"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/2098", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "외판원 순회 문제는 영어로 Traveling Salesman problem (TSP) 라고 불리는 문제로 computer science 분야에서 가장 중요하게 취급되는 문제 중 하나이다. 여러 가지 변종 문제가 있으나, 여기서는 가장 일반적인 형태의 문제를 살펴보자." }), "\n", _jsx(_components.p, { children: "1번부터 N번까지 번호가 매겨져 있는 도시들이 있고, 도시들 사이에는 길이 있다. (길이 없을 수도 있다) 이제 한 외판원이 어느 한 도시에서 출발해 N개의 도시를 모두 거쳐 다시 원래의 도시로 돌아오는 순회 여행 경로를 계획하려고 한다. 단, 한 번 갔던 도시로는 다시 갈 수 없다. (맨 마지막에 여행을 출발했던 도시로 돌아오는 것은 예외) 이런 여행 경로는 여러 가지가 있을 수 있는데, 가장 적은 비용을 들이는 여행 계획을 세우고자 한다." }), "\n", _jsx(_components.p, { children: "각 도시간에 이동하는데 드는 비용은 행렬 W[i][j]형태로 주어진다. W[i][j]는 도시 i에서 도시 j로 가기 위한 비용을 나타낸다. 비용은 대칭적이지 않다. 즉, W[i][j] 는 W[j][i]와 다를 수 있다. 모든 도시간의 비용은 양의 정수이다. W[i][i]는 항상 0이다. 경우에 따라서 도시 i에서 도시 j로 갈 수 없는 경우도 있으며 이럴 경우 W[i][j]=0이라고 하자." }), "\n", _jsx(_components.p, { children: "N과 비용 행렬이 주어졌을 때, 가장 적은 비용을 들이는 외판원의 순회 여행 경로를 구하는 프로그램을 작성하시오." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 도시의 수 N이 주어진다. (2 ≤ N ≤ 16) 다음 N개의 줄에는 비용 행렬이 주어진다. 각 행렬의 성분은 1,000,000 이하의 양의 정수이며, 갈 수 없는 경우는 0이 주어진다. W[i][j]는 도시 i에서 j로 가기 위한 비용을 나타낸다." }), "\n", _jsx(_components.p, { children: "항상 순회할 수 있는 경우만 입력으로 주어진다." }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "첫째 줄에 외판원의 순회에 필요한 최소 비용을 출력한다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsx(_components.p, { children: "현재 어느 도시까지 방문했고 마지막 도시가 어디인지가 핵심 상태다. 그래서 dp[visited][cur] 형태의 비트마스크 DP를 두고, 아직 방문하지 않은 다음 도시로 이동하는 방식으로 풀 수 있다." }), "\n", _jsx(_components.p, { children: "모든 도시를 방문한 상태에서는 시작점으로 돌아가는 비용을 더해 종료하고, 그렇지 않으면 가능한 다음 도시들을 순회하며 최소 비용을 갱신한다. 도시 수가 작기 때문에 비트마스크로 방문 집합을 표현하는 것이 가능하다." }), "\n", _jsx(_components.p, { children: "완전탐색처럼 보여도, 방문 집합과 현재 위치를 상태로 묶으면 같은 부분 문제를 반복하지 않게 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": "java", "data-theme": "nord", children: 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_jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-2098/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 2098 - 외판원 순회