hdu 2829 斜率DP

思路：dp[i][x]=dp[j][x-1]+val[i]-val[j]-sum[j]*sum[i]+sum[j]*sum[j];

其中val[i]表示1~~i是一段的权值。

然后就是普通斜率dp做法。

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
#include<cstring>
#define Maxn 1010
#define LL __int64
using namespace std;
LL dp[Maxn][Maxn],num[Maxn],sum[Maxn],val[Maxn];
int que[Maxn*10];
LL getleft(int x,int j,int k)
{
    return dp[j][x]-val[j]+sum[j]*sum[j]-(dp[k][x]-val[k]+sum[k]*sum[k]);
}
LL getright(int j,int k)
{
    return sum[j]-sum[k];
}
int main()
{
    int n,m,i,j,head,rear;
    while(scanf("%d%d",&n,&m)!=EOF,n||m){
        memset(dp,0,sizeof(dp));
        for(i=1;i<=n;i++){
            scanf("%I64d",num+i);
            sum[i]=sum[i-1]+num[i];
        }
        for(i=1;i<=n;i++){
            val[i]=val[i-1]+num[i]*sum[i-1];
            dp[i][0]=val[i];
        }
        for(j=0;j<m;j++){
            head=1,rear=0;
            que[++rear]=j;
            for(i=j+1;i<=n;i++){
                while(head<rear&&getleft(j,que[head+1],que[head])<sum[i]*getright(que[head+1],que[head]))
                    head++;
                dp[i][j+1]=dp[que[head]][j]+val[i]-val[que[head]]-sum[que[head]]*sum[i]+sum[que[head]]*sum[que[head]];
                while(head<rear&&getleft(j,i,que[rear])*getright(que[rear],que[rear-1])<=getleft(j,que[rear],que[rear-1])*getright(i,que[rear]))
                    rear--;
                que[++rear]=i;
            }
        }
        printf("%I64d
",dp[n][m]);
    }
    return 0;
}