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
nikhil2504: 2017-07-30 21:47:33

Interesting application of stacks <3

saurav52: 2017-07-26 21:17:18

AC in one go! Used stack :)

agdeva8: 2017-07-08 10:53:29

yipeee! half century on spoj completed, used divide and conquer approach with segment tree

viratian_070: 2017-07-04 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: 2017-06-20 21:27:16

simple stack algo..!!

leafbebop: 2017-06-04 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.
And then realize, after almost completing the code, a stack is much easier and faster. *Sigh.

lord_poseidon: 2017-05-29 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: 2017-05-29 10:33:10
rohit9934: 2017-05-08 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.

vineetpratik: 2017-03-25 19:35:50

nice ques , O(n) using stack

aditya9125: 2017-03-25 11:41:10

I can't digest why everything needs to be long long int...

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