/**
Kreis an die Punkte (2xN-Array) anfitten.
*/
Eigen::Vector3f fit_circle(const Eigen::Array2Xf& points) {
Eigen::Array2f mean = points.rowwise().mean();
Eigen::Array2Xf uv(points.colwise() - mean);
Eigen::Array2f Sp2 = uv.square().rowwise().sum();
Eigen::Array2f Sp3 = uv.cube().rowwise().sum();
float Suv = (uv.row(0) * uv.row(1)).sum();
float Suvv = (uv.row(0) * uv.row(1).square()).sum();
float Svuu = (uv.row(0).square() * uv.row(1)).sum();
// Rechte Seite berechnen
Eigen::Vector2f b((Sp3 + Eigen::Array2f(Suvv, Svuu)) / 2);
// Linke Seite berechnen
Eigen::Matrix2f A;
A << Sp2(0), Suv, Suv, Sp2(1);
// Gleichungssystem Lösen
Eigen::Array2f mid = A.inverse() * b;
// Quadrat des Radius berechnen
float radius = sqrt(mid.square().sum() + Sp2.sum() / points.cols());
return (Eigen::Vector3f() << (mid + mean), radius).finished();
}
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
vector<int> solution(string &S, vector<int> &P, vector<int> &Q)
{
// write your code in C++11 (g++ 4.8.2)
int n=S.size();
vector<int> Sp1(n+1,0),Sp2(n+1,0),Sp3(n+1,0),Sp4(n+1,0);
for(int i=0;i<n;i++)
{
switch(S[i])
{
case 'A':
Sp1[i+1]++;
break;
case 'C':
Sp2[i+1]++;
break;
case 'G':
Sp3[i+1]++;
break;
case 'T':
Sp4[i+1]++;
break;
}
}
for(int i=0;i<n;i++)
{
Sp1[i+1]+= Sp1[i];
Sp2[i+1]+= Sp2[i];
Sp3[i+1]+= Sp3[i];
Sp4[i+1]+= Sp4[i];
}
for(int i=0;i<Q.size();i++)
{
int r=0;
if(Sp4[Q[i]+1]-Sp4[P[i]]>0){r=4;}
if(Sp3[Q[i]+1]-Sp3[P[i]]>0){r=3;}
if(Sp2[Q[i]+1]-Sp2[P[i]]>0){r=2;}
if(Sp1[Q[i]+1]-Sp1[P[i]]>0){r=1;}
Q[i]=r;
}
return Q;
}