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[Gold III] Title: 직사각형 만들기, Time: 144 ms, Memory: 113448 KB, Score: 30 point -BaekjoonHub
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‎백준/Gold/30091. 직사각형 만들기/README.md‎

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# [Gold III] 직사각형 만들기 - 30091
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[문제 링크](https://www.acmicpc.net/problem/30091)
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### 성능 요약
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메모리: 113448 KB, 시간: 144 ms
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### 분류
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애드 혹, 자료 구조, 해시를 사용한 집합과 맵, 정렬, 집합과 맵
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### 제출 일자
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2026년 3월 1일 15:14:31
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### 문제 설명
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<p>진흥이는 나무젓가락을 <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>쌍 이용하여 직사각형 두 개를 만들려고 한다. 각 나무젓가락 쌍에는 <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-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1$</span></mjx-container>번부터 <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>번까지의 서로 다른 번호가 붙어있고, <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-c1D456 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>i</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$i$</span></mjx-container>번 나무젓가락의 길이는 <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-c1D43F 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-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mi>i</mi></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$L_i$</span></mjx-container>이다. 진흥이는 <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-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1$</span></mjx-container>부터 <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>번 중 원하는 <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-c32"></mjx-c></mjx-mn><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"><mn>2</mn><mi>M</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$2M$</span></mjx-container>개의 서로 다른 번호를 고르고, 고른 번호의 나무젓가락을 두 쌍씩 짝짓는다. 짝지은 두 쌍의 나무젓가락마다 한 나무젓가락을 가로로, 다른 나무젓가락을 세로로 하는 직사각형을 만든다.</p>
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<p style="text-align: center;"><img alt="" src="https://upload.acmicpc.net/05d7a0fd-0cf8-497f-8f67-f979303f680d/-/preview/" style="width: 611px; height: 269px;"></p>
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<p style="text-align: center;">왼쪽 그림은 길이 <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-c35"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$5$</span></mjx-container>의 나무젓가락을 가로로, 길이 <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-c36"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$6$</span></mjx-container>의 나무젓가락을 세로로 하여 직사각형을 만든 모습이다. 오른쪽 그림은 길이 <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-c37"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$7$</span></mjx-container>의 나무젓가락을 가로로, 길이 <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-c34"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$4$</span></mjx-container>의 나무젓가락을 세로로 하여 직사각형을 만든 모습이다.</p>
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<p>진흥이는 <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>을 원하는 양의 정수로 고를 수 있지만, 짝지은 나무젓가락들로 만든 직사각형의 둘 레는 모두 같아야 한다. 직사각형들의 넓이의 합을 가장 크게 하려면 어떻게 해야 할까?</p>
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### 입력
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<p>첫 번째 줄에 나무젓가락의 개수 <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>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-c32"></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-c32"></mjx-c></mjx-mn><mjx-mstyle><mjx-mspace style="width: 0.167em;"></mjx-mspace></mjx-mstyle><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>2</mn><mo>≤</mo><mi>N</mi><mo>≤</mo><mn>2</mn><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mn>000</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$2 \le N \le 2\,000$</span></mjx-container>)</p>
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<p>두 번째 줄에 <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-c1D456 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>i</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$i$</span></mjx-container>번 나무젓가락의 길이 <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-c1D43F 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-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mi>i</mi></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$L_i$</span></mjx-container>가 <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-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1$</span></mjx-container>번 나무젓가락부터 <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>번 나무젓가락까지 공백으로 구분되어 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-c1D43F 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-mstyle><mjx-mspace style="width: 0.167em;"></mjx-mspace></mjx-mstyle><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-mstyle><mjx-mspace style="width: 0.167em;"></mjx-mspace></mjx-mstyle><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>L</mi><mi>i</mi></msub><mo>≤</mo><mn>10</mn><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mn>000</mn><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mn>000</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1 \le L_i \le 10\,000\,000$</span></mjx-container>)</p>
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### 출력
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<p>첫 번째 줄에 직사각형들의 넓이 합의 최댓값을 출력한다.</p>
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‎백준/Gold/30091. 직사각형 만들기/직사각형 만들기.py‎

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N = int(input())
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ls = list(map(int, input().split()))
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hmap = {}
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for i in range(N):
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for j in range(i + 1, N):
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l = ls[i]+ ls[j]
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if l not in hmap:
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hmap[l] = {
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"number" : set(),
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"sum": 0
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}
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hmap[l]["number"].add(i)
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hmap[l]["number"].add(j)
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hmap[l]["sum"]+=ls[i]*ls[j]
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else:
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if i in hmap[l]["number"] or j in hmap[l]["number"]:
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continue
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else:
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hmap[l]["number"].add(i)
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hmap[l]["number"].add(j)
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hmap[l]["sum"]+=ls[i]*ls[j]
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ans = 0
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for k in hmap:
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if ans < hmap[k]["sum"]:
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ans = hmap[k]["sum"]
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print(ans)

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