1 #include<cstdio> 2 #include<iostream> 3 #include<algorithm> 4 #include<cmath> 5 #define eps 1e-9 6 using namespace std; 7 #define M 100008 8 double f[M]; 9 struct data 10 { 11 double k,a,b,rate,x,y; 12 int id; 13 }q[M],t[M]; 14 int zhan[M],n; 15 bool cmp(data a1,data a2) 16 { 17 return a1.k>a2.k; 18 } 19 double dp(int a1,int a2) 20 { 21 if(!a2) 22 return -1e20; 23 if(fabs(q[a1].x-q[a2].x)<eps) 24 return 1e20; 25 return (q[a1].y-q[a2].y)/(q[a1].x-q[a2].x); 26 } 27 void fen(int l,int r) 28 { 29 if(l==r) 30 { 31 f[l]=max(f[l],f[l-1]); 32 q[l].y=f[l]/(q[l].a*q[l].rate+q[l].b); 33 q[l].x=q[l].rate*q[l].y; 34 return; 35 } 36 int mid=(l+r)>>1,l1=l,l2=mid+1; 37 for(int i=l;i<=r;i++) 38 if(q[i].id<=mid) 39 t[l1++]=q[i]; 40 else 41 t[l2++]=q[i]; 42 for(int i=l;i<=r;i++) 43 q[i]=t[i]; 44 fen(l,mid); 45 int t2=0; 46 for(int i=l;i<=mid;i++) 47 { 48 for(;t2>1&&dp(zhan[t2-1],zhan[t2])<dp(zhan[t2],i)+eps;t2--); 49 zhan[++t2]=i; 50 } 51 t2++; 52 zhan[t2]=0; 53 int t1=1; 54 for(int i=mid+1;i<=r;i++) 55 { 56 for(;t1<t2&&dp(zhan[t1],zhan[t1+1])+eps>q[i].k;) 57 t1++; 58 f[q[i].id]=max(f[q[i].id],q[zhan[t1]].x*q[i].a+q[zhan[t1]].y*q[i].b); 59 } 60 fen(mid+1,r); 61 l1=l; 62 l2=mid+1; 63 for(int i=l;i<=r;i++) 64 if(((q[l1].x<q[l2].x||(fabs(q[l1].x-q[l2].x)<eps&&q[l1].y<q[l2].y))||l2>r)&&l1<=mid) 65 t[i]=q[l1++]; 66 else 67 t[i]=q[l2++]; 68 for(int i=l;i<=r;i++) 69 q[i]=t[i]; 70 return; 71 } 72 int main() 73 { 74 scanf("%d%lf",&n,&f[0]); 75 for(int i=1;i<=n;i++) 76 { 77 scanf("%lf%lf%lf",&q[i].a,&q[i].b,&q[i].rate); 78 q[i].id=i; 79 q[i].k=-q[i].a/q[i].b; 80 } 81 sort(q+1,q+n+1,cmp); 82 fen(1,n); 83 printf("%.3lf",f[n]); 84 return 0; 85 }
这是个斜率优化dp，用cdq去做。f[i]代表到i天时的最大获利，q[i].x,q[i].y表示在第i天全部买股票能买多少
