HISTOGRA  Largest Rectangle in a Histogram
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 Specification
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 h_{1}, ..., h_{n}
, where 0 <= h_{i} <= 1000000000
.
These numbers denote the heights of the rectangles of the histogram in lefttoright order.
The width of each rectangle is 1
.
A zero follows the input for the last test case.
Output Specification
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
hide comments
Fernando Fonseca [ITA]:
20120710 05:41:17
n log n may pass, but there is a linear solution. 

Shafaet:
20120515 05:25:48
@Grandmaster: mine is nlogn. 

Grandmaster:
20120505 11:51:57
what is the required complexity to solve this problem ?? i am trying for a divide and conquer but timing out


Laplace:
20120131 23:03:46
nice question. +1 on comment of Ehor Nechiporenko 

prathamesh sonpatki:
20111229 01:28:17
i am getting TLE with long long help ! 

Aman Agarwal:
20110701 21:01:43
long long int is required 

Tornike Mandzulashvili:
20101209 13:03:27
pls give me some tests, program is working all tests, but writing WA. Last edit: 20101209 13:04:04 
Added by:  Wanderley GuimarÄƒes 
Date:  20070921 
Time limit:  0.800s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO 
Resource:  University of Ulm Local Contest 2003 