source: tspsg-svn/trunk/src/tspsolver.cpp @ 73

/*
 *  TSPSG: TSP Solver and Generator
 *  Copyright (C) 2007-2009 Lёppa <contacts[at]oleksii[dot]name>
 *
 *  $Id: tspsolver.cpp 71 2009-12-07 16:06:44Z laleppa $
 *  $URL: https://tspsg.svn.sourceforge.net/svnroot/tspsg/trunk/src/tspsolver.cpp $
 *
 *  This file is part of TSPSG.
 *
 *  TSPSG 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 3 of the License, or
 *  (at your option) any later version.
 *
 *  TSPSG 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 TSPSG.  If not, see <http://www.gnu.org/licenses/>.
 */

#include "tspsolver.h"

//! Class constructor
CTSPSolver::CTSPSolver()
        : nCities(0)
{
}

/*!
 * \brief Returns the sorted optimal path, starting from City 1.
 * \return A string, containing sorted optimal path.
 */
QString CTSPSolver::getSortedPath() const
{
        if (!root || route.isEmpty() || (route.size() != nCities))
                return QString();

int i = 0; // We start from City 1
QString path = trUtf8("City %1").arg(1) + " -> ";
        while ((i = route[i]) != 0) {
                path += trUtf8("City %1").arg(i + 1) + " -> ";
        }
        // And finish in City 1, too
        path += trUtf8("City %1").arg(1);

        return path;
}

/*!
 * \brief Returns CTSPSolver's version ID.
 * \return A string: <b>\$Id: tspsolver.cpp 71 2009-12-07 16:06:44Z laleppa $</b>.
 */
QString CTSPSolver::getVersionId()
{
        return QString("$Id: tspsolver.cpp 71 2009-12-07 16:06:44Z laleppa $");
}

/*!
 * \brief Returns whether or not the solution is definitely optimal.
 * \return \c true if solution is definitely optimal, otherwise \c false.
 *
 *  The solution may need some further interations to determine whether it is optimal.
 *  In such cases this function returns \c false.
 */
bool CTSPSolver::isOptimal() const
{
        return !mayNotBeOptimal;
}

/*!
 * \brief Solves the given task.
 * \param numCities Number of cities in the task.
 * \param task The matrix of city-to-city travel costs.
 * \param parent The parent widget for displaying messages and dialogs.
 * \return Pointer to the root of the solution tree.
 *
 * \todo TODO: Comment the algorithm.
 */
sStep *CTSPSolver::solve(int numCities, tMatrix task, QWidget *parent)
{
        if (numCities <= 1)
                return NULL;
        cleanup();
        nCities = numCities;
QProgressDialog pd(parent);
QProgressBar *pb = new QProgressBar(&pd);
        pb->setAlignment(Qt::AlignCenter);
        pb->setFormat(trUtf8("%v of %m parts found"));
        pd.setBar(pb);
        pd.setMaximum(nCities);
        pd.setMinimumDuration(1000);
        pd.setLabelText(trUtf8("Calculating optimal route..."));
        pd.setWindowTitle(trUtf8("Solution Progress"));
        pd.setWindowModality(Qt::ApplicationModal);
        pd.setValue(0);

sStep *step = new sStep();
        step->matrix = task;
        step->price = align(step->matrix);
        root = step;

sStep *left, *right;
int nRow, nCol;
bool firstStep = true;
double check;
        while (this->route.size() < nCities) {
//              forbidden.clear();
                step->alts = findCandidate(step->matrix,nRow,nCol);
                while (hasSubCycles(nRow,nCol)) {
//                      forbidden[nRow] = nCol;
                        step->matrix[nRow][nCol] = INFINITY;
                        step->price += align(step->matrix);
                        step->alts = findCandidate(step->matrix,nRow,nCol);
                }
                if ((nRow == -1) || (nCol == -1) || pd.wasCanceled()) {
                        root = NULL;
                        break;
                }

                // Route with (nRow,nCol) path
                right = new sStep();
                right->matrix = step->matrix;
                for (int k = 0; k < nCities; k++) {
                        if (k != nCol)
                                right->matrix[nRow][k] = INFINITY;
                        if (k != nRow)
                                right->matrix[k][nCol] = INFINITY;
                }
                right->price = step->price + align(right->matrix);
                // Forbid selected route to exclude its reuse in next steps.
                right->matrix[nCol][nRow] = INFINITY;
                right->matrix[nRow][nCol] = INFINITY;

                // Route without (nRow,nCol) path
                left = new sStep();
                left->matrix = step->matrix;
                left->matrix[nRow][nCol] = INFINITY;
                left->price = step->price + align(left->matrix);

                step->candidate.nRow = nRow;
                step->candidate.nCol = nCol;
                step->plNode = left;
                step->prNode = right;

                if (right->price <= left->price) {
                        // Route with (nRow,nCol) path is cheaper
                        step = right;
                        this->route[nRow] = nCol;
                        pd.setValue(this->route.size());
                        if (firstStep) {
                                check = left->price;
                                firstStep = false;
                        }
                } else {
                        // Route without (nRow,nCol) path is cheaper
                        step = left;
                        qApp->processEvents();
                        if (firstStep) {
                                check = right->price;
                                firstStep = false;
                        }
                }
        }

        if (!root && !pd.wasCanceled()) {
                pd.reset();
                QMessageBox(QMessageBox::Warning,trUtf8("Solution Result"),trUtf8("Unable to find solution.\nMaybe, this task has no solutions."),QMessageBox::Ok,parent).exec();
        }

        qApp->processEvents();

        if (root) {
                route = this->route;
                mayNotBeOptimal = (check < step->price);
        }
        return root;
}

/* Privates **********************************************************/

double CTSPSolver::align(tMatrix &matrix)
{
double r = 0;
double min;
        for (int k = 0; k < nCities; k++) {
                min = findMinInRow(k,matrix);
                if (min > 0) {
                        r += min;
                        subRow(matrix,k,min);
                }
        }
        for (int k = 0; k < nCities; k++) {
                min = findMinInCol(k,matrix);
                if (min > 0) {
                        r += min;
                        subCol(matrix,k,min);
                }
        }
        return r;
}

void CTSPSolver::cleanup()
{
        route.clear();
        mayNotBeOptimal = false;
}

bool CTSPSolver::findCandidate(const tMatrix &matrix, int &nRow, int &nCol) const
{
        nRow = -1;
        nCol = -1;
bool alts = false;
double h = -1;
double sum;
        for (int r = 0; r < nCities; r++)
                for (int c = 0; c < nCities; c++)
//                      if ((matrix.at(r).at(c) == 0) && !forbidden.values(r).contains(c)) {
                        if (matrix.at(r).at(c) == 0) {
                                sum = findMinInRow(r,matrix,c) + findMinInCol(c,matrix,r);
                                if (sum > h) {
                                        h = sum;
                                        nRow = r;
                                        nCol = c;
                                        alts = false;
                                } else if ((sum == h) && !hasSubCycles(r,c))
                                        alts = true;
                        }
        return alts;
}

double CTSPSolver::findMinInCol(int nCol, const tMatrix &matrix, int exr) const
{
double min = INFINITY;
        for (int k = 0; k < nCities; k++)
                if ((k != exr) && (min > matrix.at(k).at(nCol)))
                        min = matrix.at(k).at(nCol);
        return min == INFINITY ? 0 : min;
}

double CTSPSolver::findMinInRow(int nRow, const tMatrix &matrix, int exc) const
{
double min = INFINITY;
        for (int k = 0; k < nCities; k++)
                if (((k != exc)) && (min > matrix.at(nRow).at(k)))
                        min = matrix.at(nRow).at(k);
        return min == INFINITY ? 0 : min;
}

bool CTSPSolver::hasSubCycles(int nRow, int nCol) const
{
        if ((nRow < 0) || (nCol < 0) || route.isEmpty() || !(route.size() < nCities - 1) || !route.contains(nCol))
                return false;
int i = nCol;
        while (true) {
                if ((i = route[i]) == nRow)
                        return true;
                if (!route.contains(i))
                        return false;
        }
        return false;
}

void CTSPSolver::subCol(tMatrix &matrix, int nCol, double val)
{
        for (int k = 0; k < nCities; k++)
                if (k != nCol)
                        matrix[k][nCol] -= val;
}

void CTSPSolver::subRow(tMatrix &matrix, int nRow, double val)
{
        for (int k = 0; k < nCities; k++)
                if (k != nRow)
                        matrix[nRow][k] -= val;
}