裸斜率優化

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<iomanip>
#include<cstring>
#include<cmath>
#include<ctime>
#include<vector>
#include<stack>
#include<queue>
#include<set>
#include<bitset>
#include<map>
using namespace std;
#define MAXN 3010
#define MAXM 10010
#define INF 1000000000
#define MOD 1000000007
#define ll long long
#define eps 1e-8
ll f[MAXN][MAXN];
ll a[MAXN];
ll s[MAXN];
int q[MAXN][MAXN];
int hd[MAXN],tl[MAXN];
int n,m;
double xl(int x,int y,int z){
	z--;
	return 1.0*(f[x][z]-f[y][z]+s[x]*s[x]-s[y]*s[y])/(s[x]-s[y]);
}
int main(){
	int i,j,k;
	scanf("%d%d",&n,&m);
	for(i=1;i<=n;i++){
		scanf("%lld",&a[i]);
	}
	int tot=0;
	for(i=1;i<=n;i++){
		if(a[i]!=0){
			a[++tot]=a[i];
		}
		s[i]=s[i-1]+a[i];
	}
	n=tot;
	q[1][++tl[1]]=0;
	for(i=1;i<=n;i++){
		for(j=1;j<=min(m,i);j++){
			while(hd[j]<tl[j]&&xl(q[j][hd[j]+1],q[j][hd[j]],j)<2*s[i]){
				hd[j]++;
			}
			k=q[j][hd[j]];
			f[i][j]=f[k][j-1]+(s[i]-s[k])*(s[i]-s[k]);
			if(j==m){
				continue ;
			}
			while(hd[j+1]<tl[j+1]&&xl(q[j+1][tl[j+1]-1],q[j+1][tl[j+1]],j+1)>xl(q[j+1][tl[j+1]],i,j+1)){
				tl[j+1]--;
			}
			q[j+1][++tl[j+1]]=i;
		}
	}
	printf("%lld\n",f[n][m]*m-s[n]*s[n]);
	return 0;
}

/*
10 3
1 2 3 4 5 6 7 8 9 10
*/