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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.

7 2 1 4 5 1 3 3
4 1000 1000 1000 1000
0

8
4000

#include<iostream>
#include<cstring>
#include<cmath>
using namespace std;
#define M 100005
typedef long long in;
in l[M],r[M],h[M];

int main(){
    in n;
    while(cin>>n && n){
        in i,j;
        for(i=0;i<=n;i++){
            l[i]=i;
            r[i]=i;
        }
        for(i=1;i<=n;i++){
            cin>>h[i];
            j=i-1;
            while(l[i]!=1 && h[i]<=h[j]){
                l[i]=l[j];
                j=l[j]-1;
            }
        }
        for(i=n;i>=1;i--){
            j=i+1;
            while(r[i]!=n && h[i]<=h[j]){
                r[i]=r[j];
                j=r[j]+1;
            }
        }
        in ans=0;
        for(i=1;i<=n;i++){
            ans=max(ans,(r[i]-l[i]+1)*h[i]);
        }
        cout<<ans<<endl;
    }
    return 0;
}

hdu 1506 Largest Rectangle in a Histogram DP

标签：hduj   c++   

原文地址：http://blog.csdn.net/hyccfy/article/details/42869613