Solved the Job Assignment Problem using both brute force as well as branch and bound. The code contains 5 functions:

job_assignment(cost_matrix): Find an optimal solution to the job assignment problem using branch and bound. Input: an nxn matrix where a row represents a person and a column represents the cost each person takes to complete the jobs. Return: the minimal cost, an optimal solution, and the number of partial or full solutions evaluated.

get_csf(cost_matrix, partial_solution): Input: an nxn cost matrix and a partial solution. Return: the partial solution's Cost So Far (CSF). A partial solution is represented as a list of n elements, where an undecided element is denoted by a -1. For instance, a partial solution [2, -1, -1] represents assigning job 2 to person 0 and leaving the assignments of person 1 and person 2 undecided.

get_gfc(cost_matrix, partial_solution): Input: an nxn cost matrix and a partial solution. Return: the partial solution's Guaranteed Future Cost (GFC).

get_ffc(cost_matrix, partial_solution): Input: an nxn cost matrix and a partial solution. Return: the partial solution's Feasible Futre Cost (FFC)

brute_force(cost_matrix): This function finds an optimal solution for the job assignment problem using brute force. Input: an nxn cost matrix. Return: the minimal total cost, an optimal solution, and the number of full solutions investigated.