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 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

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 follown integers h₁,...,h_n, where 0<=h_i<=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

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

Hint

Huge input, scanf is recommended.

Source

Ulm Local 2003

 

刚开始竟然没有注意到区间长度的累计，各种算错。

维护一个单增的单调栈，每步更新区间长度和答案即可。

 

/*by SilverN*/
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
const int mxn=100020;
struct stk{
    long long h,p;
}st[mxn];
int top;
int n;
long long ans;
int main(){
    while(scanf("%d",&n) && n){
        ans=0;
        int i,j;
        int num;
        for(i=1;i<=n+1;i++){
            if(i>n)num=0;//数据读完后清栈 
            else scanf("%I64d",&num);
            if(num>=st[top].h) st[++top].h=num,st[top].p=1;//计算新区间 
            else{
                int len=0;
                while(top && num<=st[top].h){
                    len+=st[top].p;
                    ans=max(ans,len*st[top].h);
                    top--;
                }
                st[++top].p=len+1;//累计长度 
                st[top].h=num;//更新高度 
            }
        }
        printf("%I64d\n",ans);
    }
    return 0;
}