from pulp import LpMaximize, LpProblem, LpVariable

def gomory_ilpp(ob, con, cof):
    # Create an ILP problem
    prob = LpProblem("Gomory_Cut_Example", LpMaximize)

    # Define decision variables
    x = LpVariable("x", lowBound=0, cat='Integer')
    y = LpVariable("y", lowBound=0, cat='Integer')

    # Add the objective function
    prob += ob[0] * x + ob[1] * y, "Objective"

    # Add constraints
    prob += con[0][0] * x + con[0][1] * y <= cof[0], "Constraint 1"
    prob += con[1][0] * x + con[1][1] * y <= cof[1], "Constraint 2"

    # Function to check if a solution is integer
    def is_integer_solution(variables):
        for var in variables:
            if abs(var.varValue - round(var.varValue)) > 1e-5:
                return False
        return True

    while True:
        # Solve the relaxation of the ILP problem
        prob.solve()

        # Check if the solution is integer
        if is_integer_solution([x, y]):
            break

        print("Non-integer solution found. Adding Gomory cut...")

        # Find the fractional variable
        fractional_var = None
        for var in [x, y]:
            var_solution = var.varValue
            if abs(var_solution - round(var_solution)) > 1e-5:
                fractional_var = var
                break

        # Add Gomory cut
        gomory_cut = fractional_var >= int(fractional_var.varValue) + 1
        prob += gomory_cut

    # Store the final solution
    optimal_solution = {x.name: x.varValue, y.name: y.varValue}
    objective_value = prob.objective.value()

    return optimal_solution, objective_value


if __name__ == "__main__":
    pass
