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
Arka Roy:
20170817 22:57:27
nice question on stack !! wow 

ace_of_spades:
20170801 16:15:00
Last edit: 20170802 22:43:05 

nikhil2504:
20170730 21:47:33
Interesting application of stacks <3 

saurav52:
20170726 21:17:18
AC in one go! Used stack :) 

agdeva8:
20170708 10:53:29
yipeee! half century on spoj completed, used divide and conquer approach with segment tree 

viratian_070:
20170704 09:27:56
one of the best questions....but i too cannot digest the fact that everything needs to be long long....but finally AC 

aman_9899:
20170620 21:27:16
simple stack algo..!! 

leafbebop:
20170604 18:30:18
I come with a O(N log n) algorithms with sq table (for rmq query) and binary search (to determine the range) with few seconds.


lord_poseidon:
20170529 10:32:47
WTF? the same code was accepted in C++14 , but was giving WA on simple C++ compiler, but the code was made for simple C++ and thanks to segment trees Last edit: 20170529 10:33:10 

rohit9934:
20170508 19:21:22
GeeksForGeeks Tutorial really helped tackling this problem.AC after 2 compilation errors,obviously because i thought that H[i] should be that large. 
Added by:  Wanderley GuimarÄƒes 
Date:  20070921 
Time limit:  0.409s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO 
Resource:  University of Ulm Local Contest 2003 