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
pprathamesh:
20200127 21:10:12
I got 'time limit exceeded' 

x4fectax:
20200111 19:32:54
@hirbod313


hirbod313:
20191208 14:16:50
Could you please talk about the idea of solving the problem with stack? Last edit: 20191208 14:17:06 

codefresher:
20191123 10:53:48
Nice problem...excellent example of stack... 

sa_chin123:
20190714 10:30:41
how to take number of test cases 

mgroovyank:
20190613 07:45:31
Use everything as long long int 

hetp111:
20190529 17:14:32
how to do it without stacks? 

wingman__7:
20190519 08:32:44
If you are using CPP, d&c, segment trees then just use long long everywhere ... you'll get AC Last edit: 20190519 08:35:26 

iceelement:
20190506 13:09:18
sparse table and binary search also works O(nlogn) 

stones:
20190416 23:44:00
It can also be done using Union and Find in O(nlogn). 
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 