/**************************************************************************
 *                                                                        *
 *  Regina - A Normal Surface Theory Calculator                           *
 *  Computational Engine                                                  *
 *                                                                        *
 *  Copyright (c) 1999-2025, Ben Burton                                   *
 *  For further details contact Ben Burton (bab@debian.org).              *
 *                                                                        *
 *  This program is free software; you can redistribute it and/or         *
 *  modify it under the terms of the GNU General Public License as        *
 *  published by the Free Software Foundation; either version 2 of the    *
 *  License, or (at your option) any later version.                       *
 *                                                                        *
 *  As an exception, when this program is distributed through (i) the     *
 *  App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or     *
 *  (iii) Google Play by Google Inc., then that store may impose any      *
 *  digital rights management, device limits and/or redistribution        *
 *  restrictions that are required by its terms of service.               *
 *                                                                        *
 *  This program is distributed in the hope that it will be useful, but   *
 *  WITHOUT ANY WARRANTY; without even the implied warranty of            *
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU     *
 *  General Public License for more details.                              *
 *                                                                        *
 *  You should have received a copy of the GNU General Public License     *
 *  along with this program. If not, see <https://www.gnu.org/licenses/>. *
 *                                                                        *
 **************************************************************************/

#include <algorithm>
#include "manifold/sfs.h"
#include "triangulation/dim3.h"
#include "subcomplex/plugtrisolidtorus.h"

namespace regina {

std::ostream& PlugTriSolidTorus::writeName(std::ostream& out) const {
    long params[3];
    int nParams = 0;

    int i;
    for (i = 0; i < 3; i++)
        if (chainType_[i] != CHAIN_NONE) {
            if (chainType_[i] == CHAIN_MAJOR)
                params[nParams++] = chain_[i]->index();
            else
                params[nParams++] = -chain_[i]->index();
        }
    std::sort(params, params + nParams);

    out << (equatorType_ == EQUATOR_MAJOR ? "P(" : "P'(");
    if (nParams == 0)
        return out << "0)";
    for (i = 0; i < nParams; i++) {
        if (i > 0)
            out << ',';
        out << params[i];
    }
    return out << ')';
}

std::ostream& PlugTriSolidTorus::writeTeXName(std::ostream& out) const {
    long params[3];
    int nParams = 0;

    int i;
    for (i = 0; i < 3; i++)
        if (chainType_[i] != CHAIN_NONE) {
            if (chainType_[i] == CHAIN_MAJOR)
                params[nParams++] = chain_[i]->index();
            else
                params[nParams++] = -chain_[i]->index();
        }
    std::sort(params, params + nParams);

    out << (equatorType_ == EQUATOR_MAJOR ? "P_{" : "P'_{");
    if (nParams == 0)
        return out << "0}";
    for (i = 0; i < nParams; i++) {
        if (i > 0)
            out << ',';
        out << params[i];
    }
    return out << '}';
}

void PlugTriSolidTorus::writeTextLong(std::ostream& out) const {
    out << "Plugged triangular solid torus: ";
    writeName(out);
}

std::unique_ptr<Manifold> PlugTriSolidTorus::manifold() const {
    std::unique_ptr<SFSpace> ans(new SFSpace());
    ans->insertFibre(2, -1);
    ans->insertFibre(3, 1);

    long rot = (equatorType_ == EQUATOR_MAJOR ? 5 : 4);
    for (int i = 0; i < 3; i++)
        if (chainType_[i] != CHAIN_NONE) {
            if (chainType_[i] == equatorType_)
                rot += chain_[i]->index();
            else
                rot -= chain_[i]->index();
        }
    if (rot != 0)
        ans->insertFibre(rot, 1);
    else
        return nullptr;

    ans->reduce();
    return ans;
}

std::unique_ptr<PlugTriSolidTorus> PlugTriSolidTorus::recognise(
        Component<3>* comp) {
    // Each triangular solid torus is tested three times since we
    // can't call Tetrahedron<3>::index() from within a component only.
    // TODO: Update - yes we can now.  This constraint was from an
    // ancient version of regina.  Fix this code accordingly.

    // Basic property checks.
    if ((! comp->isClosed()) || (! comp->isOrientable()))
        return nullptr;

    if (comp->countVertices() > 1)
        return nullptr;

    size_t nTet = comp->size();
    if (nTet < 5)
        return nullptr;

    // We have a 1-vertex closed orientable component with at least
    // 5 tetrahedra.

    // Hunt for a core.  Make sure we find each triangular solid torus
    // just once.
    size_t tetIndex;
    std::unique_ptr<TriSolidTorus> core;
    Tetrahedron<3>* coreTet[3];
    Edge<3>* axis[3];
    Perm<4> coreRoles[3];
    Tetrahedron<3>* base[2];
    Perm<4> baseRoles[2];
    int i, j;
    bool error;

    Tetrahedron<3>* plugTet[3][2];
    Perm<4> plugRoles[3][2];
    Perm<4> realPlugRoles[2];

    std::optional<LayeredChain> chain[3];
    int chainType[3];
    int equatorType = 0;

    for (tetIndex = 0; tetIndex < nTet - 2; tetIndex++)
        for (auto corePerm: Perm<4>::Sn) {
            if (corePerm[0] > corePerm[3])
                continue;

            core = TriSolidTorus::recognise(
                comp->tetrahedron(tetIndex), corePerm);
            if (! core)
                continue;

            for (i = 0; i < 3; i++) {
                coreTet[i] = core->tetrahedron(i);
                coreRoles[i] = core->vertexRoles(i);
                axis[i] = coreTet[i]->edge(
                    Edge<3>::edgeNumber[coreRoles[i][0]][coreRoles[i][3]]);
            }

            if (axis[0] == axis[1] || axis[1] == axis[2] ||
                    axis[2] == axis[0]) {
                continue;
            }

            // We have the triangular solid torus and we know the three
            // axis edges are distinct.

            // Hunt for chains.
            for (i = 0; i < 3; i++) {
                base[0] = coreTet[(i + 1) % 3]->adjacentTetrahedron(
                    coreRoles[(i + 1) % 3][2]);
                base[1] = coreTet[(i + 2) % 3]->adjacentTetrahedron(
                    coreRoles[(i + 2) % 3][1]);
                if (base[0] != base[1]) {
                    // No chain.
                    chainType[i] = CHAIN_NONE;
                    continue;
                }

                // Have we layered over the major axis?
                baseRoles[0] = coreTet[(i + 1) % 3]->
                    adjacentGluing(coreRoles[(i + 1) % 3][2]) *
                    coreRoles[(i + 1) % 3] * Perm<4>(0, 3, 2, 1);
                baseRoles[1] = coreTet[(i + 2) % 3]->
                    adjacentGluing(coreRoles[(i + 2) % 3][1]) *
                    coreRoles[(i + 2) % 3] * Perm<4>(2, 1, 0, 3);
                if (baseRoles[0] == baseRoles[1]) {
                    chainType[i] = CHAIN_MAJOR;
                    chain[i] = LayeredChain(base[0], baseRoles[0]);
                    while (chain[i]->extendAbove())
                        ;
                    continue;
                }

                // Have we layered over the minor axis?
                baseRoles[0] = coreTet[(i + 1) % 3]->
                    adjacentGluing(coreRoles[(i + 1) % 3][2]) *
                    coreRoles[(i + 1) % 3] * Perm<4>(3, 0, 2, 1);
                baseRoles[1] = coreTet[(i + 2) % 3]->
                    adjacentGluing(coreRoles[(i + 2) % 3][1]) *
                    coreRoles[(i + 2) % 3] * Perm<4>(2, 1, 3, 0);
                if (baseRoles[0] == baseRoles[1]) {
                    chainType[i] = CHAIN_MINOR;
                    chain[i] = LayeredChain(base[0], baseRoles[0]);
                    while (chain[i]->extendAbove())
                        ;
                    continue;
                }

                // It's not a chain but it can't be a plug either.
                // We'll notice the error because i will be less than 3.
                break;
            }

            // Check whether we broke out of the previous loop with an error.
            // Check also whether one of the chains is another in
            // reverse, and that we've found the correct number of
            // tetrahedra in total.
            error = false;
            if (i < 3)
                error = true;
            else if (chain[0] && chain[1] &&
                    chain[0]->bottom() == chain[1]->top())
                error = true;
            else if (chain[1] && chain[2] &&
                    chain[1]->bottom() == chain[2]->top())
                error = true;
            else if (chain[2] && chain[0] &&
                    chain[2]->bottom() == chain[0]->top())
                error = true;
            else if ((chain[0] ? chain[0]->index() : 0) +
                    (chain[1] ? chain[1]->index() : 0) +
                    (chain[2] ? chain[2]->index() : 0) +
                    5 != nTet)
                error = true;

            if (error) {
                for (j = 0; j < 3; j++)
                    chain[j].reset();
                continue;
            }

            // Still hanging in.
            // We know there's only 2 tetrahedra left.
            // Now we need to check the plug.
            error = false;

            for (i = 0; i < 3; i++) {
                if (chain[i]) {
                    plugTet[i][0] = chain[i]->top()->adjacentTetrahedron(
                        chain[i]->topVertexRoles()[3]);
                    plugTet[i][1] = chain[i]->top()->adjacentTetrahedron(
                        chain[i]->topVertexRoles()[0]);
                    plugRoles[i][0] = chain[i]->top()->
                        adjacentGluing(chain[i]->
                        topVertexRoles()[3]) *
                        chain[i]->topVertexRoles() *
                        (chainType[i] == CHAIN_MAJOR ? Perm<4>(0, 1, 2, 3) :
                        Perm<4>(1, 0, 2, 3));
                    plugRoles[i][1] = chain[i]->top()->
                        adjacentGluing(chain[i]->
                        topVertexRoles()[0]) *
                        chain[i]->topVertexRoles() *
                        (chainType[i] == CHAIN_MAJOR ? Perm<4>(2, 3, 1, 0) :
                        Perm<4>(3, 2, 1, 0));
                } else {
                    plugTet[i][0] = coreTet[(i + 1) % 3]->
                        adjacentTetrahedron(coreRoles[(i + 1) % 3][2]);
                    plugTet[i][1] = coreTet[(i + 2) % 3]->
                        adjacentTetrahedron(coreRoles[(i + 2) % 3][1]);
                    plugRoles[i][0] = coreTet[(i + 1) % 3]->
                        adjacentGluing(coreRoles[(i + 1) % 3][2])
                        * coreRoles[(i + 1) % 3] * Perm<4>(0, 3, 1, 2);
                    plugRoles[i][1] = coreTet[(i + 2) % 3]->
                        adjacentGluing(coreRoles[(i + 2) % 3][1])
                        * coreRoles[(i + 2) % 3] * Perm<4>(0, 3, 2, 1);
                }
            }

            // Make sure we meet precisely two tetrahedra, three times
            // each.  Note that this implies that the plug tetrahedra are
            // in fact thus far unseen.
            for (i = 0; i < 2; i++)
                if (plugTet[0][i] != plugTet[1][i] ||
                        plugTet[1][i] != plugTet[2][i]) {
                    error = true;
                    break;
                }

            // Make sure also that the gluing permutations for the plug
            // are correct.
            if (! error) {
                if (plugRoles[0][0][0] == plugRoles[1][0][0] &&
                        plugRoles[1][0][0] == plugRoles[2][0][0]) {
                    // Type EQUATOR_MINOR.
                    realPlugRoles[0] = plugRoles[0][0] * Perm<4>(3, 2, 1, 0);
                    realPlugRoles[1] = plugRoles[0][1] * Perm<4>(3, 0, 2, 1);

                    if (realPlugRoles[0] != plugRoles[1][0] *
                            Perm<4>(1, 3, 2, 0))
                        error = true;
                    else if (realPlugRoles[0] != plugRoles[2][0] *
                            Perm<4>(2, 1, 3, 0))
                        error = true;
                    else if (realPlugRoles[1] != plugRoles[1][1] *
                            Perm<4>(2, 3, 0, 1))
                        error = true;
                    else if (realPlugRoles[1] != plugRoles[2][1] *
                            Perm<4>(0, 2, 3, 1))
                        error = true;
                    else
                        equatorType = EQUATOR_MINOR;
                } else if (plugRoles[0][0][1] == plugRoles[1][0][1] &&
                        plugRoles[1][0][1] == plugRoles[2][0][1]) {
                    // Type EQUATOR_MAJOR.
                    realPlugRoles[0] = plugRoles[0][0] * Perm<4>(3, 2, 0, 1);
                    realPlugRoles[1] = plugRoles[0][1] * Perm<4>(3, 1, 2, 0);

                    if (realPlugRoles[0] != plugRoles[1][0] *
                            Perm<4>(0, 3, 2, 1))
                        error = true;
                    else if (realPlugRoles[0] != plugRoles[2][0] *
                            Perm<4>(2, 0, 3, 1))
                        error = true;
                    else if (realPlugRoles[1] != plugRoles[1][1] *
                            Perm<4>(2, 3, 1, 0))
                        error = true;
                    else if (realPlugRoles[1] != plugRoles[2][1] *
                            Perm<4>(1, 2, 3, 0))
                        error = true;
                    else
                        equatorType = EQUATOR_MAJOR;
                } else
                    error = true;
            }

            // Finally check the internal triangle of the plug.
            if (! error) {
                if (plugTet[0][0]->adjacentTetrahedron(realPlugRoles[0][3])
                        != plugTet[0][1])
                    error = true;
                else if (plugTet[0][0]->adjacentGluing(
                        realPlugRoles[0][3]) * realPlugRoles[0] !=
                        realPlugRoles[1])
                    error = true;
            }

            if (error) {
                for (j = 0; j < 3; j++)
                    chain[j].reset();
                continue;
            }

            // Success!
            std::unique_ptr<PlugTriSolidTorus> plug(
                new PlugTriSolidTorus(*core));
            for (i = 0; i < 3; i++) {
                plug->chain_[i] = std::move(chain[i]);
                plug->chainType_[i] = chainType[i];
            }
            plug->equatorType_ = equatorType;
            return plug;
        }

    // Nothing was found.
    return nullptr;
}

} // namespace regina