【BZOJ-1492】货币兑换Cash DP + 斜率优化 + CDQ分治

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
#define maxn 200010
struct DayNode
{
    double A,B,Ra,k; int id;
    bool operator < (const DayNode & T) const
        {return k<T.k;}
}a[maxn];
struct PointNode{double x,y;}p[maxn];
int N;
double dp[maxn];
int tmp[maxn],stack[maxn],top;
#define inf 1e9
#define eps 1e-9
double slope(int l1,int l2)
{
    if (l1==0) return -inf;
    if (l2==0) return inf;
    if (fabs(p[l1].x-p[l2].x)<=eps) return -inf;
    return (p[l1].y-p[l2].y)/(p[l1].x-p[l2].x);
}
void CDQ(int l,int r)
{
    if (l==r)
        {
            dp[l]=max(dp[l],dp[l-1]);
            p[l].y=dp[l]/(a[l].Ra*a[l].A+a[l].B);
            p[l].x=a[l].Ra*p[l].y;
            return;
        }
    int mid=(l+r)>>1,L,R;
    L=l; R=mid+1;
    for (int i=l; i<=r; i++)
        if (a[i].id<=mid) tmp[L++]=i; else tmp[R++]=i;
    for (int i=l; i<=r; i++) p[i]=p[tmp[i]];
    CDQ(l,mid);
    top=0;
    for (int i=l; i<=mid; i++)
        {
            while (top>1 && slope(stack[top],stack[top-1])<slope(i,stack[top-1])+eps) top--;
            stack[++top]=i;
        }
    int Top=1;
    for (int i=r; i>=mid+1; i--)
        {
            while (Top<top && slope(stack[Top],stack[Top+1])+eps>a[i].k) Top++;
            dp[a[i].id]=max(dp[a[i].id],p[stack[Top]].x*a[i].A+p[stack[Top]].y*a[i].B);
        }
    CDQ(mid+1,r);
    L=l,R=mid+1;
    for (int i=l; i<=r; i++)
        if(((p[L].x<p[R].x+eps || (fabs(p[L].x-p[R].x)<=eps && p[L].y<p[R].y+eps)) || R>r) && L<=mid) 
            tmp[i]=L++;
        else tmp[i]=R++;
    for (int i=l; i<=r; i++) p[i]=p[tmp[i]];
}
int main()
{
    scanf("%d%lf",&N,&dp[0]);
    for (int i=1; i<=N; i++) 
        scanf("%lf%lf%lf",&a[i].A,&a[i].B,&a[i].Ra),a[i].k=-a[i].A/a[i].B,a[i].id=i;
    sort(a+1,a+N+1);
    CDQ(1,N);
    //for (int i=1; i<=N; i++) printf("%d  %d  %.3lf  %.3lf  %.3lf  %.3lf  \n",i,a[i].id,a[i].A,a[i].B,a[i].Ra,a[i].k);
    printf("%.3lf\n",dp[N]);
    return 0;
}