bzoj1652 / P2858 [USACO06FEB]奶牛零食Treats for the Cows

P2858 [USACO06FEB]奶牛零食Treats for the Cows

区间dp

设$f[l][r]$为取区间$[l,r]$的最优解，蓝后倒着推

$f[l][r]=max(f[l+1][r]+a[l]*p,f[l][r-1]+a[r]*p)$

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int max(int a,int b){return a>b?a:b;}
#define N 2010
int a[N],f[N][N],n;
int main(){
    //freopen("P2858.in","r",stdin);
    scanf("%d",&n);
    for(int i=1;i<=n;++i)
        scanf("%d",&a[i]),f[i][i]=a[i]*n;
    for(int i=2;i<=n;++i)
        for(int l=1,r,p;l+i-1<=n;++l){
            r=l+i-1; p=n-i+1;
            f[l][r]=max(f[l+1][r]+a[l]*p,f[l][r-1]+a[r]*p);
        }
    printf("%d",f[1][n]);
    return 0;
}