기 소비율이 증가하여 전기가 많이 부족한 상황이 되었다. 따라서 서강 나라의 대통령은 최근 개발이 완료된 YNY발전소 프로젝트를 진행 하기로 하였다. 발전소를 만들 때 중요한 것은 발전소 건물과 도시로 전기를 공급해 줄 케이블이다. 발전소는 이미 특정 도시에 건설되어 있고, 따라서 추가적으로 드는 비용은 케이블을 설치할 때 드는 비용이 전부이다. 이 프로젝트의 문제는 케이블을 설치할 때 드는 비용이 굉장히 크므로 이를 최소화해서 설치하여 모든 도시에 전기를 공급하는 것이다. 여러분은 N개의 도시가 있고 M개의 두 도시를 연결하는 케이블의 정보와 K개의 YNY발전소가 설치된 도시가 주어지면 케이블 설치 비용을 최소로 사용하여 모든 도시에 전기가 공급할 수 있도록 해결해야 한다. 중요한 점은 어느 한 도시가 두 개의 발전소에서 전기를 공급받으면 낭비가 되므로 케이블이 연결되어있는 도시에는 발전소가 반드시 하나만 존재해야 한다. 아래 Figure 1를 보자. 9개의 도시와 3 개의 YNY발전소(A,B,I)가 있고, 각각의 도시들을 연결할 때 드는 비용이 주어진다." }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-10423/assets/img1.png", alt: "" }) }), "\n", _jsx(_components.p, { children: "Figure 1" }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-10423/assets/img2.png", alt: "" }) }), "\n", _jsx(_components.p, { children: "Figure 2" }), "\n", _jsx(_components.p, { children: "이 예제에서 모든 도시에 전기를 공급하기 위하여 설치할 케이블의 최소 비용은 22이고, Figure 2의 굵은 간선이 연결한 케이블이다. B 도시는 연결된 도시가 하나도 없지만, 발전소가 설치된 도시는 전기가 공급될 수 있기 때문에 상관없다." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫째 줄에는 도시의 개수 N(1 <= N <= 1,000)과 설치 가능한 케이블의 수 M(1 <= M <= 100,000)개, 발전소의 개수 K(1 <= K <= N)개가 주어진다. 둘째 줄에는 발전소가 설치된 도시의 번호가 주어진다. 셋째 줄부터 M개의 두 도시를 연결하는 케이블의 정보가 u, v, w로 주어진다. 이는 u도시와 v도시를 연결하는 케이블을 설치할 때 w의 비용이 드는 것을 의미한다. w는 10,000보다 작거나 같은 양의 정수이다." }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "모든 도시에 전기를 공급할 수 있도록 케이블을 설치하는 데 드는 최소비용을 출력한다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsx(_components.p, { children: "기본은 크루스칼 MST인데, 발전소가 있는 도시들끼리는 사실상 이미 전원이 연결된 집합처럼 보면 된다. 따라서 두 발전소 집합을 굳이 다시 잇는 간선은 선택하면 안 된다." }), "\n", _jsxs(_components.p, { children: ["코드에서는 각 집합이 발전소를 포함하는지 ", _jsx(_components.code, { children: "isPlant[]" }), "로 관리한다. 간선을 비용순으로 보면서 두 정점이 이미 같은 집합이면 건너뛰고, 둘 다 발전소 집합이면 역시 건너뛴다. 그 외에는 union 하면서 비용을 더한다."] }), "\n", _jsx(_components.p, { children: "결국 여러 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_jsx(_components.mi, { children: "M" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "O(M \\log M)" })] }) }) }), _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: "0.109em" }, children: "M" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mop", children: ["lo", _jsx(_components.span, { style: { marginRight: "0.0139em" }, children: "g" })] }), _jsx(_components.span, { className: "mspace", 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"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: "0.109em" }, children: "N" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _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: "0.109em" }, children: "M" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] })] }), "\n"] }), "\n", _jsx(_components.h2, { children: "마무리" }), "\n", _jsx(_components.p, { children: "MST 문제지만 루트가 하나가 아니라 여러 발전소라는 점이 다르다. 발전소 집합끼리만 다시 합치지 않게 막아주면 크루스칼로 깔끔하게 해결된다." }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-10423/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 10423 - 전기가 부족해