学步园

#include <cstdio>
#include <cstring>
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
#define INF 1200000000

const int maxn = 5003;
const int maxk = 1670;
int d[maxn][2][maxk],v[maxn],n;
bool vis[maxn][2][maxk];
int dp(int i,int j,int k){
if(vis[i][j][k]) return d[i][j][k];
vis[i][j][k] = true;

if(k==0) return d[i][j][k]=0;
int& ans=d[i][j][k];
ans=dp(i+2,1,k-1)+(v[i+1]-v[i+2])*(v[i+1]-v[i+2]);
if(n-i-1>=k*3) ans=min(ans,dp(i+1,0,k));
return ans;
}
int main()
{
    int T,k;
    scanf("%d",&T);
    while(T--){
          scanf("%d %d",&k,&n);
          k+=8;
          for(int i=1;i<=n;i++) scanf("%d",&v[i]);
          for(int i=0;i<=n;i++)
              for(int j=0;j<2;j++)
                 for(int kk=0;kk<=k;kk++) vis[i][j][kk]=false;
          printf("%d\n",dp(0,0,k));
    }
    return 0;
}

上面的版本是当时为了找到状态转移方程多加了一维，其实完全没必要

#include <cstdio>
#include <cstring>
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
#define INF 1200000000

const int maxn = 5003;
const int maxk = 1670;
int d[maxn][maxk],v[maxn],n;
bool vis[maxn][maxk];
int dp(int i,int k){
if(vis[i][k]) return d[i][k];
vis[i][k] = true;

if(k==0) return d[i][k]=0;
int& ans=d[i][k];
ans=dp(i+2,k-1)+(v[i+1]-v[i+2])*(v[i+1]-v[i+2]);
if(n-i-1>=k*3) ans=min(ans,dp(i+1,k));
return ans;
}
int main()
{
    int T,k;
    scanf("%d",&T);
    while(T--){
          scanf("%d %d",&k,&n);
          k+=8;
          for(int i=1;i<=n;i++) scanf("%d",&v[i]);
          for(int i=0;i<=n;i++)
                 for(int kk=0;kk<=k;kk++) vis[i][kk]=false;
          printf("%d\n",dp(0,k));
    }
    return 0;
}