Computes the optimal (minimal cost) assignment of jobs to workers (or other
analogous) concepts given a cost matrix of each pair of job and worker, using
the algorithm by James Munkres in "Algorithms for the Assignment and
Transportation Problems", with additional optimizations as described by Jin
Kue Wong in "A New Implementation of an Algorithm for the Optimal Assignment
Problem: An Improved Version of Munkres' Algorithm". The algorithm runs in
O(n^3) time and need O(n^2) auxiliary space where n is the number of jobs or
workers, whichever is greater.
Construct a new problem instance with the specified cost matrix. The cost
matrix must be rectangular, though not necessarily square. If one dimension
is greater than the other, some elements in the greater dimension will not
be assigned. The input cost matrix will not be modified.
Get the optimal assignments. The returned array will have the same number
of elements as the number of elements as the number of rows in the input
cost matrix. Each element will indicate which column should be assigned to
that row or -1 if no column should be assigned, i.e. if result[i] = j then
row i should be assigned to column j. Subsequent invocations of this method
will simply return the same object without additional computation.