{"componentChunkName":"component---src-templates-blog-post-js","path":"/Problem-Solving/2021-03-10-2512번-예산/","result":{"data":{"site":{"siteMetadata":{"title":"Hun's Footsteps 🥷","author":"전여훈","siteUrl":"https://jeonyeohun.netlify.app","comment":{"disqusShortName":"","utterances":"jeonyeohun/jeonyeohun.github.io"},"sponsor":{"buyMeACoffeeId":"jeonyeohun"}}},"markdownRemark":{"id":"367c8e47-3e2f-5c26-a3a1-8d21f14c2bb2","excerpt":"https://www.acmicpc.net/problem/251…","html":"<p><a href=\"https://www.acmicpc.net/problem/2512\">https://www.acmicpc.net/problem/2512</a></p>\n<h2 id=\"문제\" style=\"position:relative;\"><a href=\"#%EB%AC%B8%EC%A0%9C\" aria-label=\"문제 permalink\" class=\"anchor before\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"16\" version=\"1.1\" viewBox=\"0 0 16 16\" width=\"16\"><path fill-rule=\"evenodd\" d=\"M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z\"></path></svg></a>문제</h2>\n<p><strong>문제</strong><br></p>\n<p>국가의 역할 중 하나는 여러 지방의 예산요청을 심사하여 국가의 예산을 분배하는 것이다. 국가예산의 총액은 미리 정해져 있어서 모든 예산요청을 배정해 주기는 어려울 수도 있다. 그래서 정해진 총액 이하에서 가능한 한 최대의 총 예산을 다음과 같은 방법으로 배정한다.</p>\n<p>모든 요청이 배정될 수 있는 경우에는 요청한 금액을 그대로 배정한다.\n모든 요청이 배정될 수 없는 경우에는 특정한 정수 상한액을 계산하여 그 이상인 예산요청에는 모두 상한액을 배정한다. 상한액 이하의 예산요청에 대해서는 요청한 금액을 그대로 배정한다.\n예를 들어, 전체 국가예산이 485이고 4개 지방의 예산요청이 각각 120, 110, 140, 150이라고 하자. 이 경우, 상한액을 127로 잡으면, 위의 요청들에 대해서 각각 120, 110, 127, 127을 배정하고 그 합이 484로 가능한 최대가 된다.</p>\n<p>여러 지방의 예산요청과 국가예산의 총액이 주어졌을 때, 위의 조건을 모두 만족하도록 예산을 배정하는 프로그램을 작성하시오.</p>\n<p><strong>입력</strong><br></p>\n<p>첫째 줄에는 지방의 수를 의미하는 정수 N이 주어진다. N은 3 이상 10,000 이하이다. 다음 줄에는 각 지방의 예산요청을 표현하는 N개의 정수가 빈칸을 사이에 두고 주어진다. 이 값들은 모두 1 이상 100,000 이하이다. 그 다음 줄에는 총 예산을 나타내는 정수 M이 주어진다. M은 N 이상 1,000,000,000 이하이다.</p>\n<p><strong>출력</strong><br></p>\n<p>첫째 줄에는 배정된 예산들 중 최댓값인 정수를 출력한다.</p>\n<h2 id=\"풀이\" style=\"position:relative;\"><a href=\"#%ED%92%80%EC%9D%B4\" aria-label=\"풀이 permalink\" class=\"anchor before\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"16\" version=\"1.1\" viewBox=\"0 0 16 16\" width=\"16\"><path fill-rule=\"evenodd\" d=\"M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z\"></path></svg></a>풀이</h2>\n<p>이 문제 역시 이분탐색으로 풀 수 있는 문제이다. 이분탐색으로 찾을 대상을 예산 상한으로 설정하고, 한번 상한액을 설정할 때마다 예산 배정 결과를 계산해본다. 만약 계산된 예산이 현재 예산보다 작다면, 상한액을 올려야하기 때문에 head 를 mid + 1 로 바꾸고, 상액이 예산보다 크다면 tail을 mid - 1 로 바꾼다. 이 문제에서는 가능한 최대의 예산을 배정해야하기 때문에 상한액이 딱 떨어지지 않아도 총 예산보다 작다면 정답 후보로 계속 업데이트를 해주어야 한다.</p>\n<h2 id=\"코드\" style=\"position:relative;\"><a href=\"#%EC%BD%94%EB%93%9C\" aria-label=\"코드 permalink\" class=\"anchor before\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"16\" version=\"1.1\" viewBox=\"0 0 16 16\" width=\"16\"><path fill-rule=\"evenodd\" d=\"M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z\"></path></svg></a>코드</h2>\n<div class=\"gatsby-highlight\" data-language=\"cpp\"><pre class=\"language-cpp\"><code class=\"language-cpp\"><span class=\"token string\">' '</span>\n<span class=\"token macro property\"><span class=\"token directive-hash\">#</span><span class=\"token directive keyword\">include</span> <span class=\"token string\">&lt;cstdio></span></span>\n<span class=\"token macro property\"><span class=\"token directive-hash\">#</span><span class=\"token directive keyword\">include</span> <span class=\"token string\">&lt;algorithm></span></span>\n<span class=\"token macro property\"><span class=\"token directive-hash\">#</span><span class=\"token directive keyword\">include</span> <span class=\"token string\">&lt;vector></span></span>\n\n<span class=\"token keyword\">using</span> <span class=\"token keyword\">namespace</span> std<span class=\"token punctuation\">;</span>\n\n<span class=\"token keyword\">typedef</span> <span class=\"token keyword\">long</span> <span class=\"token keyword\">long</span> ll<span class=\"token punctuation\">;</span>\n\nvector<span class=\"token operator\">&lt;</span>ll<span class=\"token operator\">></span> budgets<span class=\"token punctuation\">;</span>\n\nll <span class=\"token function\">calcBudget</span> <span class=\"token punctuation\">(</span>ll maxBudget<span class=\"token punctuation\">)</span><span class=\"token punctuation\">{</span>\n    ll sum <span class=\"token operator\">=</span> <span class=\"token number\">0</span><span class=\"token punctuation\">;</span>\n    <span class=\"token keyword\">for</span> <span class=\"token punctuation\">(</span><span class=\"token keyword\">auto</span> budget <span class=\"token operator\">:</span> budgets<span class=\"token punctuation\">)</span><span class=\"token punctuation\">{</span>\n        <span class=\"token keyword\">if</span> <span class=\"token punctuation\">(</span>budget <span class=\"token operator\">&lt;=</span> maxBudget<span class=\"token punctuation\">)</span> sum <span class=\"token operator\">+=</span> budget<span class=\"token punctuation\">;</span>\n        <span class=\"token keyword\">else</span> sum <span class=\"token operator\">+=</span> maxBudget<span class=\"token punctuation\">;</span>\n    <span class=\"token punctuation\">}</span>\n\n    <span class=\"token keyword\">return</span> sum<span class=\"token punctuation\">;</span>\n<span class=\"token punctuation\">}</span>\n\nll <span class=\"token function\">binarySearch</span><span class=\"token punctuation\">(</span>ll head<span class=\"token punctuation\">,</span> ll tail<span class=\"token punctuation\">,</span> ll target<span class=\"token punctuation\">)</span><span class=\"token punctuation\">{</span>\n    ll closest <span class=\"token operator\">=</span> <span class=\"token number\">0</span><span class=\"token punctuation\">;</span>\n\n    <span class=\"token keyword\">while</span><span class=\"token punctuation\">(</span>head <span class=\"token operator\">&lt;=</span> tail<span class=\"token punctuation\">)</span><span class=\"token punctuation\">{</span>\n        ll mid <span class=\"token operator\">=</span> <span class=\"token punctuation\">(</span>head <span class=\"token operator\">+</span> tail<span class=\"token punctuation\">)</span> <span class=\"token operator\">/</span> <span class=\"token number\">2</span><span class=\"token punctuation\">;</span>\n        ll calcResult <span class=\"token operator\">=</span> <span class=\"token function\">calcBudget</span><span class=\"token punctuation\">(</span>mid<span class=\"token punctuation\">)</span><span class=\"token punctuation\">;</span>\n\n        <span class=\"token keyword\">if</span> <span class=\"token punctuation\">(</span>calcResult <span class=\"token operator\">></span> target<span class=\"token punctuation\">)</span> tail <span class=\"token operator\">=</span> mid <span class=\"token operator\">-</span> <span class=\"token number\">1</span><span class=\"token punctuation\">;</span>\n        <span class=\"token keyword\">else</span> <span class=\"token keyword\">if</span> <span class=\"token punctuation\">(</span>calcResult <span class=\"token operator\">&lt;=</span> target<span class=\"token punctuation\">)</span> <span class=\"token punctuation\">{</span>\n            closest <span class=\"token operator\">=</span> mid<span class=\"token punctuation\">;</span>\n            head <span class=\"token operator\">=</span> mid <span class=\"token operator\">+</span> <span class=\"token number\">1</span><span class=\"token punctuation\">;</span>\n        <span class=\"token punctuation\">}</span>\n    <span class=\"token punctuation\">}</span>\n\n    <span class=\"token keyword\">return</span> closest<span class=\"token punctuation\">;</span>\n<span class=\"token punctuation\">}</span>\n\n<span class=\"token keyword\">int</span> <span class=\"token function\">main</span> <span class=\"token punctuation\">(</span><span class=\"token punctuation\">)</span><span class=\"token punctuation\">{</span>\n    <span class=\"token keyword\">int</span> N<span class=\"token punctuation\">;</span>\n    ll M<span class=\"token punctuation\">,</span> longest <span class=\"token operator\">=</span> <span class=\"token number\">0</span><span class=\"token punctuation\">;</span>\n    <span class=\"token function\">scanf</span><span class=\"token punctuation\">(</span><span class=\"token string\">\"%d\"</span><span class=\"token punctuation\">,</span> <span class=\"token operator\">&amp;</span>N<span class=\"token punctuation\">)</span><span class=\"token punctuation\">;</span>\n\n    <span class=\"token keyword\">for</span> <span class=\"token punctuation\">(</span><span class=\"token keyword\">int</span> i <span class=\"token operator\">=</span> <span class=\"token number\">0</span> <span class=\"token punctuation\">;</span> i <span class=\"token operator\">&lt;</span> N <span class=\"token punctuation\">;</span> i<span class=\"token operator\">++</span><span class=\"token punctuation\">)</span><span class=\"token punctuation\">{</span>\n        ll budget<span class=\"token punctuation\">;</span>\n        <span class=\"token function\">scanf</span><span class=\"token punctuation\">(</span><span class=\"token string\">\"%lld\"</span><span class=\"token punctuation\">,</span> <span class=\"token operator\">&amp;</span>budget<span class=\"token punctuation\">)</span><span class=\"token punctuation\">;</span>\n\n        budgets<span class=\"token punctuation\">.</span><span class=\"token function\">push_back</span><span class=\"token punctuation\">(</span>budget<span class=\"token punctuation\">)</span><span class=\"token punctuation\">;</span>\n\n        longest <span class=\"token operator\">=</span> <span class=\"token function\">max</span><span class=\"token punctuation\">(</span>longest<span class=\"token punctuation\">,</span> budget<span class=\"token punctuation\">)</span><span class=\"token punctuation\">;</span>\n    <span class=\"token punctuation\">}</span>\n\n    <span class=\"token function\">scanf</span><span class=\"token punctuation\">(</span><span class=\"token string\">\"%lld\"</span><span class=\"token punctuation\">,</span> <span class=\"token operator\">&amp;</span>M<span class=\"token punctuation\">)</span><span class=\"token punctuation\">;</span>\n\n    <span class=\"token function\">printf</span><span class=\"token punctuation\">(</span><span class=\"token string\">\"%lld\"</span><span class=\"token punctuation\">,</span> <span class=\"token function\">binarySearch</span><span class=\"token punctuation\">(</span><span class=\"token number\">0</span><span class=\"token punctuation\">,</span> longest<span class=\"token punctuation\">,</span> M<span class=\"token punctuation\">)</span><span class=\"token punctuation\">)</span><span class=\"token punctuation\">;</span>\n\n<span class=\"token punctuation\">}</span></code></pre></div>","frontmatter":{"title":"[백준 알고리즘] 2512번: 예산","date":"March 10, 2021"}}},"pageContext":{"slug":"/Problem-Solving/2021-03-10-2512번-예산/","previous":{"fields":{"slug":"/Problem-Solving/2021-03-10-1654번-랜선자르기/"},"frontmatter":{"title":"[백준 알고리즘] 1654번: 랜선 자르기","category":"Problem-Solving","draft":false}},"next":{"fields":{"slug":"/Problem-Solving/2021-03-11-1715번-카드정렬하기/"},"frontmatter":{"title":"[백준 알고리즘] 1715번: 카드 정렬하기","category":"Problem-Solving","draft":false}}}},"staticQueryHashes":["2486386679","3128451518"]}