//
//
//Given an array of n integers where n > 1, nums, return an array output such that output[i] is equal to the product of all the elements of nums except nums[i].
//
//Solve it without division and in O(n).
//
//For example, given [1,2,3,4], return [24,12,8,6].
//
//Follow up:
// Could you solve it with constant space complexity? (Note: The output array does not count as extra space for the purpose of space complexity analysis.)
//
vector<int> productExceptSelf1(vector<int>& nums)
{
vector<int>product(nums.size(), 1);
vector<int>productl(nums.size(), 1);
for (int i = 1; i < nums.size(); i++)
{
productl[i] = productl[i-1]*nums[i-1];
}
vector<int>productr(nums.size(), 1);
for (int i = nums.size()-2; i >= 0; i--)
{
productr[i] = productr[i+1]*nums[i+1];
}
for (int i = 0; i < nums.size(); i++)
{
product[i] = productl[i]*productr[i];
}
return product;
}
inline TR TrX(const T1& rho1, arma::uvec sys, arma::uvec dim) {
const auto& p = as_Mat(rho1);
bool checkV = true;
if (p.n_cols == 1)
checkV = false;
#ifndef QICLIB_NO_DEBUG
if (p.n_elem == 0)
throw Exception("qic::TrX", Exception::type::ZERO_SIZE);
if (checkV)
if (p.n_rows != p.n_cols)
throw Exception("qic::TrX",
Exception::type::MATRIX_NOT_SQUARE_OR_CVECTOR);
if (dim.n_elem == 0 || arma::any(dim == 0))
throw Exception("qic::TrX", Exception::type::INVALID_DIMS);
if (arma::prod(dim) != p.n_rows)
throw Exception("qic::TrX", Exception::type::DIMS_MISMATCH_MATRIX);
if (dim.n_elem < sys.n_elem || arma::any(sys == 0) ||
arma::any(sys > dim.n_elem) ||
sys.n_elem != arma::find_unique(sys, false).eval().n_elem)
throw Exception("qic::TrX", Exception::type::INVALID_SUBSYS);
#endif
if (sys.n_elem == dim.n_elem)
return {arma::trace(p)};
_internal::dim_collapse_sys(dim, sys);
const arma::uword n = dim.n_elem;
const arma::uword m = sys.n_elem;
arma::uvec keep(n - m);
arma::uword keep_count(0);
for (arma::uword run = 0; run < n; ++run) {
if (!arma::any(sys == run + 1)) {
keep.at(keep_count) = run + 1;
++keep_count;
}
}
arma::uword dimtrace = arma::prod(dim(sys - 1));
arma::uword dimkeep = p.n_rows / dimtrace;
arma::uvec product(n, arma::fill::ones);
for (arma::sword i = n - 2; i > -1; --i)
product.at(i) = product.at(i + 1) * dim.at(i + 1);
arma::uvec productr(n - m, arma::fill::ones);
for (arma::sword i = n - m - 2; i > -1; --i)
productr.at(i) = productr.at(i + 1) * dim.at(keep.at(i + 1) - 1);
arma::Mat<trait::eT<T1> > tr_p(dimkeep, dimkeep, arma::fill::zeros);
const arma::uword loop_no = 2 * n;
arma::uword* loop_counter = new arma::uword[loop_no + 1];
arma::uword* MAX = new arma::uword[loop_no + 1];
for (arma::uword i = 0; i < n; ++i) {
MAX[i] = dim.at(i);
if (arma::any(sys == (i + 1)))
MAX[i + n] = 1;
else
MAX[i + n] = dim.at(i);
}
MAX[loop_no] = 2;
for (arma::uword i = 0; i < loop_no + 1; ++i) loop_counter[i] = 0;
arma::uword p1 = 0;
while (loop_counter[loop_no] == 0) {
arma::uword I(0), J(0), K(0), L(0), n_to_k(0);
for (arma::uword i = 0; i < n; ++i) {
if (arma::any(sys == i + 1)) {
I += product.at(i) * loop_counter[i];
J += product.at(i) * loop_counter[i];
} else {
I += product.at(i) * loop_counter[i];
J += product.at(i) * loop_counter[i + n];
}
if (arma::any(keep == i + 1)) {
K += productr.at(n_to_k) * loop_counter[i];
L += productr.at(n_to_k) * loop_counter[i + n];
++n_to_k;
}
}
tr_p.at(K, L) += checkV ? p.at(I, J) : p.at(I) * std::conj(p.at(J));
++loop_counter[0];
while (loop_counter[p1] == MAX[p1]) {
loop_counter[p1] = 0;
loop_counter[++p1]++;
if (loop_counter[p1] != MAX[p1])
p1 = 0;
}
}
delete[] loop_counter;
delete[] MAX;
return tr_p;
}
inline TR sysperm(const T1& rho1, const arma::uvec& sys,
const arma::uvec& dim) {
const auto& p = as_Mat(rho1);
const arma::uword n = dim.n_elem;
bool checkV = true;
if (p.n_cols == 1)
checkV = false;
#ifndef QICLIB_NO_DEBUG
if (p.n_elem == 0)
throw Exception("qic::sysperm", Exception::type::ZERO_SIZE);
if (checkV)
if (p.n_rows != p.n_cols)
throw Exception("qic::sysperm",
Exception::type::MATRIX_NOT_SQUARE_OR_CVECTOR);
if (dim.n_elem == 0 || arma::any(dim == 0))
throw Exception("qic::sysperm", Exception::type::INVALID_DIMS);
if (arma::prod(dim) != p.n_rows)
throw Exception("qic::sysperm", Exception::type::DIMS_MISMATCH_MATRIX);
if (n != sys.n_elem || arma::any(sys == 0) || arma::any(sys > n) ||
sys.n_elem != arma::find_unique(sys, false).eval().n_elem)
throw Exception("qic::sysperm", Exception::type::PERM_INVALID);
#endif
arma::uvec product(n, arma::fill::ones);
for (arma::sword i = n - 2; i >= 0; --i)
product.at(i) = product.at(i + 1) * dim.at(i + 1);
arma::uvec productr(n, arma::fill::ones);
for (arma::sword i = n - 2; i >= 0; --i)
productr.at(i) = productr.at(i + 1) * dim.at(sys.at(i + 1) - 1);
if (checkV) {
arma::Mat<trait::eT<T1> > p_r(p.n_rows, p.n_cols, arma::fill::zeros);
const arma::uword loop_no = 2 * n;
arma::uword* loop_counter = new arma::uword[loop_no + 1];
arma::uword* MAX = new arma::uword[loop_no + 1];
for (arma::uword i = 0; i < n; ++i) {
MAX[i] = dim.at(i);
MAX[i + n] = dim.at(i);
}
MAX[loop_no] = 2;
for (arma::uword i = 0; i < loop_no + 1; ++i) loop_counter[i] = 0;
arma::uword p1 = 0;
while (loop_counter[loop_no] == 0) {
arma::uword I(0), J(0), K(0), L(0);
for (arma::uword i = 0; i < n; ++i) {
I += product.at(i) * loop_counter[i];
J += product.at(i) * loop_counter[i + n];
K += productr.at(i) * loop_counter[sys.at(i) - 1];
L += productr.at(i) * loop_counter[sys.at(i) + n - 1];
}
p_r.at(K, L) = p.at(I, J);
++loop_counter[0];
while (loop_counter[p1] == MAX[p1]) {
loop_counter[p1] = 0;
loop_counter[++p1]++;
if (loop_counter[p1] != MAX[p1])
p1 = 0;
}
}
delete[] loop_counter;
delete[] MAX;
return p_r;
} else {
arma::Col<trait::eT<T1> > p_r(p.n_rows, arma::fill::zeros);
const arma::uword loop_no = n;
arma::uword* loop_counter = new arma::uword[loop_no + 1];
arma::uword* MAX = new arma::uword[loop_no + 1];
for (arma::uword i = 0; i < n; ++i) MAX[i] = dim.at(i);
MAX[loop_no] = 2;
for (arma::uword i = 0; i < loop_no + 1; ++i) loop_counter[i] = 0;
arma::uword p1 = 0;
while (loop_counter[loop_no] == 0) {
arma::uword I(0), K(0);
for (arma::uword i = 0; i < n; ++i) {
I += product.at(i) * loop_counter[i];
K += productr.at(i) * loop_counter[sys.at(i) - 1];
}
p_r.at(K) = p.at(I);
++loop_counter[0];
while (loop_counter[p1] == MAX[p1]) {
loop_counter[p1] = 0;
loop_counter[++p1]++;
if (loop_counter[p1] != MAX[p1])
p1 = 0;
}
}
delete[] loop_counter;
delete[] MAX;
return p_r;
}
}
