1652: [Usaco2006 Feb]Treats for the Cows

区间DP，逆向递推；

dp[i][j]表示i到j编号能取到的最大值；

状态转移方程为dp[i][j] = max(dp[i][j-1]+v[j]*day, dp[i+1][j]+v[i]*day);

注意，区间dp是随着区间增大逐步更新数据，于是要把“区间”放在循环的最外层。

#include <iostream>

using namespace std;

int N, dp[2010][2010], v[2010];

int main() {
    cin >> N;
    for (int i = 1; i <= N; ++i) cin >> v[i];
    for (int i = 1; i <= N; ++i) dp[i][i] = v[i] * N;
    
    int day = N;
    for (int sp = 1; sp <= N; ++sp) {
        day --;
        for (int st = 1; st <= N; ++ st) {
            if (st + sp > N) break;
            dp[st][st+sp] = max(dp[st][st+sp-1] + v[st+sp] * day, dp[st+1][st+sp] + v[st] * day);
        }
    }
    cout << dp[1][N] << endl;
    return 0;
}