本文主要是介绍POJ 2559 / HDU 1506 / LightOJ 1083 Largest Rectangle in a Histogram (单调栈)，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
Largest Rectangle in a Histogram
http://poj.org/problem?id=2559
http://acm.hdu.edu.cn/showproblem.php?pid=1506
http://lightoj.com/volume_showproblem.php?problem=1083
Time Limit: 1000MS
Memory Limit: 65536K
Description
A histogram is a polygon composed of a sequence of rectangles aligned at a common base line. The rectangles have equal widths but may have different heights. For example, the figure on the left shows the histogram that consists of rectangles with the heights 2, 1, 4, 5, 1, 3, 3, measured in units where 1 is the width of the rectangles:
Usually, histograms are used to represent discrete distributions, e.g., the frequencies of characters in texts. Note that the order of the rectangles, i.e., their heights, is important. Calculate the area of the largest rectangle in a histogram that is aligned at the common base line, too. The figure on the right shows the largest aligned rectangle for the depicted histogram.
Usually, histograms are used to represent discrete distributions, e.g., the frequencies of characters in texts. Note that the order of the rectangles, i.e., their heights, is important. Calculate the area of the largest rectangle in a histogram that is aligned at the common base line, too. The figure on the right shows the largest aligned rectangle for the depicted histogram.
Input
The input contains several test cases. Each test case describes a histogram and starts with an integer n, denoting the number of rectangles it is composed of. You may assume that 1<=n<=100000. Then follow n integers h1,...,hn, where 0<=hi<=1000000000. These numbers denote the heights of the rectangles of the histogram in left-to-right order. The width of each rectangle is 1. A zero follows the input for the last test case.
Output
For each test case output on a single line the area of the largest rectangle in the specified histogram. Remember that this rectangle must be aligned at the common base line.
Sample Input
7 2 1 4 5 1 3 3 4 1000 1000 1000 1000 0
Sample Output
8 4000
单调栈模板题。
完整代码：
/*POJ: 157ms,1728KB*/
/*HDU: 78ms,1792KB*/
/*LightOJ: 0.112s,2040KB*/#include<cstdio>
#include<algorithm>
using namespace std;
const int N = 100010;__int64 h[N];
int l[N], r[N];int main(void)
{int n, i, j;__int64 ans;while (~scanf("%d", &n), n){for (i = 1; i <= n; ++i)scanf("%I64d", &h[i]);for (i = 1; i <= n; ++i){j = i;while (j > 1 && h[j - 1] >= h[i]) /// 压栈否j = l[j - 1]; /// 出栈l[i] = j;}for (i = n; i >= 1; --i){j = i;while (j < n && h[j + 1] >= h[i]) /// 压栈否j = r[j + 1]; /// 出栈r[i] = j;}ans = 0;for (i = 1; i <= n; ++i)ans = max(ans, h[i] * (r[i] - l[i] + 1));printf("%I64d\n", ans);}return 0;
}
这篇关于POJ 2559 / HDU 1506 / LightOJ 1083 Largest Rectangle in a Histogram (单调栈)的文章就介绍到这儿，希望我们推荐的文章对编程师们有所帮助！
