hdu 3480

排个序，很容易可以证明出四边形不等式

#include <cstdio>
#include <cstring>
const int MAXN = 1000 + 123;
int dp[MAXN][MAXN], cost[MAXN][MAXN];
int s[MAXN][MAXN];
int sum[MAXN], a[MAXN];
int main()
{
    int n, m;
    while(scanf("%d%d", &n, &m) != EOF)
    {
        if(n == 0 && m == 0)  break;
        sum[0] = 0;
        for(int i = 1; i <= n; i++)
        {
            scanf("%d", &a[i]);
            sum[i] = sum[i-1] + a[i];
        }
        memset(cost, 0, sizeof(cost));
        for(int i = 1; i <= n; i++)
          for(int j = i + 1; j <= n; j++)
          {
              cost[i][j] = cost[i][j-1] + (sum[j-1] - sum[i-1]) * a[j];
          }

        for(int i = 0; i <= n; i++)
        {
            s[i][0] = 1;
            dp[i][0] = cost[1][i];
        }

        for(int k = 1; k <= m; k++)
        {
            s[n+1][k] = n - 1;
            for(int i = n; i > k; i--)
            {
              dp[i][k]=dp[k][k-1]+cost[k+1][i];
              s[i][k]=k;
              for(int j=s[i][k-1];j<=s[i+1][k];j++)
              {
                  int temp = dp[j][k-1]+cost[j+1][i];
                  if(temp<dp[i][k])
                  {
                      dp[i][k]=temp;
                      s[i][k]=j;
                  }
              }
            }
        }

        printf("%d\n",dp[n][m]);
    }
    return 0;
}

滚动数组版本

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int MAXN = 10000 + 10;
const int MAXM = 5000 + 10;
int dp[2][MAXN];
int s[2][MAXN];
int a[MAXN];
int main()
{
    int T;
    int cas = 1;
    scanf("%d", &T);
    while(T--)
    {
        int n, m;
        scanf("%d%d", &n, &m);
        m--;

        for(int i = 1; i <= n; i++)  scanf("%d", &a[i]);
        sort(a+1, a+1+n);


        for(int i = 1; i <= n; i++)
        {
            dp[1][i] = (a[i] - a[1]) * (a[i] - a[1]);
            s[1][i] = 1;
        }

        for(int k = 1; k <= m; k++)
        {
            memcpy(dp[0], dp[1], sizeof(dp[1]));
            memcpy(s[0], s[1], sizeof(s[1]));
            s[1][n + 1] = n - 1;
            for(int i = n; i >= k + 1; i--)
            {
                dp[1][i] = dp[0][k] + (a[i] - a[k+1]) * (a[i] - a[k+1]);
                s[1][i] = k;
                for(int j = s[0][i]; j <= s[1][i+1]; j++)
                {
                    int temp = dp[0][j] + (a[i] - a[j+1]) * (a[i] - a[j+1]);
                    if(temp < dp[1][i])
                    {
                        dp[1][i] = temp;
                        s[1][i] = j;
                    }
                }
            }
        }

        printf("Case %d: %d\n",cas++, dp[1][n]);
    }
    return 0;
}