Hungarian.cpp

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// SPDX-FileCopyrightText: 2016 Cong Ma
//
// SPDX-License-Identifier: BSD-3-Clause
 
// Hungarian.cpp: Implementation file for Class HungarianAlgorithm.
//
// This is a C++ wrapper with slight modification of a hungarian algorithm implementation by Markus Buehren.
// The original implementation is a few mex-functions for use in MATLAB, found here:
// http://www.mathworks.com/matlabcentral/fileexchange/6543-functions-for-the-rectangular-assignment-problem
//
// Both this code and the orignal code are published under the BSD license.
// by Cong Ma, 2016
//
 
#include "Hungarian.h"
 
using namespace std;
 
HungarianAlgorithm::HungarianAlgorithm() {}
HungarianAlgorithm::~HungarianAlgorithm() {}
 
//********************************************************//
// A single function wrapper for solving assignment problem.
//********************************************************//
double HungarianAlgorithm::Solve(
    vector<vector<double>> &DistMatrix,
    vector<int> &Assignment)
{
    unsigned int nRows = DistMatrix.size();
    unsigned int nCols = DistMatrix[0].size();
 
    double *distMatrixIn = new double[nRows * nCols];
    int *assignment = new int[nRows];
    double cost = 0.0;
 
    // Fill in the distMatrixIn. Mind the index is "i + nRows * j".
    // Here the cost matrix of size MxN is defined as a double precision array of N*M elements.
    // In the solving functions matrices are seen to be saved MATLAB-internally in row-order.
    // (i.e. the matrix [1 2; 3 4] will be stored as a vector [1 3 2 4], NOT [1 2 3 4]).
    for (unsigned int i = 0; i < nRows; i++)
        for (unsigned int j = 0; j < nCols; j++)
            distMatrixIn[i + nRows * j] = DistMatrix[i][j];
 
    // call solving function
    assignmentoptimal(assignment, &cost, distMatrixIn, nRows, nCols);
 
    Assignment.clear();
    for (unsigned int r = 0; r < nRows; r++)
        Assignment.push_back(assignment[r]);
 
    delete[] distMatrixIn;
    delete[] assignment;
    return cost;
}
 
//********************************************************//
// Solve optimal solution for assignment problem using Munkres algorithm, also known as Hungarian Algorithm.
//********************************************************//
void HungarianAlgorithm::assignmentoptimal(
    int *assignment,
    double *cost,
    double *distMatrixIn,
    int nOfRows,
    int nOfColumns)
{
    double *distMatrix, *distMatrixTemp, *distMatrixEnd, *columnEnd, value, minValue;
    bool *coveredColumns, *coveredRows, *starMatrix, *newStarMatrix, *primeMatrix;
    int nOfElements, minDim, row, col;
 
    /* initialization */
    *cost = 0;
    for (row = 0; row < nOfRows; row++)
        assignment[row] = -1;
 
    /* generate working copy of distance Matrix */
    /* check if all matrix elements are positive */
    nOfElements = nOfRows * nOfColumns;
    distMatrix = (double *)malloc(nOfElements * sizeof(double));
    distMatrixEnd = distMatrix + nOfElements;
 
    for (row = 0; row < nOfElements; row++)
    {
        value = distMatrixIn[row];
        if (value < 0)
            cerr << "All matrix elements have to be non-negative." << endl;
        distMatrix[row] = value;
    }
 
    /* memory allocation */
    coveredColumns = (bool *)calloc(nOfColumns, sizeof(bool));
    coveredRows = (bool *)calloc(nOfRows, sizeof(bool));
    starMatrix = (bool *)calloc(nOfElements, sizeof(bool));
    primeMatrix = (bool *)calloc(nOfElements, sizeof(bool));
    newStarMatrix = (bool *)calloc(nOfElements, sizeof(bool)); /* used in step4 */
 
    /* preliminary steps */
    if (nOfRows <= nOfColumns)
    {
        minDim = nOfRows;
 
        for (row = 0; row < nOfRows; row++)
        {
            /* find the smallest element in the row */
            distMatrixTemp = distMatrix + row;
            minValue = *distMatrixTemp;
            distMatrixTemp += nOfRows;
            while (distMatrixTemp < distMatrixEnd)
            {
                value = *distMatrixTemp;
                if (value < minValue)
                    minValue = value;
                distMatrixTemp += nOfRows;
            }
 
            /* subtract the smallest element from each element of the row */
            distMatrixTemp = distMatrix + row;
            while (distMatrixTemp < distMatrixEnd)
            {
                *distMatrixTemp -= minValue;
                distMatrixTemp += nOfRows;
            }
        }
 
        /* Steps 1 and 2a */
        for (row = 0; row < nOfRows; row++)
            for (col = 0; col < nOfColumns; col++)
                if (fabs(distMatrix[row + nOfRows * col]) < DBL_EPSILON)
                    if (!coveredColumns[col])
                    {
                        starMatrix[row + nOfRows * col] = true;
                        coveredColumns[col] = true;
                        break;
                    }
    }
    else /* if(nOfRows > nOfColumns) */
    {
        minDim = nOfColumns;
 
        for (col = 0; col < nOfColumns; col++)
        {
            /* find the smallest element in the column */
            distMatrixTemp = distMatrix + nOfRows * col;
            columnEnd = distMatrixTemp + nOfRows;
 
            minValue = *distMatrixTemp++;
            while (distMatrixTemp < columnEnd)
            {
                value = *distMatrixTemp++;
                if (value < minValue)
                    minValue = value;
            }
 
            /* subtract the smallest element from each element of the column */
            distMatrixTemp = distMatrix + nOfRows * col;
            while (distMatrixTemp < columnEnd)
                *distMatrixTemp++ -= minValue;
        }
 
        /* Steps 1 and 2a */
        for (col = 0; col < nOfColumns; col++)
            for (row = 0; row < nOfRows; row++)
                if (fabs(distMatrix[row + nOfRows * col]) < DBL_EPSILON)
                    if (!coveredRows[row])
                    {
                        starMatrix[row + nOfRows * col] = true;
                        coveredColumns[col] = true;
                        coveredRows[row] = true;
                        break;
                    }
        for (row = 0; row < nOfRows; row++)
            coveredRows[row] = false;
    }
 
    /* move to step 2b */
    step2b(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
 
    /* compute cost and remove invalid assignments */
    computeassignmentcost(assignment, cost, distMatrixIn, nOfRows);
 
    /* free allocated memory */
    free(distMatrix);
    free(coveredColumns);
    free(coveredRows);
    free(starMatrix);
    free(primeMatrix);
    free(newStarMatrix);
 
    return;
}
 
/********************************************************/
void HungarianAlgorithm::buildassignmentvector(
    int *assignment,
    bool *starMatrix,
    int nOfRows,
    int nOfColumns)
{
    for (int row = 0; row < nOfRows; row++)
        for (int col = 0; col < nOfColumns; col++)
            if (starMatrix[row + nOfRows * col])
            {
#ifdef ONE_INDEXING
                assignment[row] = col + 1; /* MATLAB-Indexing */
#else
                assignment[row] = col;
#endif
                break;
            }
}
 
/********************************************************/
void HungarianAlgorithm::computeassignmentcost(
    int *assignment,
    double *cost,
    double *distMatrix,
    int nOfRows)
{
    int row, col;
 
    for (row = 0; row < nOfRows; row++)
    {
        col = assignment[row];
        if (col >= 0)
            *cost += distMatrix[row + nOfRows * col];
    }
}
 
/********************************************************/
void HungarianAlgorithm::step2a(
    int *assignment,
    double *distMatrix,
    bool *starMatrix,
    bool *newStarMatrix,
    bool *primeMatrix,
    bool *coveredColumns,
    bool *coveredRows,
    int nOfRows,
    int nOfColumns,
    int minDim)
{
    bool *starMatrixTemp, *columnEnd;
    int col;
 
    /* cover every column containing a starred zero */
    for (col = 0; col < nOfColumns; col++)
    {
        starMatrixTemp = starMatrix + nOfRows * col;
        columnEnd = starMatrixTemp + nOfRows;
        while (starMatrixTemp < columnEnd)
        {
            if (*starMatrixTemp++)
            {
                coveredColumns[col] = true;
                break;
            }
        }
    }
 
    /* move to step 3 */
    step2b(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
}
 
/********************************************************/
void HungarianAlgorithm::step2b(
    int *assignment,
    double *distMatrix,
    bool *starMatrix,
    bool *newStarMatrix,
    bool *primeMatrix,
    bool *coveredColumns,
    bool *coveredRows,
    int nOfRows,
    int nOfColumns,
    int minDim)
{
    int col, nOfCoveredColumns;
 
    /* count covered columns */
    nOfCoveredColumns = 0;
    for (col = 0; col < nOfColumns; col++)
        if (coveredColumns[col])
            nOfCoveredColumns++;
 
    if (nOfCoveredColumns == minDim)
    {
        /* algorithm finished */
        buildassignmentvector(assignment, starMatrix, nOfRows, nOfColumns);
    }
    else
    {
        /* move to step 3 */
        step3(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
    }
}
 
/********************************************************/
void HungarianAlgorithm::step3(
    int *assignment,
    double *distMatrix,
    bool *starMatrix,
    bool *newStarMatrix,
    bool *primeMatrix,
    bool *coveredColumns,
    bool *coveredRows,
    int nOfRows,
    int nOfColumns,
    int minDim)
{
    bool zerosFound;
    int row, col, starCol;
 
    zerosFound = true;
    while (zerosFound)
    {
        zerosFound = false;
        for (col = 0; col < nOfColumns; col++)
            if (!coveredColumns[col])
                for (row = 0; row < nOfRows; row++)
                    if ((!coveredRows[row]) && (fabs(distMatrix[row + nOfRows * col]) < DBL_EPSILON))
                    {
                        /* prime zero */
                        primeMatrix[row + nOfRows * col] = true;
 
                        /* find starred zero in current row */
                        for (starCol = 0; starCol < nOfColumns; starCol++)
                            if (starMatrix[row + nOfRows * starCol])
                                break;
 
                        if (starCol == nOfColumns) /* no starred zero found */
                        {
                            /* move to step 4 */
                            step4(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim, row, col);
                            return;
                        }
                        else
                        {
                            coveredRows[row] = true;
                            coveredColumns[starCol] = false;
                            zerosFound = true;
                            break;
                        }
                    }
    }
 
    /* move to step 5 */
    step5(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
}
 
/********************************************************/
void HungarianAlgorithm::step4(
    int *assignment,
    double *distMatrix,
    bool *starMatrix,
    bool *newStarMatrix,
    bool *primeMatrix,
    bool *coveredColumns,
    bool *coveredRows,
    int nOfRows,
    int nOfColumns,
    int minDim,
    int row,
    int col)
{
    int n, starRow, starCol, primeRow, primeCol;
    int nOfElements = nOfRows * nOfColumns;
 
    /* generate temporary copy of starMatrix */
    for (n = 0; n < nOfElements; n++)
        newStarMatrix[n] = starMatrix[n];
 
    /* star current zero */
    newStarMatrix[row + nOfRows * col] = true;
 
    /* find starred zero in current column */
    starCol = col;
    for (starRow = 0; starRow < nOfRows; starRow++)
        if (starMatrix[starRow + nOfRows * starCol])
            break;
 
    while (starRow < nOfRows)
    {
        /* unstar the starred zero */
        newStarMatrix[starRow + nOfRows * starCol] = false;
 
        /* find primed zero in current row */
        primeRow = starRow;
        for (primeCol = 0; primeCol < nOfColumns; primeCol++)
            if (primeMatrix[primeRow + nOfRows * primeCol])
                break;
 
        /* star the primed zero */
        newStarMatrix[primeRow + nOfRows * primeCol] = true;
 
        /* find starred zero in current column */
        starCol = primeCol;
        for (starRow = 0; starRow < nOfRows; starRow++)
            if (starMatrix[starRow + nOfRows * starCol])
                break;
    }
 
    /* use temporary copy as new starMatrix */
    /* delete all primes, uncover all rows */
    for (n = 0; n < nOfElements; n++)
    {
        primeMatrix[n] = false;
        starMatrix[n] = newStarMatrix[n];
    }
    for (n = 0; n < nOfRows; n++)
        coveredRows[n] = false;
 
    /* move to step 2a */
    step2a(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
}
 
/********************************************************/
void HungarianAlgorithm::step5(
    int *assignment,
    double *distMatrix,
    bool *starMatrix,
    bool *newStarMatrix,
    bool *primeMatrix,
    bool *coveredColumns,
    bool *coveredRows,
    int nOfRows,
    int nOfColumns,
    int minDim)
{
    double h, value;
    int row, col;
 
    /* find smallest uncovered element h */
    h = DBL_MAX;
    for (row = 0; row < nOfRows; row++)
        if (!coveredRows[row])
            for (col = 0; col < nOfColumns; col++)
                if (!coveredColumns[col])
                {
                    value = distMatrix[row + nOfRows * col];
                    if (value < h)
                        h = value;
                }
 
    /* add h to each covered row */
    for (row = 0; row < nOfRows; row++)
        if (coveredRows[row])
            for (col = 0; col < nOfColumns; col++)
                distMatrix[row + nOfRows * col] += h;
 
    /* subtract h from each uncovered column */
    for (col = 0; col < nOfColumns; col++)
        if (!coveredColumns[col])
            for (row = 0; row < nOfRows; row++)
                distMatrix[row + nOfRows * col] -= h;
 
    /* move to step 3 */
    step3(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
}