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

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

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

题意很直观，就是求一个直方图当中矩形最大的面积。从图片就可以看出，就是判断他向左或者向右延伸的位置，然后判断是否是个最大的矩形。重点就是这次的dp和以往的不同，他是一直找下去不回头的那种，就和深搜有些像。

#include<stdio.h>
#include<string.h>
#include<algorithm>
#define inf 0x3f3f3f3f
using namespace std;
long long int h[101010],l[101010],r[101010],n;
int main()
{
    while(~scanf("%lld",&n)&&n)
    {
        long long int sum,maxx=-1;
        h[0]=-1;
        h[n+1]=-inf;
        for(int i=1; i<=n; i++)
        {
            scanf("%lld",&h[i]);
            l[i]=i;
            r[i]=i;
        }
        for(int i=1; i<=n; i++)
        {
            while(h[l[i]-1]>=h[i])
                l[i]=l[l[i]-1];
        }
        for(int i=n; i>0; i--)
        {
            while(h[r[i]+1]>=h[i])
                r[i]=r[r[i]+1];
        }
        for(int i=1; i<=n; i++)
        {
            sum=(r[i]-l[i]+1)*h[i];
            maxx=max(sum,maxx);
        }
        printf("%lld\n",maxx);
    }
    return 0;
}