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
ameyanator:
20180125 17:41:18
Great question on stacks! :D 

Luis Manuel Díaz Barón:
20180112 03:16:08
Nice problem, this helped me a lot since I couldn't come with a accurate idea:


rohansaraf033:
20171228 16:58:53
long long :) 

chetan4060:
20171219 18:08:50
using stack AC in one go:) 

sarwar__05:
20171204 19:03:00
Divide and Conquer with Segment tree gave me TLE, got AC using Sparse Table 

avm5998:
20171012 20:13:06
Don't forget to put everything long long...cost me 3 WA's. 

shikhars387:
20171009 07:13:14
took me 4 hours to get AC!!


xaer0_:
20170828 17:26:32
This was tough!! Great question! 

Arka Roy:
20170817 22:57:27
nice question on stack !! wow 

ace_of_spades:
20170801 16:15:00
Last edit: 20170802 22:43:05 
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 