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[Gold III] Title: 탑 보기, Time: 32 ms, Memory: 4120 KB -BaekjoonHub
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| # [Gold III] 탑 보기 - 22866 | ||
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| [문제 링크](https://www.acmicpc.net/problem/22866) | ||
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| ### 성능 요약 | ||
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| 메모리: 4120 KB, 시간: 32 ms | ||
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| ### 분류 | ||
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| 자료 구조, 스택 | ||
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| ### 제출 일자 | ||
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| 2024년 4월 26일 02:07:37 | ||
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| ### 문제 설명 | ||
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| <p>일직선으로 다양한 높이의 건물이 총 <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>개가 존재한다. 각 건물 옥상에서 양 옆에 존재하는 건물의 옆을 몇 개 볼 수 있는지 궁금해졌다.</p> | ||
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| <p><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>번째 건물 기준으로 <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-mo class="mjx-n" space="3"><mjx-c class="mjx-c2212"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><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"><mi>i</mi><mo>−</mo><mn>1</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$i - 1$</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-c1D456 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2212"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>−</mo><mn>2</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$i - 2$</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-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>번째 건물은 왼쪽에, <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-mo class="mjx-n" space="3"><mjx-c class="mjx-c2B"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><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"><mi>i</mi><mo>+</mo><mn>1</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$i + 1$</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-c1D456 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2B"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>+</mo><mn>2</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$i + 2$</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-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>번째 건물은 오른쪽에 있다. 각 건물 사이의 거리는 다 동일하다.</p> | ||
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| <p>현재 있는 건물의 높이가 <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-c1D43F 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>L</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$L$</span></mjx-container>이라고 가정하면 높이가 <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-c1D43F 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>L</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$L$</span></mjx-container>보다 큰 곳의 건물만 볼 수 있다.</p> | ||
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| <p>바라보는 방향으로 높이가 <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-c1D43F 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>L</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$L$</span></mjx-container>인 건물 뒤에 높이가 <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-c1D43F 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>L</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$L$</span></mjx-container>이하인 건물이 있다면 가려져서 보이지 않는다.</p> | ||
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| <table class="table table-bordered table-center-50 td-center"> | ||
| <tbody> | ||
| <tr> | ||
| <td>번호</td> | ||
| <td>1</td> | ||
| <td>2</td> | ||
| <td>3</td> | ||
| <td>4</td> | ||
| <td>5</td> | ||
| <td>6</td> | ||
| <td>7</td> | ||
| <td>8</td> | ||
| </tr> | ||
| <tr> | ||
| <td>높이</td> | ||
| <td>3</td> | ||
| <td>7</td> | ||
| <td>1</td> | ||
| <td>6</td> | ||
| <td>3</td> | ||
| <td>5</td> | ||
| <td>1</td> | ||
| <td>7</td> | ||
| </tr> | ||
| <tr> | ||
| <td>보이는 건물 번호</td> | ||
| <td>2</td> | ||
| <td>x</td> | ||
| <td>2, 4, 8</td> | ||
| <td>2, 8</td> | ||
| <td>2,4,6,8</td> | ||
| <td>2,4,8</td> | ||
| <td>2,4,6,8</td> | ||
| <td>x</td> | ||
| </tr> | ||
| </tbody> | ||
| </table> | ||
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| <p>각 건물에서 볼 수 있는 건물들이 어떤것이 있는지 구해보자.</p> | ||
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| ### 입력 | ||
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| <p>첫번째 줄에 건물의 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.</p> | ||
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| <p>두번째 줄에는 <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>개의 건물 높이가 공백으로 구분되어 주어진다.</p> | ||
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| ### 출력 | ||
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| <p><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-mo class="mjx-n"><mjx-c class="mjx-c28"></mjx-c></mjx-mo><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-c1D456 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-mo class="mjx-n"><mjx-c class="mjx-c29"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo stretchy="false">(</mo><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>N</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$i(1 \le i \le N)$</span></mjx-container>번째 건물에서 볼 수 있는 건물의 개수를 출력한다.</p> | ||
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| <p>만약 볼 수 있는 건물의 개수가 1개 이상이라면 <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>번째 건물에서 거리가 가장 가까운 건물의 번호 중 작은 번호로 출력한다.</p> | ||
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| #include <iostream> | ||
| #include <algorithm> | ||
| #include <vector> | ||
| #include <stack> | ||
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| using namespace std; | ||
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| int main() { | ||
| ios_base::sync_with_stdio(0); | ||
| cin.tie(0); | ||
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| int n; | ||
| cin >> n; | ||
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| vector<int> arr(n+1, 0); | ||
| vector<int> size(n+1, 0); | ||
| vector<pair<int, int>> dist(n+1, {-1, -1}); | ||
| for(int i = 1; i <= n; i++) { | ||
| cin >> arr[i]; | ||
| } | ||
| stack <int> l; | ||
| stack <int> r; | ||
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| for (int i = n-1; i >= 1; i--) { | ||
| if (arr[i+1] > arr[i]) { | ||
| while (!r.empty() && arr[r.top()] <= arr[i+1]) { | ||
| r.pop(); | ||
| } | ||
| r.push(i+1); | ||
| } else { | ||
| while (!r.empty() && arr[r.top()] <= arr[i]) { | ||
| r.pop(); | ||
| } | ||
| } | ||
| size[i] += r.size(); | ||
| if (!r.empty()) dist[i].second = r.top(); | ||
| } | ||
| for (int i = 2; i <= n; i++) { | ||
| if (arr[i-1] < arr[i]) { | ||
| while (!l.empty() && arr[l.top()] <= arr[i]) { | ||
| l.pop(); | ||
| } | ||
| } else if (arr[i-1] > arr[i]) { | ||
| while (!l.empty() && arr[l.top()] <= arr[i-1]) { | ||
| l.pop(); | ||
| } | ||
| l.push(i-1); | ||
| } | ||
| size[i] += l.size(); | ||
| if (!l.empty()) dist[i].first = l.top(); | ||
| } | ||
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| for (int i = 1; i <= n; i++) { | ||
| cout << size[i] << " "; | ||
| if (size[i] > 0) { | ||
| if (dist[i].first == -1) { | ||
| cout << dist[i].second; | ||
| } else if (dist[i].second == -1) { | ||
| cout << dist[i].first; | ||
| } else { | ||
| if ((i - dist[i].first) <= (dist[i].second - i)) { | ||
| cout << dist[i].first; | ||
| } else { | ||
| cout << dist[i].second; | ||
| } | ||
| } | ||
| } | ||
| cout << '\n'; | ||
| } | ||
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| return 0; | ||
| } |