POJ 2559 largest Rectangle in a histogram

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 18942		Accepted: 6083

Description

A histogram is a polygon composed of a sequence of rectangles aligned at a common base line. The rectangles has equal widths but could 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 is used to represent discrete distributions, e.g., the frequencies of characters in texts. Note the order of the rectangles, i.e, their heights, is important. Calculate the area of the largest rectangle in a histogram that's aligned at the common base line, too. The shows the largest aligned rectangle for the depicted histogram.

Input

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. Assume that 1<=n<=100000. Then follow NIntegers H1,..., HN, where 0<=hi<=1000000000. These numbers denote the heights of the rectangles in histogram order. The width of each rectangle is 1. A Zero follows the input for the last test case.

Output

The For all test case is output on a single line, the area of the largest rectangle in the specified histogram. Remember that this rectangle must is aligned at the common base line.

Sample Input

7 2 1 4 5 1 3 34 1000 1000 1000 10000

Sample Output

84000

Hint

Huge input, scanf is recommended.

Source

ULM Local 2003

At first did not notice the interval length of the accumulation, various calculation errors.

Maintain a monocytogenes monotonic stack, updating interval lengths and answers every step.

1 /*by Silvern*/2#include <iostream>3#include <algorithm>4#include <cstring>5#include <cstdio>6#include <cmath>7 using namespacestd;8 Const intmxn=100020;9 structstk{Ten     Long Longh,p; One }ST[MXN]; A inttop; - intN; - Long Longans; the intMain () { -      while(SCANF ("%d", &n) &&N) { -ans=0; -         inti,j; +         intnum; -          for(i=1; i<=n+1; i++){ +             if(i>n) num=0;//after reading the data, clear the stack A             Elsescanf"%i64d",&num); at             if(num>=st[top].h) st[++top].h=num,st[top].p=1;//calculate the new zone between -             Else{ -                 intlen=0; -                  while(Top && num<=st[top].h) { -len+=ST[TOP].P; -Ans=max (ans,len*st[top].h); intop--; -                 } tost[++top].p=len+1;//Cumulative Length +St[top].h=num;//Update Height -             } the         } *printf"%i64d\n", ans); $     }Panax Notoginseng     return 0; -}

POJ 2559 largest Rectangle in a histogram