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
Ankit Jain:
20140105 12:57:33
nice prob... 

humble_coder:
20131022 00:01:02
more test cases please anyone ..


suryadev:
20130817 08:39:53
Last edit: 20130817 09:04:13 

Vaibhav Agarwal:
20130722 14:57:45
nice prob.... learnt a lot. O(nlogn) passed. 

(T_T):
20130719 20:12:07
I solved using disjoint sets :) 

SudShekhar:
20130203 11:22:02
Ensure to take all numbers + ans as long long .. worked for me 

Anick Saha:
20121020 16:06:04
Last edit: 20121020 16:07:21 

Fernando Fonseca [ITA]:
20120710 05:41:17
n log n may pass, but there is a linear solution. 

Shafaet:
20120515 05:25:48
@Grandmaster: mine is 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 