element.cpp

// --------------------------------------- Perm ------------------------------------------ //
// constructor for permutation - also generates string name for element, and cycle_lengths
// TODO: huge performance boost via moving computation of string name to printing
//      - have to do something about const in << operator!
//Perm::Perm(std::vector<int> p) {
//    // dec true if 1-indexed
//    bool dec = false;
//    this->n = p.size(); this->p = p;
//    TR(x, p) dec |= x == n;
//    if (dec) TR(x, p) x--;
//
//    // find all cycles
//    bool used[n];
//    memset(used, false, sizeof used);
//    F(i,n) if (!used[i] and p[i] != i) {
//        int curr = 1;
//        name += "(" + std::to_string(i + 1);
//        used[i] = true;
//        while (!used[i = p[i]]) name += std::to_string(i + 1), used[i] = true, curr++;
//        name += ")";
//        cycle_lengths.push_back(curr);
//    }
//
//    cycle_lengths.insert(cycle_lengths.begin(), cycle_lengths.size());
//
//    if (name.empty())
//        name = "e";
//}
//
//Perm Perm::dot(Perm const &b) const {
//    std::vector<int> res(n);
//    // compose permutation
//    F(i,n) res[i] = p[b.p[i]];
//    return Perm(res);
//}
//
//// first compare number of cycles; fewer means smaller.
////     if equal, compare lexicographically lengths of cycles
////     if equal, finally compare actual permutation
//bool Perm::operator<(const Perm &rhs) const {
//    return (cycle_lengths == rhs.cycle_lengths) ? p < rhs.p : cycle_lengths < rhs.cycle_lengths;
//}
//
//std::ostream &operator<<(std::ostream &os, const Perm &b) {
//    return os << b.name;
//}