[APIO2014]序列分割

 1 #include<bits/stdc++.h>
 2 #define N 100005
 3 #define ll long long
 4 using namespace std;
 5 int n,k,a[N],q[N],l,r,pre[N][205];
 6 ll s[N],f[N],g[N];
 7 double slope(int j,int k){
 8     if(s[j]==s[k])return -1e10;
 9     return (double)((g[j]-s[j]*s[j])-(g[k]-s[k]*s[k]))/(s[k]-s[j]);
10 }
11 int main(){
12     scanf("%d%d",&n,&k);
13     for(int i=1;i<=n;i++)scanf("%d",&a[i]),s[i]=s[i-1]+a[i];
14     for(int t=1;t<=k;t++){
15         int l=1,r=0;
16         q[++r]=0;
17         for(int i=1;i<=n;i++){
18             while(l<r&&slope(q[l],q[l+1])<=s[i])l++;
19             f[i]=g[q[l]]+(s[i]-s[q[l]])*s[q[l]];
20             pre[i][t]=q[l];
21             while(l<r&&slope(q[r],i)<=slope(q[r-1],q[r]))r--;
22             q[++r]=i;
23         }
24         memcpy(g,f,sizeof(f));
25     }
26     printf("%lld\n",f[n]);
27     int x=pre[n][k];
28     printf("%d",x);
29     for(int i=k-1;i>=1;i--){
30         x=pre[x][i];
31         printf(" %d",x);
32     }
33     return 0;
34 }