HDU 1506 Largest Rectangle in a Histogram （DP）

POJ 2559 / HDU 1506 Largest Rectangle in a Histogram （DP）2014-07-14 synapse7 Largest Rectangle in a Histogram

http://poj.org/problem？id=2559

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.

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 integersh₁,...,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 34 1000 1000 1000 10000

Sample Output

思路：

用2个数组r[i]，l[i]表示以h[i]为高的最大矩形的左右边界位置。

注意：

要用先前已经算出来的r，l来加快r[i]，l[i]的计算（要不然会TLE）。