思路：

平形四边形不等式优化dp

同上一篇博客

代码：

#pragma GCC optimize(2)#pragma GCC optimize(3)#pragma GCC optimize(4)#include
     
      #include
      
       #include
       
        using namespace std;#define y1 y11#define fi first#define se second#define pi acos(-1.0)#define LL long long#define LD long double//#define mp make_pair#define pb push_back#define ls rt<<1, l, m#define rs rt<<1|1, m+1, r#define ULL unsigned LL#define pll pair
        
         #define pli pair
         
          #define pii pair
          
           #define piii pair
           
            #define pdd pair
            
             #define mem(a, b) memset(a, b, sizeof(a))#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);//headconst int N = 1e3 + 5;LL dp[N][N], w[N][N];int n, m, s[N][N], a[N];int main() { while(~scanf("%d %d", &n, &m) && n && m) { for (int i = 1; i <= n; ++i) scanf("%d", &a[i]); for (int i = 0; i <= m+1; ++i) for (int j = 0; j <= n; ++j) dp[i][j] = 1LL<<58; for (int i = 1; i <= n; ++i) { w[i][i] = 0; int s = a[i]; for (int j = i+1; j <= n; ++j) { w[i][j] = w[i][j-1]+s*a[j]; s += a[j]; } } dp[0][0] = 0; for (int i = 1; i <= m+1; ++i) { w[i][n+1] = n-1; for (int j = n; j >= 1; --j) { for (int k = w[i-1][j]; k <= w[i][j+1]; ++k) { if(k+1 <= j && dp[i-1][k]+w[k+1][j] < dp[i][j]) { dp[i][j] = dp[i-1][k]+w[k+1][j]; w[i][j] = k; } } } } printf("%d\n", dp[m+1][n]); } return 0;}