Bzoj1911 [Apio2010]特别行动队

 1 /*by SilverN*/
 2 #include<iostream>
 3 #include<algorithm>
 4 #include<cstring>
 5 #include<cstdio>
 6 #include<cmath>
 7 #define LL long long
 8 using namespace std;
 9 const int mxn=1e6+10;
10 int read(){
11     int x=0,f=1;char ch=getchar();
12     while(ch<‘0‘ || ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();}
13     while(ch>=‘0‘ && ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();}
14     return x*f;
15 }
16 LL f[mxn];
17 int n;
18 int a,b,c;
19 int x[mxn];
20 LL s[mxn];
21 LL gdp(int i,int x){
22     return f[x]+a*(s[i]-s[x])*(s[i]-s[x])+b*(s[i]-s[x])+c;
23 }
24 LL gup(int x,int y){
25     return f[x]-f[y]+a*(s[x]*s[x]-s[y]*s[y])-b*(s[x]-s[y]);
26 }
27 LL gdown(int x,int y){
28     return -2*a*s[x]+2*a*s[y];
29 }
30 int hd=0,tl=0;
31 int q[mxn];
32 int main(){
33     n=read();
34     a=read();b=read();c=read();
35     int i,j;
36     for(i=1;i<=n;i++){
37         x[i]=read();
38         s[i]=s[i-1]+x[i];
39     }
40     for(i=1;i<=n;i++){
41         while(hd<tl && gup(q[hd],q[hd+1])<=-s[i]*gdown(q[hd],q[hd+1]))hd++;
42         f[i]=gdp(i,q[hd]);
43         while(hd<tl && gup(q[tl],i)*gdown(q[tl-1],q[tl])>=gup(q[tl-1],q[tl])*gdown(q[tl],i))tl--;
44         q[++tl]=i;
45     }
46     printf("%lld\n",f[n]);
47     return 0;
48 }