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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);
}
Hungarian.h
HungarianAlgorithm::~HungarianAlgorithm
~HungarianAlgorithm()
Definition Hungarian.cpp:21
HungarianAlgorithm::HungarianAlgorithm
HungarianAlgorithm()
Definition Hungarian.cpp:20
HungarianAlgorithm::Solve
double Solve(std::vector< std::vector< double > > &DistMatrix, std::vector< int > &Assignment)
Definition Hungarian.cpp:26