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.
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.
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.
7 2 1 4 5 1 3 3
4 1000 1000 1000 1000
0
要维护两个单调队列，lft和rit。lft [i]表示i点，左边连续有比i点高的柱子的话，把最左边的柱子编号记录在lft [i]。 rit 同理，记录i的最右边连续比i高的柱子的编号。
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <malloc.h>
#include <ctype.h>
#include <math.h>
#include <string>
#include <iostream>
#include <algorithm>
using namespace std;
#include <stack>
#include <queue>
#include <vector>
#include <deque>
#include <set>
#include <map>
long long h[100010],lft[100010],rit[100010];
int main()
{
long long n,m,t;
while(cin>>n,n)
{
for(long long i=1;i<=n;i++)
{
cin>>h[i];
lft[i]=rit[i]=i;
}
h[0]=h[n+1]=-1;
for(long long i=1;i<=n;i++)
{
while(h[i]<=h[lft[i]-1])
lft[i]=lft[lft[i]-1];
}
for(long long i=n;i>=1;i--)
{
while(h[i]<=h[rit[i]+1])
rit[i]=rit[rit[i]+1];
}
long long maxx=0;
for(long long i=1;i<=n;i++)
maxx=max(maxx,h[i]*(rit[i]-lft[i]+1));
printf("%I64d\n",maxx);
for(int i=1;i<=n;i++)
{
printf("%d ",lft[i]);
}
puts("");
for(int i=1;i<=n;i++)
{
printf("%d ",rit[i]);
}
puts("");
}
return 0;
}
/*
7 2 1 4 5 1 3 3
4 1000 1000 1000 1000
0
*/
