【BZOJ 1592】[Usaco2008 Feb]Making the Grade 路面修整 dp优化之转移变状态

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define N 2010
using namespace std;
inline int read()
{
  register int sum=0;register char ch=getchar();
  while(ch<‘0‘||ch>‘9‘)ch=getchar();
  while(ch>=‘0‘&&ch<=‘9‘)sum=(sum<<1)+(sum<<3)+ch-‘0‘,ch=getchar();
  return sum;
}
int a[N],f[N][N],ans,n,pos[N],len,Hash[N];
int comp(const int x,const int y){
  return a[x]<a[y];
}
inline int Min(int x,int y){
  return x<y?x:y;
}
inline int Abs(int x){
  return x<0?-x:x;
}
inline int get_Min(){
  memset(f,0x7f,sizeof(f));register int ans=0x7fffffff;
  for(register int i=1;i<=len;i++)f[1][i]=Min(f[1][i-1],Abs(Hash[i]-Hash[a[1]]));
  for(register int i=2;i<=n;i++)
    for(register int j=1;j<=len;j++)
      f[i][j]=Min(f[i][j-1],f[i-1][j]+Abs(Hash[j]-Hash[a[i]]));
  for(register int i=1;i<=len;i++)ans=Min(ans,f[n][i]);
  return ans;
}
inline int get_Max(){
  memset(f,0x7f,sizeof(f));register int ans=0x7fffffff;
  for(register int i=1;i<=len;i++)f[1][i]=Min(f[1][i+1],Abs(Hash[i]-Hash[a[1]]));
  for(register int i=2;i<=n;i++)
    for(register int j=len;j>0;j--)
      f[i][j]=Min(f[i][j+1],f[i-1][j]+Abs(Hash[j]-Hash[a[i]]));
  for(register int i=1;i<=len;i++)ans=Min(ans,f[n][i]);
  return ans;
}
int main(){
  n=read();for(register int i=1;i<=n;i++)a[i]=read(),pos[i]=i;
  sort(pos+1,pos+n+1,comp);
  for(register int i=1;i<=n;i++)
    if(i==1||a[pos[i]]!=a[pos[i-1]])Hash[++len]=a[pos[i]],a[pos[i]]=len;
    else a[pos[i]]=len;
  printf("%d",Min(get_Min(),get_Max()));
}