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
nilabja16180:
20170305 20:20:18
Geeksforgeeks helped!


akshay31057:
20170130 14:38:11
Take all variables of long long type


scorpion_ajay:
20170122 17:44:45
it seems easy first, but then you are screwed XD 

sarvagya:
20161206 08:33:59
O(n) without a stack ^_^ 

Shubham:
20161203 16:54:36
Accepted, But In g++ 5.1, I have to use long long for both n and heights....I thought long should suffice ( < 10^9). 

chinmay0906:
20161029 07:24:33
the best problem on stack....O(n) solution 

davidgalehouse:
20161016 23:22:42
Wow, great problem. I looked at times after debating divide and conquer and O(n^2) approaches, and figured there must be an O(n) solution. Not sure if I got lucky thinking of a solution. Subconsciously at least, the experience of ARRAYSUB and HOTELS helped me. Last edit: 20161016 23:23:18 

sieunhanbom04:
20160819 19:15:20
printf("%lld\n",ans); = accepted;


mohit_23:
20160619 11:10:04
thank god. finally accepted 

lt:
20160617 09:15:29
AC on first go!

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 