int main () {
Euler1 euler1(1000);
euler1.solve();
std::cout << euler1.getResult();
return 0;
}
void euler1(int u) {
c[u]++;
for (int v = 0; v < 26; v++)
if (g[u][v]) {
g[u][v]--;
c[u]--;
euler1(v);
}
}
int main()
{
int n = 0;
euler1(&n);
printf("solution 1: %d\n", n);
IEuler* euler;
HRESULT h = createEuler(&euler);
euler->answer(0, &n);
printf("the final answer: %d\n", n);
}
TString MillePedeTrees::Alpha(const TString &tree, bool betaMpiPpi) const
{
// a la AlignmentTransformations::eulerAngles
// double rot[3][3];
// rot[0][0] = Rot[0]; // Rot from tree
// rot[0][1] = Rot[1];
// rot[0][2] = Rot[2];
// rot[1][0] = Rot[3];
// rot[1][1] = Rot[4];
// rot[1][2] = Rot[5];
// rot[2][0] = Rot[6];
// rot[2][1] = Rot[7];
// rot[2][2] = Rot[8];
TString euler1("TMath::ASin(Rot[6])");
if (!betaMpiPpi) euler1.Prepend("TMath::Pi() - ");
TString euler0("TMath::ATan(-Rot[7]/Rot[8]) + (TMath::Pi() * (TMath::Cos(");
euler0 += euler1;
euler0 += ") * Rot[8] <= 0))";
TString result(Form("(TMath::Abs(Rot[6] - 1.0) >= 1.e-6) * (%s)", euler0.Data()));
result.ReplaceAll("Rot[", tree + "Rot[");
return result;
// if (TMath::Abs(Rot[6] - 1.0) > 1.e-6) { // If angle1 is not +-PI/2
// if (flag == 0) // assuming -PI/2 < angle1 < PI/2
// euler[1] = TMath::ASin(Rot[6]); // New beta sign convention
// else // assuming angle1 < -PI/2 or angle1 >PI/2
// euler[1] = TMath::Pi() - TMath::ASin(Rot[6]); // New beta sign convention
// if (TMath::Cos(euler[1]) * Rot[8] > 0)
// euler[0] = TMath::ATan(-Rot[7]/Rot[8]);
// else
// euler[0] = TMath::ATan(-Rot[7]/Rot[8]) + TMath::Pi();
// if (TMath::Cos(euler[1]) * Rot[0] > 0)
// euler[2] = TMath::ATan(-Rot[3]/Rot[0]);
// else
// euler[2] = TMath::ATan(-Rot[3]/Rot[0]) + TMath::Pi();
// } else { // if angle1 == +-PI/2
// euler[1] = TMath::PiOver2(); // chose positve Solution
// if(Rot[8] > 0) {
// euler[2] = TMath::ATan(Rot[5]/Rot[4]);
// euler[0] = 0;
// }
// }
}
int main() {
int t;
scanf("%d", &t) == 1;
while (t--) {
scanf("%d", &n) == 1;
memset(g, 0, sizeof(g));
memset(c, 0, sizeof(c));
memset(s, '\0', sizeof(s));
int cnt = n;
while (cnt--) {
scanf("%s", s) == 1;
g[s[0]-'a'][s[strlen(s)-1]-'a']++;
}
for (int i = 0; i < 26; i++)
for (int j = 0; j < 26; j++)
if (g[i][j]) {
euler1(i);
euler2(i);
goto start;
}
start:
bool iscon = true;
for (int i = 0; i < 26; i++)
for (int j = 0; j < 26; j++)
if (g[i][j]) {
iscon = false;
goto end;
}
end:
int dcnt = 0;
for (int i = 0; i < 26; i++)
if (c[i]) dcnt++;
if (!iscon || dcnt > 2) {
printf("The door cannot be opened.\n");
continue;
}
printf("Ordering is possible.\n");
// for (int i = 0; i < 26; i++) {
// for (int j = 0; j < 26; j++)
// printf("%d", g[i][j]);
// printf("\n");
// }
// printf("\n");
}
return 0;
}
TString MillePedeTrees::Gamma(const TString &tree, bool betaMpiPpi) const
{
TString euler1("TMath::ASin(Rot[6])");
if (!betaMpiPpi) euler1.Prepend("TMath::Pi() - ");
TString euler2("TMath::ATan(-Rot[3]/Rot[0]) + (TMath::Pi() * (TMath::Cos(");
euler2 += euler1;
euler2 += ") * Rot[0] <= 0))";
TString result(Form("(TMath::Abs(Rot[6] - 1.0) >= 1.e-6) * (%s)", euler2.Data()));
result += "+ (TMath::Abs(Rot[6] - 1.0) < 1.e-6) * (TMath::ATan(Rot[5]/Rot[4]))";
result.ReplaceAll("Rot[", tree + "Rot[");
return result;
/*
if (TMath::Abs(Rot[6] - 1.0) > 1.e-6) { // If angle1 is not +-PI/2
if (flag == 0) // assuming -PI/2 < angle1 < PI/2
euler[1] = TMath::ASin(Rot[6]); // New beta sign convention
else // assuming angle1 < -PI/2 or angle1 >PI/2
euler[1] = TMath::Pi() - TMath::ASin(Rot[6]); // New beta sign convention
if (TMath::Cos(euler[1]) * Rot[8] > 0)
euler[0] = TMath::ATan(-Rot[7]/Rot[8]);
else
euler[0] = TMath::ATan(-Rot[7]/Rot[8]) + TMath::Pi();
if (TMath::Cos(euler[1]) * Rot[0] > 0)
euler[2] = TMath::ATan(-Rot[3]/Rot[0]);
else
euler[2] = TMath::ATan(-Rot[3]/Rot[0]) + TMath::Pi();
} else { // if angle1 == +-PI/2
euler[1] = TMath::PiOver2(); // chose positve Solution
if(Rot[8] > 0) {
euler[2] = TMath::ATan(Rot[5]/Rot[4]);
euler[0] = 0;
}
}
*/
}
int main( void ) {
// init
time_t seed = time(NULL);
printf("seed: %ld\n", seed);
srand((unsigned int)seed); // might break in 2038
aa_test_ulimit();
for( size_t i = 0; i < 1000; i++ ) {
/* Random Data */
static const size_t k=2;
double E[2][7], S[2][8], T[2][12], dx[2][6];
for( size_t j = 0; j < k; j ++ ) {
rand_tf(E[j], S[j], T[j]);
aa_vrand(6,dx[j]);
}
//printf("%d\n",i);
/* Run Tests */
rotvec(E[0]);
euler(dx[0]);
euler1(dx[0]);
eulerzyx(E[0]);
chain(E,S,T);
quat(E);
duqu();
rel_q();
rel_d();
slerp();
theta2quat();
rotmat(E[0]);
tfmat();
tfmat_inv(T[0]);
mzlook(dx[0]+0, dx[0]+3, dx[1]+0);
integrate(E[0], S[0], T[0], dx[0]);
tf_conj(E, S);
qdiff(E,dx);
}
return 0;
}
void Custom6DOF::SubmitConstraints (dFloat timestep, int threadIndex)
{
dMatrix matrix0;
dMatrix matrix1;
// calculate the position of the pivot point and the Jacobian direction vectors, in global space.
CalculateGlobalMatrix (matrix0, matrix1);
// add the linear limits
const dVector& p0 = matrix0.m_posit;
const dVector& p1 = matrix1.m_posit;
dVector dp (p0 - p1);
for (int i = 0; i < 3; i ++) {
if ((m_minLinearLimits[i] == 0.0f) && (m_maxLinearLimits[i] == 0.0f)) {
NewtonUserJointAddLinearRow (m_joint, &p0[0], &p1[0], &matrix0[i][0]);
NewtonUserJointSetRowStiffness (m_joint, 1.0f);
} else {
// it is a limited linear dof, check if it pass the limits
dFloat dist = dp.DotProduct3(matrix1[i]);
if (dist > m_maxLinearLimits[i]) {
dVector q1 (p1 + matrix1[i].Scale (m_maxLinearLimits[i]));
// clamp the error, so the not too much energy is added when constraint violation occurs
dFloat maxDist = (p0 - q1).DotProduct3(matrix1[i]);
if (maxDist > D_6DOF_ANGULAR_MAX_LINEAR_CORRECTION) {
q1 = p0 - matrix1[i].Scale(D_6DOF_ANGULAR_MAX_LINEAR_CORRECTION);
}
NewtonUserJointAddLinearRow (m_joint, &p0[0], &q1[0], &matrix0[i][0]);
NewtonUserJointSetRowStiffness (m_joint, 1.0f);
// allow the object to return but not to kick going forward
NewtonUserJointSetRowMaximumFriction (m_joint, 0.0f);
} else if (dist < m_minLinearLimits[i]) {
dVector q1 (p1 + matrix1[i].Scale (m_minLinearLimits[i]));
// clamp the error, so the not too much energy is added when constraint violation occurs
dFloat maxDist = (p0 - q1).DotProduct3(matrix1[i]);
if (maxDist < -D_6DOF_ANGULAR_MAX_LINEAR_CORRECTION) {
q1 = p0 - matrix1[i].Scale(-D_6DOF_ANGULAR_MAX_LINEAR_CORRECTION);
}
NewtonUserJointAddLinearRow (m_joint, &p0[0], &q1[0], &matrix0[i][0]);
NewtonUserJointSetRowStiffness (m_joint, 1.0f);
// allow the object to return but not to kick going forward
NewtonUserJointSetRowMinimumFriction (m_joint, 0.0f);
}
}
}
dVector euler0(0.0f);
dVector euler1(0.0f);
dMatrix localMatrix (matrix0 * matrix1.Inverse());
localMatrix.GetEulerAngles(euler0, euler1);
AngularIntegration pitchStep0 (AngularIntegration (euler0.m_x) - m_pitch);
AngularIntegration pitchStep1 (AngularIntegration (euler1.m_x) - m_pitch);
if (dAbs (pitchStep0.GetAngle()) > dAbs (pitchStep1.GetAngle())) {
euler0 = euler1;
}
dVector euler (m_pitch.Update (euler0.m_x), m_yaw.Update (euler0.m_y), m_roll.Update (euler0.m_z), 0.0f);
//dTrace (("(%f %f %f) (%f %f %f)\n", m_pitch.m_angle * 180.0f / 3.141592f, m_yaw.m_angle * 180.0f / 3.141592f, m_roll.m_angle * 180.0f / 3.141592f, euler0.m_x * 180.0f / 3.141592f, euler0.m_y * 180.0f / 3.141592f, euler0.m_z * 180.0f / 3.141592f));
bool limitViolation = false;
for (int i = 0; i < 3; i ++) {
if (euler[i] < m_minAngularLimits[i]) {
limitViolation = true;
euler[i] = m_minAngularLimits[i];
} else if (euler[i] > m_maxAngularLimits[i]) {
limitViolation = true;
euler[i] = m_maxAngularLimits[i];
}
}
if (limitViolation) {
//dMatrix pyr (dPitchMatrix(m_pitch.m_angle) * dYawMatrix(m_yaw.m_angle) * dRollMatrix(m_roll.m_angle));
dMatrix p0y0r0 (dPitchMatrix(euler[0]) * dYawMatrix(euler[1]) * dRollMatrix(euler[2]));
dMatrix baseMatrix (p0y0r0 * matrix1);
dMatrix rotation (matrix0.Inverse() * baseMatrix);
dQuaternion quat (rotation);
if (quat.m_q0 > dFloat (0.99995f)) {
//dVector p0 (matrix0[3] + baseMatrix[1].Scale (MIN_JOINT_PIN_LENGTH));
//dVector p1 (matrix0[3] + baseMatrix[1].Scale (MIN_JOINT_PIN_LENGTH));
//NewtonUserJointAddLinearRow (m_joint, &p0[0], &p1[0], &baseMatrix[2][0]);
//NewtonUserJointSetRowMinimumFriction(m_joint, 0.0f);
//dVector q0 (matrix0[3] + baseMatrix[0].Scale (MIN_JOINT_PIN_LENGTH));
//NewtonUserJointAddLinearRow (m_joint, &q0[0], &q0[0], &baseMatrix[1][0]);
//NewtonUserJointAddLinearRow (m_joint, &q0[0], &q0[0], &baseMatrix[2][0]);
} else {
dMatrix basis (dGrammSchmidt (dVector (quat.m_q1, quat.m_q2, quat.m_q3, 0.0f)));
dVector q0 (matrix0[3] + basis[1].Scale (MIN_JOINT_PIN_LENGTH));
dVector q1 (matrix0[3] + rotation.RotateVector(basis[1].Scale (MIN_JOINT_PIN_LENGTH)));
NewtonUserJointAddLinearRow (m_joint, &q0[0], &q1[0], &basis[2][0]);
NewtonUserJointSetRowMinimumFriction(m_joint, 0.0f);
//dVector q0 (matrix0[3] + basis[0].Scale (MIN_JOINT_PIN_LENGTH));
//NewtonUserJointAddLinearRow (m_joint, &q0[0], &q0[0], &basis[1][0]);
//NewtonUserJointAddLinearRow (m_joint, &q0[0], &q0[0], &basis[2][0]);
}
}
}
int main(void) {
printf("%d\n", euler1(3, 5, 1000));
}
