1911: [Apio2010]特别行动队（斜率优化）

链接

思路

　　斜率优化dp。

 

代码

 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<cstring>
 4 #include<iostream>
 5 #include<cmath>
 6 
 7 using namespace std;
 8 typedef long long LL;
 9 int n,L,R;
10 LL A,B,C,s[1000100],q[1000100],f[1000100];
11 
12 inline int read() {
13     int x = 0,f = 1;char ch = getchar();
14     for (; !isdigit(ch); ch=getchar()) if(ch=='-') f=-1;
15     for (; isdigit(ch); ch=getchar()) x = x*10+ch-'0';
16     return x * f;
17 }
18 double Y(int x) {
19     return double(f[x]+A*s[x]*s[x]-B*s[x]);
20 }
21 double slope(int i,int j) {
22     return (Y(i)-Y(j))/double(s[i]-s[j]);
23 }
24 int main() {
25     n = read(),A = read(),B = read(),C = read();
26     for (int i=1; i<=n; ++i) s[i] = read(),s[i] += s[i-1];
27     
28     int L = 1,R = 0;
29     q[++R] = 0;
30     for (int i=1; i<=n; ++i) {
31         while (L<R && slope(q[L],q[L+1])>2.0*A*s[i]) L++;
32         int j = q[L];
33         f[i] = f[j]+A*(s[i]-s[j])*(s[i]-s[j])+B*(s[i]-s[j])+C;
34         while (L<R && slope(q[R-1],q[R])<slope(q[R],i)) R--;
35         q[++R] = i;
36     }
37     cout << f[n];
38     return 0;
39 }

 

posted @ 2018-04-28 21:27  MJT12044  阅读(180)  评论(0)  编辑  收藏  举报