HDU---1506:Largest Rectangle in a Histogram【单调栈】

Description:

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:
HDU---1506:Largest Rectangle in a Histogram【单调栈】_第1张图片
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.

题解:

枚举每一个单位矩形,那么每一个单位矩形所能构成的最大面积矩形为:从前面第一个比它矮的到它后面第一个比它矮的,单调栈找出两边第一个比它矮的

代码:

#include 
#include 
#include 
#include 
#include 
using namespace std;
typedef long long ll;
const int MAXN = 1e5+55;
int head[MAXN];  //前面第一个比它矮的
int rear[MAXN];  //后面第一个比它矮的
int a[MAXN];
int main()
{
    int n;
    while(cin>>n&&n)
    {
        for(int i=1; i<=n; ++i)
            scanf("%d",&a[i]);
        stack h;
        for(int i=1; i<=n; ++i)
        {
            while(!h.empty()&&a[h.top()]>=a[i])
                h.pop();
            if(!h.empty())
                head[i] = h.top();
            else head[i] = 0;
            h.push(i);
        }
        while(!h.empty()) h.pop();
        for(int i=n; i>0; --i)
        {
            while(!h.empty()&&a[h.top()]>=a[i])
                h.pop();
            if(!h.empty())
                rear[i] = h.top();
            else rear[i] = n+1;
            h.push(i);
        }
        ll ans = 0;
        for(int i=1; i<=n; ++i)
        {
            ans = max(ans,1ll*(rear[i]-head[i]-1)*a[i]);
        }
        cout<

 

你可能感兴趣的:(基础实用技巧)