【BZOJ2328】 [HNOI2011]赛车游戏

BZOJ2328 [HNOI2011]赛车游戏

前言

这道题目我真的佛了,卡精度+卡时间这就是下一个聊天鬼才.

Solution

首先可以二分出最大速度，然后考虑下坡的话可能有更好的解，然后这样子算一下就好了.

代码实现

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<iostream>
#define ll long long
#define re register
using namespace std;
inline int gi(){
    int f=1,sum=0;char ch=getchar();
    while(ch>'9' || ch<'0'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0' && ch<='9'){sum=(sum*10)+ch-'0';ch=getchar();}
    return f*sum;
}
const int N=10010;
const double eps=1e-15;
struct node
{
    double x,y,k,len;
}p[N];
int n;
double a,b,mx,f;
bool check(double mid)
{
    double need=0.0;
    for(int i=1;i<=n;i++)
    {
        need+=max(a*mid+b*p[i].k,0.0)*p[i].len;
        if(need+eps>=f)return false;
    }
    return true;
}
double calc(double V)
{
    double res=0.0;
    for(int i=1;i<=n;i++)
    {
        double tmp=a*V+b*p[i].k;
        if(tmp<=eps)
        {
            double v=(-b*p[i].k)/a;
            v=min(v,mx);
            res+=p[i].len/v;
        }
        else
        {
            if(V<=eps)return 0;
            res+=p[i].len/V;
        }
    }
    return res;
}
void solve()
{
    double l=0,r=mx;int times=0;
    while(times<=500)
    {
        double mid=(l+r)/2.0;
        if(check(mid))l=mid;
        else r=mid;
        times++;
    }
    double Time=calc(l);
    if(Time<=eps)puts("IMPOSSIBLE");
    else printf("%.5lf\n",Time);
}
int main(){
    int T=gi();
    while(T--)
    {
        scanf("%lf%lf%lf%lf%d",&a,&b,&mx,&f,&n);
        for(int i=1;i<=n;i++)
        {
            scanf("%lf%lf",&p[i].x,&p[i].y);
            p[i].x/=1000.0;p[i].y/=1000.0;
            p[i].k=p[i].y/p[i].x;
            p[i].len=sqrt(p[i].x*p[i].x+p[i].y*p[i].y);
        }
        solve();
    }
    return 0;
}