Here is the full source code and examples:

https://github.com/fastrgv/HungarianAlgorithm/releases/download/v1.0.0/hu9nov20.7z

Type "7z x filename" to extract the archive.

• Although written in Ada, this code could be considered an algorithmic description.

The proper command to extract the archive and maintain the directory structure is "7z x filename".

The Hungarian algorithm can be described as optimally solving a workers versus jobs assignment problem that minimizes total cost. This implementation assumes a square cost matrix, i.e. the number of jobs equals the number of workers to do them.

A simple example, whose solution is almost immediately obvious follows.

job #1 #2 #3

A $2 $3 $3

B $3 $2 $3

C $3 $3 $2

The Hungarian method, when applied to the above table would give the minimum cost of $6, by assigning A to job 1, B to job 2, and C to job 3.

munktest.adb solves an 11 x 11 (hardcoded) job assignment problem. To compile it, type lcmp.sh on linux, ocmp.sh on OSX, or wcmp.bat on Windows.

This algorithm was copied on 20sep18 from: https://users.cs.duke.edu/~brd/Teaching/Bio/asmb/current/Handouts/munkres.html and modified to correct some errors.

It is currently being used as an integral part of a highly capable sokoban solver [hbox4] that has been developed. Thusly, it has now been tested on thousands of actual testcases and seems to be working properly.

Here are the links to the sokoban solver:

* https://sourceforge.net/projects/hbox4/files/8nov2022/
* https://github.com/fastrgv/hbox4

Please send any improvements or further corrections to: [email protected]

I have searched for a correct version online, but found none. I found several that "almost" worked but were all flawed, mainly, I think, due to the age and nature of the original algorithmic description. It was invented before computers were widely available, so was described in terms of hand computations, parts of which are quite confusing, possibly due to language ambiguities. [Kuhn, 1955]

I now have another project titled "hbox4", which is a sokoban puzzle solver that makes heavy use of the Hungarian Algorithm. It demonstrates its remarkable power because without it, the solver becomes severely disabled.

Copyright (C) 2018 [email protected]

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 3 of the License, or (at your option) any later version.

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 may read the full text of the GNU General Public License at http://www.gnu.org/licenses/.