[NOI2007]货币兑换Cash（DP+动态凸包）

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<algorithm>
 4 #include<iostream>
 5 #include<set>
 6 #include<cmath>
 7 using namespace std;
 8 const double esp=1e-7;
 9 const int maxn=101000;
10 int dcmp(double a) {
11     if (fabs(a)<esp) return 0;
12     return a<0?-1:1;
13 }
14 struct node{
15     double x,y,k;bool f;
16     node(double _x,double _y):x(_x),y(_y),f(0){}
17     node():f(0){}
18     inline bool error(){return x>1e50;}
19 }error(1e51,0);
20 inline bool operator == (const node x,const node y) {return dcmp(x.x-y.x)==0;}
21 inline bool operator < (const node x,const node y){
22     if (x.f||y.f) return dcmp(x.k-y.k)>0;
23     else return dcmp(x.x-y.x)<0;
24 }
25 inline double operator *(const node x,const node y) {return x.x*y.y-x.y*y.x;}
26 inline node operator -(const node x,const node y){
27     node tmp;
28     tmp.x=x.x-y.x;tmp.y=x.y-y.y;
29     return tmp;
30 }
31 inline double calc_k(node x,node y) {return (x.y-y.y)/(x.x-y.x);}
32 set<node> gap;
33 typedef set<node>::iterator iter;
34 inline node lower(node x) {
35    iter it=gap.lower_bound(x);
36    return it==gap.end()?error:*it;
37 }
38 inline node next(node x) {
39     iter it=gap.upper_bound(x);
40     return it==gap.end()?error:*it;
41 }
42 inline node pre(node x) {
43     iter it=gap.lower_bound(x);
44     return it==gap.begin()?error:*(--it);
45 }
46 inline void ins(node a) {
47     if (gap.empty()) {a.k=0;gap.insert(a);return;}
48     node d1=pre(a),d2=lower(a);
49     if (d1.error()&&d2.y>a.y) return ;
50     if ((!d1.error())&&(!d2.error())&&(dcmp((d2-d1)*(a-d1))<=0)) return ;
51     if (d2==a) return;
52     node p1,p2=next(a);
53     for (;;){
54         p1=p2;p2=next(p2);
55         if (p1.error()||p2.error()) break;
56         if (dcmp((p1-a)*(p2-a))<=0) break;
57         gap.erase(p1);
58     }
59     p2=pre(a);
60     for (;;){
61         p1=p2;p2=pre(p2);
62         if (p1.error()||p2.error()) break;
63         if (dcmp((p1-a)*(p2-a))>=0) break;
64         gap.erase(p1);
65     }
66     d1=pre(a),d2=next(a);
67     if (d1.error()) a.k=0;else a.k=calc_k(d1,a);gap.insert(a);
68     if (!d2.error()) gap.erase(d2),d2.k=calc_k(a,d2),gap.insert(d2);
69 }
70 inline double get_k(double a,double b) {
71     node tmp;tmp.f=1;tmp.k=-a/b;
72     tmp=*(--gap.lower_bound(tmp));
73     return a*tmp.x+b*tmp.y;
74 }
75 double a[maxn],b[maxn],r[maxn],na[maxn],nb[maxn],f[maxn];
76 int main(){
77     int n,s;
78     scanf("%d%d",&n,&s);
79     for (int i=1;i<=n;i++) scanf("%lf%lf%lf",a+i,b+i,r+i);
80     f[1]=s;
81     nb[1]=f[1]/(a[1]*r[1]+b[1]);
82     na[1]=nb[1]*r[1];
83     ins(node(na[1],nb[1]));
84     for (int i=2;i<=n;i++) {
85         f[i]=max(f[i-1],get_k(a[i],b[i]));
86         nb[i]=f[i]/(a[i]*r[i]+b[i]);
87         na[i]=nb[i]*r[i];
88         ins(node(na[i],nb[i]));
89     }
90     printf("%.3f\n",f[n]);
91 }
92