[DP] BZOJ 4897 [Thu Summer Camp2016]成绩单

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f[i][j][down][up] 表示在区间[i,j]取数 还剩下[down,up]中的数的最小代价
转移f[i][j][down][up]=min{初始值,f[i][k][down][up]+f[k+1][j][down][up]}
其中 初始值 为[i,j]中去掉头尾连续的都处于值区间的数后取完的最小代价
取完的代价g[i][j]=min{f[i][j][down][up]+去掉剩下的数的代价}

#include<cstdio>#include<cstdlib>  #include<algorithm>  #include<cstring>  using namespace std;  typedef long long ll;  inline char nc()  {      static char buf[100000],*p1=buf,*p2=buf;      if (p1==p2) { p2=(p1=buf)+fread(buf,1,100000,stdin); if (p1==p2) return EOF; }      return *p1++;  }  inline void read(int &x)  {      char c=nc(),b=1;      for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1;      for (x=0;c>='0' && c<='9';x=x*10+c-'0',c=nc()); x*=b;  }  inline ll sqr(int x){      return x*x;  }  const int N=51;  int sx[N],icnt;  inline int Bin(int x){      return lower_bound(sx+1,sx+icnt+1,x)-sx;  }  int n,x[N];  int a,b;  ll ans,f[N][N][N][N],g[N][N];  int main()  {      int l,r,down,up,tl,tr,maxv,minv;      freopen("t.in","r",stdin);      freopen("t.out","w",stdout);      read(n); read(a); read(b);      for (int i=1;i<=n;i++) read(x[i]),sx[++icnt]=x[i];      sort(sx+1,sx+icnt+1); icnt=unique(sx+1,sx+icnt+1)-sx-1;      for (int i=1;i<=n;i++) x[i]=Bin(x[i]);      for (int i=1;i<=n;i++)          for (int j=1;j+i-1<=n;j++)          {              l=j,r=j+i-1;              maxv=-1<<30,minv=1<<30;              for (int k=l;k<=r;k++) maxv=max(maxv,x[k]),minv=min(minv,x[k]);              g[l][r]=a+sqr(sx[maxv]-sx[minv])*b;              for (down=1;down<=icnt;down++)                  for (up=down;up<=icnt;up++)                  {                      if (up<minv || down>maxv) continue;                      tl=l-1,tr=r+1;                      for (int k=l;k<=r;k++) if (down<=x[k] && x[k]<=up) tl=k; else break;                      for (int k=r;k>=l;k--) if (down<=x[k] && x[k]<=up) tr=k; else break;                      if (tl>=tr)                          f[l][r][down][up]=0;                      else                          f[l][r][down][up]=g[tl+1][tr-1];                      for (int k=l;k<r;k++)                          f[l][r][down][up]=min(f[l][r][down][up],f[l][k][down][up]+f[k+1][r][down][up]);                      g[l][r]=min(g[l][r],f[l][r][down][up]+a+sqr(sx[up]-sx[down])*b);                  }              for (down=maxv+1;down<=icnt;down++)                  for (up=down;up<=icnt;up++)                      f[l][r][down][up]=g[l][r];              for (up=1;up<minv;up++)                  for (down=1;down<=up;down++)                      f[l][r][down][up]=g[l][r];          }      printf("%lld\n",g[1][n]);      return 0;  }