An implementation of the Hungarian algorithm for solving the assignment problem. An instance of the assignment problem consists of a number of workers along with a number of jobs and a cost matrix which gives the cost of assigning the i'th worker to the j'th job at position (i, j). The goal is to find an assignment of workers to jobs so that no job is assigned more than one worker and so that no worker is assigned to more than one job in such a manner so as to minimize the total cost of completing the jobs.

An assignment for a cost matrix that has more workers than jobs will necessarily include unassigned workers, indicated by an assignment value of -1; in no other circumstance will there be unassigned workers. Similarly, an assignment for a cost matrix that has more jobs than workers will necessarily include unassigned jobs; in no other circumstance will there be unassigned jobs. For completeness, an assignment for a square cost matrix will give exactly one unique worker to each job.

This version of the Hungarian algorithm runs in time O(n^3), where n is the maximum among the number of workers and the number of jobs.

This is a Go implementation of the Java version found at https://github.com/KevinStern/software-and-algorithms/