문제
A histogram has bars of width 1 with the given heights. Find the area of the largest rectangle that lies entirely within the bars. A monotonic stack gives an O(n) solution.
Implement largest_rectangle(heights).
Input
heights: Bar heights from left to right.
Output
Return the largest area.
제약 조건
0 ≤ length ≤ 200,000; 0 ≤ height ≤ 1,000,000,000
예시
입력:
heights = [2, 1, 5, 6, 2, 3]
예상 출력:
expected = 10입력:
std::vector<long long> heights = {2, 1, 5, 6, 2, 3};
예상 출력:
long long expected = 10;입력:
long[] heights = new long[] {2, 1, 5, 6, 2, 3};
예상 출력:
long expected = 10;설명
Bars 5 and 6 together give a 2-wide rectangle of height 5: area 10.
입력:
heights = [4]
예상 출력:
expected = 4입력:
std::vector<long long> heights = {4};
예상 출력:
long long expected = 4;입력:
long[] heights = new long[] {4};
예상 출력:
long expected = 4;설명
A single bar of height 4 has area 4.
접근 방법
먼저 스스로 풀어 본 뒤 힌트를 하나씩 열어 보세요.
힌트 1
The best rectangle for a bar depends on how far it can extend before a shorter bar blocks it.
힌트 2
Use a monotonic increasing stack to find each bar’s nearest smaller bar on both sides.
힌트 3
Don’t forget bars that never get popped until the end, and handle equal heights consistently.
예상 복잡도
O(n) time, O(n) extra space
참고 자료
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