luogu P4072 [SDOI2016]征途 斜率dp

#include<map>
#include<queue>
#include<time.h>
#include<limits.h>
#include<cmath>
#include<ostream>
#include<iterator>
#include<set>
#include<stack>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define rep_1(i,m,n) for(int i=m;i<=n;i++)
#define mem(st) memset(st,0,sizeof st)
int read()
{
	int res=0,ch,flag=0;
	if((ch=getchar())=='-')             //判断正负
		flag=1;
	else if(ch>='0'&&ch<='9')           //得到完整的数
		res=ch-'0';
	while((ch=getchar())>='0'&&ch<='9')
		res=res*10+ch-'0';
	return flag?-res:res;
}
typedef long long ll;
typedef pair<int,int> pii;
typedef unsigned long long ull;
typedef pair<double,double> pdd;
const int inf = 0x3f3f3f3f;
const int N=3030;
int n, m, sum[N], q[N], hh,tt;
long long f[N], g[N];
double Y(int i)
{
	return g[i]+sum[i]*sum[i];
}
double X(int i)
{
	return sum[i];
}
double slope(int i,int j)
{
	return (Y(i)-Y(j))/(X(i)-X(j));
}
int main()
{
	n=read(),m=read();
	for(int i = 1; i <= n; i++)
	{
		sum[i] = read();
		sum[i] += sum[i - 1];
		g[i] = 1ll * sum[i] * sum[i];
	} 
	for(int k=1; k<m; k++)
	{
		hh=0,tt=0;
		q[++tt]=k;
		for(int i=k+1; i<=n; i++)
		{
			while(hh<tt && slope(q[hh],q[hh+1])<2*sum[i])
				hh++;
			f[i]=g[q[hh]]+(sum[i]-sum[q[hh]])*(sum[i]-sum[q[hh]]);
			while(hh<tt && slope(i,q[tt-1])<slope(q[tt],q[tt-1]))
				tt--;
			q[++tt]=i;
		}
		for(int i=1; i<=n; i++)
			g[i]=f[i];
	}
	//最后乘上m 
	cout<<m*f[n]-sum[n]*sum[n]<<endl;
	return 0;
}