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 h1, ..., hn, where 0 <= hi <= 1000000000. These numbers denote the heights of the rectangles of the histogram in left-to-right 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

Sample Output


hide comments
SudShekhar: 2013-02-03 11:22:02

Ensure to take all numbers + ans as long long .. worked for me

Anick Saha: 2012-10-20 16:06:04

Last edit: 2012-10-20 16:07:21
Fernando Fonseca [ITA]: 2012-07-10 05:41:17

n log n may pass, but there is a linear solution.

Shafaet: 2012-05-15 05:25:48

@Grandmaster: mine is nlogn.

Grandmaster: 2012-05-05 11:51:57

what is the required complexity to solve this problem ?? i am trying for a divide and conquer but timing out

@^ thanks ...

Last edit: 2012-05-26 05:15:46
Laplace: 2012-01-31 23:03:46

nice question. +1 on comment of Ehor Nechiporenko

prathamesh sonpatki: 2011-12-29 01:28:17

i am getting TLE with long long help !

Aman Agarwal: 2011-07-01 21:01:43

long long int is required

Tornike Mandzulashvili: 2010-12-09 13:03:27

pls give me some tests, program is working all tests, but writing WA.

Last edit: 2010-12-09 13:04:04

Added by:Wanderley Guimarăes
Time limit:0.800s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO
Resource:University of Ulm Local Contest 2003