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
ameyanator: 2018-01-25 17:41:18

Great question on stacks! :D

Luis Manuel Díaz Barón: 2018-01-12 03:16:08

Nice problem, this helped me a lot since I couldn't come with a accurate idea:

rohansaraf033: 2017-12-28 16:58:53

long long :)

chetan4060: 2017-12-19 18:08:50

using stack AC in one go:)

sarwar__05: 2017-12-04 19:03:00

Divide and Conquer with Segment tree gave me TLE, got AC using Sparse Table

avm5998: 2017-10-12 20:13:06

Don't forget to put everything long long...cost me 3 WA's.

shikhars387: 2017-10-09 07:13:14

took me 4 hours to get AC!!
Great Question.

xaer0_: 2017-08-28 17:26:32

This was tough!! Great question!

Arka Roy: 2017-08-17 22:57:27

nice question on stack !! wow

ace_of_spades: 2017-08-01 16:15:00

Last edit: 2017-08-02 22:43:05

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