P3195 [HNOI2008]玩具装箱

[HNOI2008]玩具装箱

 

 f[i] =max( f[j]+  (s[i]-s[j] + i-j+1 )^2

 设 a[i] =fi + si ,b[i] =s[i]+i+1

 f[i] =max( f[j] + (a[i]-b[j])^2

 　　=max{ f[j]+a[j]^2+b[j]^2 -2*a[j]*b[j])

 

然后斜率优化： 考虑2个点j k, j<k ,  func(j)<func(k) ，得到斜率的柿子

 

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#include <iostream> #include <cmath> #include <cstdio> #include <algorithm> using namespace std;  const int  N =5e4+2;  #define int long long  int f[N];  int n,m, s[N];  int q[N],hh,tt;     int a(int i){    return s[i]+i;  }  int b(int i){    return a(i)+m+1;  }  int Y(int i){    return f[i]+b(i)*b(i);  }  long double slope(int i,int j){    return 1.0*(Y(i)-Y(j))/(b(i)-b(j));  } signed main(){    cin>>n>>m;    int i;    for(i=1;i<=n;i++) cin>>s[i],s[i]+=s[i-1];         hh=tt=1;    for(i=1;i<=n;++i){        while(hh<tt&&slope(q[hh],q[hh+1])<=2.0*a(i))        hh++;        f[i]=f[q[hh]]+(a(i)-b(q[hh]))*(a(i)-b(q[hh]));        while(hh<tt&&slope(q[tt-1],q[tt])>slope(q[tt],i))        tt--;        q[++tt]=i;    }    cout<<f[n]<<endl; }