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
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!


aspro:
20160607 17:37:09
also solve CTGAME prob 

ajay_5097:
20160602 14:41:24
Segment tree ...


piyushhh:
20160601 21:51:33
a good problem on stack implementation 

pamyjeela:
20160518 11:58:05
there exists O(n) solution Last edit: 20160518 12:03:44 

karthik1997:
20160508 13:10:22
dwij 28 ... Instead of linear search , why dont you try approach like segment trees for range minimum query , It would compress your complexity toO( N*log(N)).. By the way ,, use long long int guys...... Had a lot of wa coz of this :( Last edit: 20160509 09:34:36 

dwij28:
20160426 15:30:37
Well I had to use stack. Divide and Conquer did not work for me. It gives a TLE. Divide and Conquer should be O(n^2) and not O(nlog(n)). I did a linear search in the code for my crossing part. Binary search does not seem viable as the array is not sorted. Correct me if I am wrong. 
Added by:  Wanderley GuimarÄƒes 
Date:  20070921 
Time limit:  0.409s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JS 
Resource:  University of Ulm Local Contest 2003 