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[Gold II] Title: 할로윈의 양아치, Time: 856 ms, Memory: 560304 KB -BaekjoonHub
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‎백준/Gold/20303. 할로윈의 양아치/README.md‎

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# [Gold II] 할로윈의 양아치 - 20303
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[문제 링크](https://www.acmicpc.net/problem/20303)
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### 성능 요약
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메모리: 560304 KB, 시간: 856 ms
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### 분류
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자료 구조, 분리 집합, 다이나믹 프로그래밍, 그래프 이론, 그래프 탐색, 배낭 문제
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### 제출 일자
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2025년 2월 5일 15:37:47
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### 문제 설명
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<p>Trick or Treat!!</p>
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<p>10월 31일 할로윈의 밤에는 거리의 여기저기서 아이들이 친구들과 모여 사탕을 받기 위해 돌아다닌다. 올해 할로윈에도 어김없이 많은 아이가 할로윈을 즐겼지만 단 한 사람, 일찍부터 잠에 빠진 스브러스는 할로윈 밤을 즐길 수가 없었다. 뒤늦게 일어나 사탕을 얻기 위해 혼자 돌아다녀 보지만 이미 사탕은 바닥나 하나도 얻을 수 없었다.</p>
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<p>단단히 화가 난 스브러스는 거리를 돌아다니며 다른 아이들의 사탕을 빼앗기로 마음을 먹는다. 다른 아이들보다 몸집이 큰 스브러스에게 사탕을 빼앗는 건 어렵지 않다. 또한, 스브러스는 매우 공평한 사람이기 때문에 한 아이의 사탕을 뺏으면 그 아이 친구들의 사탕도 모조리 뺏어버린다. (친구의 친구는 친구다?!)</p>
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<p>사탕을 빼앗긴 아이들은 거리에 주저앉아 울고 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$K$</span></mjx-container>명 이상의 아이들이 울기 시작하면 울음소리가 공명하여 온 집의 어른들이 거리로 나온다. 스브러스가 어른들에게 들키지 않고 최대로 뺏을 수 있는 사탕의 양을 구하여라.</p>
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<p>스브러스는 혼자 모든 집을 돌아다녔기 때문에 다른 아이들이 받은 사탕의 양을 모두 알고 있다. 또한, 모든 아이는 스브러스를 피해 갈 수 없다.</p>
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### 입력
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<p>첫째 줄에 정수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$N$</span></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D440 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$M$</span></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$K$</span></mjx-container>가 주어진다. <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$N$</span></mjx-container>은 거리에 있는 아이들의 수, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D440 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$M$</span></mjx-container>은 아이들의 친구 관계 수, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$K$</span></mjx-container>는 울음소리가 공명하기 위한 최소 아이의 수이다. (<mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c33"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mtext class="mjx-n"><mjx-c class="mjx-cA0"></mjx-c></mjx-mtext><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>≤</mo><mi>N</mi><mo>≤</mo><mn>30</mn><mtext> </mtext><mn>000</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1 \leq N \leq 30\ 000$</span></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D440 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mtext class="mjx-n"><mjx-c class="mjx-cA0"></mjx-c></mjx-mtext><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>M</mi><mo>≤</mo><mn>100</mn><mtext> </mtext><mn>000</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$0 \leq M \leq 100\ 000$</span></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c6D"></mjx-c><mjx-c class="mjx-c69"></mjx-c><mjx-c class="mjx-c6E"></mjx-c></mjx-mo><mjx-mrow space="2"><mjx-mo class="mjx-n"><mjx-c class="mjx-c7B"></mjx-c></mjx-mo><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2C"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="2"><mjx-c class="mjx-c33"></mjx-c></mjx-mn><mjx-mtext class="mjx-n"><mjx-c class="mjx-cA0"></mjx-c></mjx-mtext><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mo class="mjx-n"><mjx-c class="mjx-c7D"></mjx-c></mjx-mo></mjx-mrow></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>≤</mo><mi>K</mi><mo>≤</mo><mo data-mjx-texclass="OP" movablelimits="true">min</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mi>N</mi><mo>,</mo><mn>3</mn><mtext> </mtext><mn>000</mn><mo data-mjx-texclass="CLOSE">}</mo></mrow></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1 \leq K \leq \min\left\{N, 3\ 000\right\}$</span></mjx-container>)</p>
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<p>둘째 줄에는 아이들이 받은 사탕의 수를 나타내는 정수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D450 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo class="mjx-n"><mjx-c class="mjx-c2C"></mjx-c></mjx-mo><mjx-msub space="2"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D450 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo class="mjx-n"><mjx-c class="mjx-c2C"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="2"><mjx-c class="mjx-c22EF"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="2"><mjx-c class="mjx-c2C"></mjx-c></mjx-mo><mjx-msub space="2"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D450 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mi>c</mi><mi>N</mi></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$c_1, c_2, \cdots, c_N$</span></mjx-container>이 주어진다. (<mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-msub space="4"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D450 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D456 TEX-I"></mjx-c></mjx-mi></mjx-script></mjx-msub><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mtext class="mjx-n"><mjx-c class="mjx-cA0"></mjx-c></mjx-mtext><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>≤</mo><msub><mi>c</mi><mi>i</mi></msub><mo>≤</mo><mn>10</mn><mtext> </mtext><mn>000</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1 \leq c_i \leq 10\ 000$</span></mjx-container>)</p>
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<p>셋째 줄부터 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D440 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$M$</span></mjx-container>개 줄에 갈쳐 각각의 줄에 정수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44E TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$a$</span></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$b$</span></mjx-container>가 주어진다. 이는 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44E TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$a$</span></mjx-container>와 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$b$</span></mjx-container>가 친구임을 의미한다. 같은 친구 관계가 두 번 주어지는 경우는 없다. (<mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D44E TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2C"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="2"><mjx-c class="mjx-c1D44F TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>≤</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>≤</mo><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1 \leq a, b \leq N$</span></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44E TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2260"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D44F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≠</mo><mi>b</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$a \neq b$</span></mjx-container>)</p>
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### 출력
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<p>스브러스가 어른들에게 들키지 않고 아이들로부터 뺏을 수 있는 최대 사탕의 수를 출력한다.</p>
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‎백준/Gold/20303. 할로윈의 양아치/할로윈의 양아치.java‎

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import java.io.*;
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import java.util.*;
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public class Main {
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static int n, m, k, size;
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static int[] c, p;
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static int[][] memo;
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static List<target> targets;
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static StringTokenizer st;
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static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
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public static void main(String[] args) throws Exception {
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pre_setting();
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grouping();
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System.out.println(sevigi());
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}
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static int sevigi(){
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size = targets.size();
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memo = new int[size + 1][k];
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target group;
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// i: 그룹 번호
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for(int i = 1; i < targets.size() + 1; i++){
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group = targets.get(i - 1);
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for(int j = 0; j < k; j++) {
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if(j < group.k) memo[i][j] = memo[i - 1][j];
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else memo[i][j] = Math.max(memo[i - 1][j - group.k] + group.c, memo[i - 1][j]);
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}
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}
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return memo[size][k - 1];
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}
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static void grouping() {
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int[][] candies = new int[n + 1][2];
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targets = new ArrayList<>();
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int r;
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for(int i = 1; i < n + 1; i++) {
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r = find(i);
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candies[r][0]++;
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candies[r][1] += c[i];
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}
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for(int i = 1; i < n + 1; i++){
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if(candies[i][0] != 0) targets.add(new target(candies[i][0], candies[i][1]));
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}
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}
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static void pre_setting() throws Exception{
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st = new StringTokenizer(br.readLine());
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n = Integer.parseInt(st.nextToken());
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m = Integer.parseInt(st.nextToken());
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k = Integer.parseInt(st.nextToken());
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c = new int[n + 1];
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p = new int[n + 1];
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st = new StringTokenizer(br.readLine());
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for(int i = 1; i < n + 1; i++){
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c[i] = Integer.parseInt(st.nextToken());
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p[i] = i;
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}
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int a, b;
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for(int i = 0; i < m; i++){
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st = new StringTokenizer(br.readLine());
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a = Integer.parseInt(st.nextToken());
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b = Integer.parseInt(st.nextToken());
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union(a, b);
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}
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}
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static void union(int a, int b){
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a = find(a);
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b = find(b);
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if(a < b) p[b] = a;
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else p[a] = b;
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}
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static int find(int a){
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if(p[a] == a) return p[a];
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return p[a] = find(p[a]);
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}
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static class target{
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int k, c;
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target(int k, int c){
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this.k = k;
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this.c = c;
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}
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}
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}

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