BZOJ1911:[APIO2010]特别行动队(斜率优化DP)

Description

Input

Output

Sample Input

4
-1 10 -20
2 2 3 4

Sample Output

HINT

Solution

裸的斜率优化DP

Code

 1 #include<iostream>
 2 #include<cstring>
 3 #include<cstdio>
 4 #define LL long long
 5 #define N (2000000+10)
 6 using namespace std;
 7 LL n,a,b,c,x;
 8 LL s[N],f[N];
 9 LL q[N*2],head,tail;
10 
11 LL K(LL j) { return -2*a*s[j]; }
12 LL B(LL j) { return f[j]+a*s[j]*s[j]-b*s[j]; }
13 LL Y(LL i,LL j) { return K(j)*s[i]+B(j); }
14 
15 bool cover(LL x1,LL x2,LL x3)
16 {
17     LL w1=(K(x3)-K(x1))*(B(x1)-B(x2));
18     LL w2=(K(x2)-K(x1))*(B(x1)-B(x3));
19     return w1<=w2;
20 }
21 
22 int main()
23 {
24     scanf("%lld%lld%lld%lld",&n,&a,&b,&c);
25     for (LL i=1;i<=n;++i)
26         scanf("%lld",&x),s[i]=s[i-1]+x;
27     head=1,tail=1;
28     for (LL i=1;i<=n;++i)
29     {
30         while (head<tail && Y(i,q[head])<=Y(i,q[head+1])) head++;
31         f[i]=Y(i,q[head])+a*s[i]*s[i]+b*s[i]+c;
32         while (head<tail && cover(i,q[tail],q[tail-1])) tail--;
33         q[++tail]=i;
34     }
35     printf("%lld",f[n]);
36 }