hungarian_example.cc

See also

tpl_mincost.H For min-cost flow-based assignment (solve_assignment).

tpl_bipartite.H For bipartite matching.

Author

Leandro Rabindranath Leon

/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
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  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
# include <iostream>
# include <Hungarian.H>
# include <tpl_dynMat.H>
 
using namespace std;
using namespace Aleph;
 
void example_basic_assignment()
{
  cout << "=== Basic Assignment (4x4 workers-to-tasks) ===" << endl;
  cout << endl;
  cout << "Cost matrix:" << endl;
  cout << "  Task0 Task1 Task2 Task3" << endl;
  cout << "W0:  82    83    69    92" << endl;
  cout << "W1:  77    37    49    92" << endl;
  cout << "W2:  11    69     5    86" << endl;
  cout << "W3:   8     9    98    23" << endl;
  cout << endl;
 
  const Hungarian_Assignment<int> ha({
    {82, 83, 69, 92},
    {77, 37, 49, 92},
    {11, 69,  5, 86},
    { 8,  9, 98, 23}
  });
 
  cout << "Optimal total cost: " << ha.get_total_cost() << endl;
  cout << "Assignments:" << endl;
  for (auto [r, c] : ha.get_assignments())
    cout << "  Worker " << r << " -> Task " << c << endl;
  cout << endl;
 
  // Show individual costs
  constexpr int costs[4][4] = {
    {82, 83, 69, 92},
    {77, 37, 49, 92},
    {11, 69,  5, 86},
    { 8,  9, 98, 23}
  };
  cout << "Detailed:" << endl;
  for (auto [r, c] : ha.get_assignments())
    cout << "  Worker " << r << " -> Task " << c
         << " (cost " << costs[r][c] << ")" << endl;
  cout << endl;
}
 
void example_maximization()
{
  cout << "=== Maximization (3x3 profit matrix) ===" << endl;
  cout << endl;
  cout << "Profit matrix:" << endl;
  cout << "  Job0 Job1 Job2" << endl;
  cout << "W0: 10    5   13" << endl;
  cout << "W1:  3    9   18" << endl;
  cout << "W2: 10    6   12" << endl;
  cout << endl;
 
  auto mat = DynMatrix<int>(3, 3, 0);
  mat.allocate();
  int data[3][3] = {{10, 5, 13}, {3, 9, 18}, {10, 6, 12}};
  for (size_t i = 0; i < 3; ++i)
    for (size_t j = 0; j < 3; ++j)
      mat(i, j) = data[i][j];
 
  auto result = hungarian_max_assignment(mat);
 
  cout << "Maximum total profit: " << result.total_cost << endl;
  cout << "Assignments:" << endl;
  for (auto [r, c] : result.get_pairs())
    cout << "  Worker " << r << " -> Job " << c
         << " (profit " << data[r][c] << ")" << endl;
  cout << endl;
}
 
void example_rectangular()
{
  cout << "=== Rectangular (3 workers, 5 tasks) ===" << endl;
  cout << endl;
  cout << "Cost matrix:" << endl;
  cout << "  T0 T1 T2 T3 T4" << endl;
  cout << "W0: 10  3  7  2  8" << endl;
  cout << "W1:  5  9  1  6  4" << endl;
  cout << "W2: 12 11  6  3  7" << endl;
  cout << endl;
 
  Hungarian_Assignment<int> ha({
    {10, 3, 7, 2, 8},
    { 5, 9, 1, 6, 4},
    {12, 11, 6, 3, 7}
  });
 
  cout << "Optimal total cost: " << ha.get_total_cost() << endl;
  const size_t unassigned_count = 5 - ha.get_assignments().size();
  cout << "Assignments (" << unassigned_count << " tasks left unassigned):" << endl;
  for (auto [r, c] : ha.get_assignments())
    cout << "  Worker " << r << " -> Task " << c << endl;
  cout << endl;
}
 
int main()
{
  example_basic_assignment();
  example_maximization();
  example_rectangular();
 
  return 0;
}