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
cosmopoliton:
20150815 10:22:01
O(2*n) lol no divide and conquer :) 

abhijeet:
20150808 08:58:13
to get an intuition just read divide and conquer's application to largest contiguous sum in CLRS :) 

rb:
20150724 14:47:08
C++ 4.3.2 gives me WA but c++4.9 AC :) WTF 

Varun Gambhir:
20150719 21:36:25
Divide and conquer(n*log(n)) ! :) 

Proxy:
20150707 22:17:01
getting runtime error SIGSEGV..plz help


n3gativ3:
20150622 17:10:11
nice problem..just use long long..it costed me 1 WA.. 

Hikari9:
20150601 03:34:09
Beautiful problem. Solvable using a range of O(n), O(n log n), and even O(n sqrt n) solutions :)) Last edit: 20150601 03:37:41 

Min_25:
20150402 18:45:12
I cannot see it (Google Chrome).


Francky:
20150402 18:10:42
I can see the image ! (Image updated or not ???)


Phong:
20150402 16:50:47
Can anyone describe the problem for me I cannot load the image @@ That's be very helpful. Thank you very much

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 