bzoj 1492 [NOI2007]货币兑换Cash（斜率dp+cdq分治）

 1 #include<cmath>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<algorithm>
 5 using namespace std;
 6 
 7 const int N = 1e5+10;
 8 const double inf = 1e20;
 9 const double eps = 1e-8;
10 
11 struct Pt {
12     double x,y,a,b,k,r;
13     int id;
14     bool operator < (const Pt& rhs) const {
15         return k>rhs.k;
16     }
17 }p[N],t[N];
18 
19 double f[N];
20 int n,top,st[N];
21 
22 double slop(int a,int b)
23 {
24     if(!b) return -inf;
25     if(fabs(p[a].x-p[b].x)<eps) return inf;
26     return (p[b].y-p[a].y)/(p[b].x-p[a].x);
27 }
28 void solve(int l,int r)
29 {
30     if(l==r) {
31         f[l]=max(f[l],f[l-1]);
32         p[l].y=f[l]/(p[l].a*p[l].r+p[l].b);
33         p[l].x=p[l].y*p[l].r;
34         return ;
35     }
36     int mid=(l+r)>>1,j=1,l1=l,l2=mid+1;
37     for(int i=l;i<=r;i++) {
38         if(p[i].id<=mid) t[l1++]=p[i];
39         else t[l2++]=p[i];
40     }
41     for(int i=l;i<=r;i++) p[i]=t[i];
42     solve(l,mid);
43     top=0;
44     for(int i=l;i<=mid;i++) {
45         while(top>1&&slop(st[top-1],st[top])<slop(st[top-1],i)+eps) top--;
46         st[++top]=i;
47     }
48     st[++top]=0;
49     for(int i=mid+1;i<=r;i++) {
50         while(j<top&&slop(st[j],st[j+1])+eps>p[i].k) j++;
51         f[p[i].id]=max(f[p[i].id],p[st[j]].x*p[i].a+p[st[j]].y*p[i].b);
52     }
53     solve(mid+1,r);
54     l1=l,l2=mid+1;
55     for(int i=l;i<=r;i++) {
56         if(((p[l1].x<p[l2].x||(fabs(p[l1].x-p[l2].x)<eps&&p[l1].y<p[l2].y))||l2>r)&&l1<=mid)
57             t[i]=p[l1++];
58         else t[i]=p[l2++];
59     }
60     for(int i=l;i<=r;i++) p[i]=t[i];
61 }
62 
63 int main()
64 {
65     scanf("%d%lf",&n,&f[0]);
66     for(int i=1;i<=n;i++) {
67         scanf("%lf%lf%lf",&p[i].a,&p[i].b,&p[i].r);
68         p[i].k=-p[i].a/p[i].b; p[i].id=i;
69     }
70     sort(p+1,p+n+1);
71     solve(1,n);
72     printf("%.3lf",f[n]);
73     return 0;
74 }