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
soham_12345:
20180704 17:45:30
If you are planning to binary search on seg tree to find next lesser element DONT. It will TLE. Use stacks. 

kkislay20:
20180627 18:47:44
Can someone please tell me whats wrong with my code. I'm getting WA however I have tried several testcases and all answers are correct.


rajcoolaryan:
20180622 19:10:20
best question on stack 

megatron10599:
20180618 14:19:19
Stack O(n) If you don't know about his already, then it is worth giving it some thinking time. Last edit: 20180618 14:19:40 

anshuman1117:
20180609 09:11:30
@riddhi77 Did you use anything other than C/C++?


aman_sachin200:
20180605 21:49:07
Segment Tree Rocks!! 

pravirahuja:
20180506 19:11:22
why do we need to use long long???


riddhi77:
20180211 09:16:39
<snip>


ameyanator:
20180125 17:41:18
Great question on stacks! :D 

Luis Manuel Díaz Barón:
20180112 03:16:08
Nice problem, this helped me a lot since I couldn't come with a accurate idea:

Added by:  Wanderley Guimarăes 
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 