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
honlight84:
20220211 18:46:13
be careful it should be long long ;) 

kecm2:
20210706 21:17:16
Try


Waseem Ahmed:
20210630 20:06:30
Beautiful test cases...the whole set I think. Learnt a lot. Thanks @Wanderley Guimarăes


makhan_28:
20210419 09:54:48
great problem :) 

breakplus:
20210221 01:46:25
I got WA. Can you help me?? 

shivam_kalra:
20210101 12:42:37
Giving TLE in O(nlgn) solution.


arafat_123:
20201222 14:44:31
AC in 2nd go. Interesting Question of stack!!! 

mortal_beast:
20201205 16:26:52
ac in 2nd go 

frraha:
20201102 17:55:43
Make sure variables are long long int!!!!!! 

arvind24:
20200830 10:42:45
Try these test cases also :

Added by:  Wanderley Guimarăes 
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 