HDU 1056 Largest Rectangle in a Histogram（dp）（求最大的矩形面积）

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

思路：以每一行的高度为高，看左右分别可以延伸到哪里，算出面积求优解

代码：

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
using namespace std;
#define N 100005

__int64 h[N],le[N],ri[N];

int main()
{
    __int64 n,i;

    while(scanf("%I64d",&n),n)
    {
        for(i=1;i<=n;i++)
        {
            scanf("%I64d",&h[i]);
            le[i]=ri[i]=i;
        }

        for(i=1;i<=n;i++)
            while(le[i]>1&&h[le[i]-1]>=h[i])
               le[i]=le[le[i]-1];

        for(i=n;i>=1;i--)
            while(ri[i]<n&&h[ri[i]+1]>=h[i])
            ri[i]=ri[ri[i]+1];

        __int64 ans=0;

        for(i=1;i<=n;i++)
        {
            __int64 temp=((ri[i]-le[i]+1)*h[i]);

            if(temp>ans)
                ans=temp;
        }

        printf("%I64d\n",ans);
    }
    return 0;
}

HDU 1056 Largest Rectangle in a Histogram（dp）（求最大的矩形面积）

原文：http://blog.csdn.net/u014737310/article/details/40190183