76 lines
1.9 KiB
C++
76 lines
1.9 KiB
C++
#include<stdio.h>
|
|
#include<iostream>
|
|
#include<string.h>
|
|
#include<algorithm>
|
|
using namespace std;
|
|
const int MAXN=1010;
|
|
int a[MAXN];
|
|
int sum[MAXN];
|
|
int cost[MAXN];
|
|
int q[MAXN];
|
|
int head,tail;
|
|
int n,m;
|
|
int dp[MAXN][MAXN];
|
|
int DP()
|
|
{
|
|
for(int i=1;i<=n;i++)
|
|
{
|
|
dp[i][0]=cost[i];
|
|
dp[i][i-1]=0;
|
|
}
|
|
for(int j=1;j<=m;j++)
|
|
{
|
|
head=tail=0;
|
|
q[tail++]=j;
|
|
for(int i=j+1;i<=n;i++)
|
|
{
|
|
while(head+1<tail)
|
|
{
|
|
int p1=q[head];
|
|
int p2=q[head+1];
|
|
int x1=sum[p1];
|
|
int x2=sum[p2];
|
|
int y1=dp[p1][j-1]-cost[p1]+sum[p1]*sum[p1];
|
|
int y2=dp[p2][j-1]-cost[p2]+sum[p2]*sum[p2];
|
|
if((y2-y1)<=sum[i]*(x2-x1)) head++;
|
|
else break;
|
|
}
|
|
int k=q[head];
|
|
dp[i][j]=dp[k][j-1]+cost[i]-cost[k]-sum[k]*sum[i]+sum[k]*sum[k];
|
|
while(head+1<tail)
|
|
{
|
|
int p1=q[tail-2];
|
|
int p2=q[tail-1];
|
|
int p3=i;
|
|
int x1=sum[p1];
|
|
int x2=sum[p2];
|
|
int x3=sum[p3];
|
|
int y1=dp[p1][j-1]-cost[p1]+sum[p1]*sum[p1];
|
|
int y2=dp[p2][j-1]-cost[p2]+sum[p2]*sum[p2];
|
|
int y3=dp[p3][j-1]-cost[p3]+sum[p3]*sum[p3];
|
|
if((y2-y1)*(x3-x2)>=(y3-y2)*(x2-x1))tail--;
|
|
else break;
|
|
}
|
|
q[tail++]=i;
|
|
}
|
|
}
|
|
return dp[n][m];
|
|
}
|
|
int main()
|
|
{
|
|
while(scanf("%d%d",&n,&m)==2)
|
|
{
|
|
if(n==0&&m==0)break;
|
|
sum[0]=0;
|
|
cost[0]=0;
|
|
for(int i=1;i<=n;i++)
|
|
{
|
|
scanf("%d",&a[i]);
|
|
sum[i]=sum[i-1]+a[i];
|
|
cost[i]=cost[i-1]+sum[i-1]*a[i];
|
|
}
|
|
printf("%d\n",DP());
|
|
}
|
|
return 0;
|
|
}
|