tl/dr: I need help with the "generate()" method described below... a nudge in the correct direction or perhaps, a good reference/tutorial/something that helps me understand dynamic programming better.

Roth, A. E., U. G. Rothblum, and J. H. Vande Vate. "Stable Matchings, Optimal Assignments, and Linear Programming." Mathematics of Operations Research 18, no. 4 ...