[bzoj4518] [Sdoi2016]征途

 1 #include<cstdio>
 2 #include<iostream>
 3 #include<cstring>
 4 #include<cstdlib>
 5 #include<cmath>
 6 #define d double
 7 #define ll long long
 8 using namespace std;
 9 const int maxn=3023;
10 int i,j,k,n,m,now,pre,l,r;
11 ll pr[maxn],V[maxn];
12 int dl[maxn];
13 d f[2][maxn],v1[maxn];
14 
15 
16 int ra,fh;char rx;
17 inline int read() {
18     rx=getchar(),ra=0,fh=1;
19     while((rx<‘0‘||rx>‘9‘)&&rx!=‘-‘)rx=getchar();
20     if(rx==‘-‘)fh=-1,rx=getchar();
21     while(rx>=‘0‘&&rx<=‘9‘)ra*=10,ra+=rx-48,rx=getchar();return ra*fh;
22 }
23 inline d xl(int k1,int k2){//k1<k2
24     return (d)(f[pre][k2]-f[pre][k1]+V[k2]-V[k1])/(pr[k2]-pr[k1]);
25 }
26 inline d sqr(d x){return x*x;}
27 int main(){
28     n=read(),m=read();
29     for(i=1;i<=n;i++)pr[i]=pr[i-1]+read(),V[i]=pr[i]*pr[i];
30     d avg=(d)pr[n]/m;
31     for(i=0;i<=n;i++)f[0][i]=sqr(pr[i]-avg),v1[i]=(pr[i]-avg);
32     now=1,pre=0;
33     for(i=2;i<=m;i++,swap(now,pre)){
34         l=1,r=0;
35         for(j=0;j<=n;j++){
36             while(l<r&&xl(dl[r-1],dl[r])>=xl(dl[r],j))r--;
37             dl[++r]=j;
38             while(l<r&&2*v1[j]>=xl(dl[l],dl[l+1]))l++;
39             f[now][j]=f[pre][dl[l]]+sqr(v1[j]-pr[dl[l]]);
40         }
41     }
42     printf("%lld\n",(ll)(f[pre][n]*m+0.5));
43     return 0;
44 }