随笔 - 125  文章 - 0 评论 - 16 trackbacks - 0

居然搞错斜率优化的概念。。(打脸3次啪啪啪)

先出方程,a[i]为p[i]的前缀和,b[i]为p[i]*x[i]的前缀和

f[i]=f[j]+(a[i]-a[j])x[i]+b[j]-b[i]+c[i]

=f[j]+b[j]-a[j]x[i]+a[i]-b[i]+c[i]

当J比k优,得f[j]-f[k]-a[j]x[i]+a[k]x[i]+b[j]-b[k]<0

(f[j]+b[j]-f[k]-b[k])/(a[j]-a[k])<x[i]

这样就维护一个上凸函数(是上凸还是下凸有点乱,有错请纠正一下thx)

好像还有一种做法把f[i]表示成了截距,不过还是要用斜率,这样就变成维护下凸函数(有点线性规划的味道)

= =要注意slope(x,y)看似x,y是能互换其实是不能的(当a[j]==a[k]的话)

 1 #include<bits/stdc++.h>
 2 #define inc(i,l,r) for(int i=l;i<=r;i++)
 3 #define dec(i,l,r) for(int i=l;i>=r;i--)
 4 #define link(x) for(edge *j=h[x];j;j=j->next)
 5 #define mem(a) memset(a,0,sizeof(a))
 6 #define inf 1e9
 7 #define ll long long
 8 #define succ(x) (1<<x)
 9 #define NM 1000000+5
10 using namespace std;
11 int read(){
12     int x=0,f=1;char ch=getchar();
13     while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}
14     while(isdigit(ch))x=x*10+ch-'0',ch=getchar();
15     return x*f;
16 }
17 int n,x[NM],c[NM],q[NM],qh,qt,t;
18 ll f[NM],a[NM],b[NM];
19 double slope(int l,int r){
20     return (double)(f[l]+b[l]-f[r]-b[r])/(a[l]-a[r]);
21 }
22 int main(){
23     freopen("data.in","r",stdin);
24     n=read();
25     inc(i,1,n){
26         x[i]=read();t=read();c[i]=read();
27         a[i]=a[i-1]+t;b[i]=b[i-1]+(ll)x[i]*t;
28     }
29     qh=qt=1;q[qh]=0;
30     inc(i,1,n){
31         while(qh+1<=qt&&slope(q[qh+1],q[qh])<x[i])qh++;
32         t=q[qh];
33         f[i]=f[t]+(a[i]-a[t])*x[i]+b[t]-b[i]+c[i];
34         while(qh+1<=qt&&slope(q[qt],q[qt-1])>=slope(i,q[qt]))qt--;
35         q[++qt]=i;
36     }
37 //    inc(i,1,n)printf("%d ",f[i]);printf("\n");
38     printf("%lld\n",f[n]);
39     return 0;
40 }
View Code

 

posted on 2016-01-29 21:40  onlyRP  阅读(81)  评论(0编辑  收藏