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
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noname:
20150326 17:31:43
Last edit: 20150326 17:32:04 

Shubham Garg:
20150322 10:26:48
Last edit: 20150611 10:31:04 

californiagurl:
20150109 12:47:36
nothing I do seems to work :/ and there are at least 3 different solution to this problem :' 

agaurav77:
20141227 12:49:06
Nice question. Remember to use everything as long long (C++), AC :) 

Archit Jain:
20141223 12:42:15
use long long int


N0VICE:
20141218 08:12:05
nice problem solved using Disjoint sets :) 

Guillermo:
20141215 00:46:05
I see the solution in O(n), but i dont see how i can do the problem in O(nlogn) complexity, if someone can explain me, i be grateful!!! 

candide:
20140517 19:12:28
Nice question. Well written problem statement. My stackbased O(n) solution gets AC in 0.40s (: Last edit: 20140517 19:42:04 

Zen:
20140129 20:18:55
:( 

Ankit Jain:
20140105 12:57:33
nice prob... 
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 