寻找直方图中面积最大的矩形

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.

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,...,h_n, where 0<=h_i<=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

Hint

Huge input, scanf is recommended.

中文简述：

给定直方图。每一小块的height由N个非负整数所确定，每一小块的width都为1，请找出直方图中面积最大的矩形。

如直方图中每一块的宽度都是1，每一块给定的高度各自是[2,1,5,6,2,3]：

   那么上述直方图中。面积最大的矩形便是下图所看到的的阴影部分的面积，面积= 10单位。

   实现寻找直方图中面积最大的矩形的功能，如当给定直方图各小块的高度= [2,1,5,6,2,3] ，返回10。

測试数据：http://download.csdn.net/detail/pipisorry/7861217

from:

http://blog.csdn.net/pipisorry/article/details/39037207

ref:

http://poj.org/problem?id=2559

解法： https://github.com/YuxiKou/leetcode/blob/master/ContainerWithMostWater.cc

http://blog.csdn.net/ygrx/article/details/9452341