Largest Rectangle in a Histogram POJ - 2559 （单调栈详尽版）

题意：在一个条形统计图中求最大的矩形面积，宽为1，高由题目给出。

思路：维护一个单调递增序列，若当前进栈值小于栈顶元素，说明栈顶的矩形已经不能再往右边延伸了，那么算出它的面积与ans进行比较。如此将整个数组扫一遍即可求得答案。具体看代码注释

#include<stdio.h>
#include<algorithm>
using namespace std;
typedef long long LL;
const int N=1e5+5;
int n,minn[N];
LL ans;
struct node
{
    LL x;//高度，LL型防止乘法溢出
    int y;//可以延伸到最左边的下标值
}a[N];
int main()
{
    int head,tail;
    while(~scanf("%d",&n)&&n)
    {
        ans=head=0,tail=-1;
        a[0].x=a[n+1].x=0;//手动插入第一个和最后一个值（貌似第一个不用手动进栈也行，不过最后一个是一定要的），并且最后一个的x必须是0，为的是最后将栈中的所有元素弹出，因为维护的是一个单调递增序列
        a[0].y=0,a[n+1].y=0;
        for(int i=1;i<=n;i++)
        {
            scanf("%lld",&a[i].x);//高度
            a[i].y=i;//默认可延伸到的最左边是自己
        }
        for(int i=1;i<=n+1;i++)//注意是0——n+1
        {
            while(head<=tail&&a[i].x<a[minn[tail]].x)//当前进栈的高度小于栈顶矩形的高度
            {
                ans=max(ans,(i-a[minn[tail]].y)*a[minn[tail]].x);//计算出栈顶矩形的面积
                a[i].y=a[minn[tail]].y;//将当前矩形可向左可延伸的下标换成栈顶矩形可向左可延伸的下标
                tail--;//出栈
            }
            minn[++tail]=i;//当前矩形进栈
        }
        printf("%lld\n",ans);
    }
}

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

Hint

Huge input, scanf is recommended.