HDU 6325 Problem G. Interstellar Travel（单调栈）

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原创最新推荐文章于 2026-04-19 11:40:08 发布 446 阅读 AI 写同款· GEO 优化 ›

Bayes Linear Statistics How should we use data to help us analyse our beliefs? This book is concerned with the subjectivist analysis of uncertainty, and develops methods that combine prior judgements with information derived from relevant data. Whenever we move from broadly data-focused questions, such as ‘Does this data set suggest that a certain medical treatment is likely to be effective?’, to broadly decision-motivated questions, such as ‘Are we sufficiently confident, given all that we know about this treatment, to recommend its widespread use?’, then we must make such a synthesis of data with more generalized forms of information. Because we may find this hard to achieve, we need some methodology to help us. This methodology should be clear, helpful, logically well founded and tractable. The Bayesian approach to statistics is the natural methodology for this purpose. This approach treats all uncertainties within a common probabilistic framework, combining the different sources of information using the rules of probability. This approach has a sound logical foundation and a well-developed methodology and is popular and successful in many areas of application. However, in large-scale applications, the Bayesian approach can easily become the victim of its own ambition. Representing all uncertainties in probabilistic form is a daunting task for complicated problems. This is partly because of the intrinsic difficulties in judging the value of each relevant source of knowledge. However, in large part, the task is difficult because the Bayesian approach requires us to specify our uncertainties to an extreme level of detail. In practice, it is usually beyond our ability to make meaningful specifications for our joint probability distributions for multiple outcomes. If we do wish to follow a broadly Bayesian path, then we must either choose to make specifications that do not correspond to our actual uncertainties or be more modest about our ability to render our beliefs in probabilistic form. If the data are plentiful and unambiguous in their message or if the problem is not sufficiently important to merit careful analysis, then little harm is done by somewhat misrepresenting our beliefs. However, when the issue is important and data are less plentiful, then we must be more careful and honest. When we cannot make full belief specifications, we require alternative methods that respect the limitations on our abilities to specify meaningful beliefs and allow us to conduct partial analyses strictly in terms of the actual limited aspects of our beliefs that we are able to specify. 立即下载

题目：给定平面上 n 个点，起点横坐标最小，终点横坐标最大。每次可以飞到一个横坐标严格更大的点，代价为两个坐标的叉积。求起点到终点总代价最小的飞行路线，并输出字典序最小的路线。

思路：比赛时题目那么多提交然而就几十个人过 (通过率83/946)，真的有深坑啊。重合的点只能选一个？？？fuck，就因为没看到严格大于，wa成傻逼。单调栈维护一个上凸的路径很容易就解决了，判断条件很多，排序的时候也要注意下。。。

#include<bits/stdc++.h>
using namespace std;
const int maxn=200010;
typedef long long ll;
struct node{
    int id;
    ll x,y;
}a[maxn];
int t,n,s[maxn];
bool cmp(const node &a,const node &b)
{
    if(a.x==b.x)
    {
        if(a.y==b.y)
            return a.id<b.id;
        return a.y>b.y;
    }
    return a.x<b.x;
}
bool check(int i,int j,int k)
{
    if((a[k].y-a[i].y)*(a[j].x-a[i].x)==(a[j].y-a[i].y)*(a[k].x-a[i].x))
        return a[k].id<a[j].id;///斜率相同时，看编号是不是满足字典序小的
    return (a[k].y-a[i].y)*(a[j].x-a[i].x)>(a[j].y-a[i].y)*(a[k].x-a[i].x);
}
int main()
{
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        for(int i=1;i<=n;i++)
        {
            scanf("%lld%lld",&a[i].x,&a[i].y);
            a[i].id=i;
        }
        int top=0;
        sort(a+1,a+n+1,cmp);
        for(int i=1;i<=n;i++)
        {
            if(i!=1&&a[i].x==a[i-1].x&&a[i].y==a[i-1].y)//重合的点就不要了。。。
                continue;
            while(top>1&&check(s[top-1],s[top],i))
                top--;
            s[++top]=i;
        }
        for(int i=1;i<top;i++)
            printf("%d ",a[s[i]].id);
        printf("%d\n",a[s[top]].id);
    }
    return 0;
}
/*
1
5
0 0
1 8
3 8
2 8
3 0
*/

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