# https://www.cs.cmu.edu/~dgolovin/papers/nips08.pdf

# Define SAT solvers
# solvers = [solver1, solver2, ..., solver_n]

# # Define the objective function
# def submodular_function(S):
#     # Example: number of solved SAT problems given allocation S
#     return number_of_solved_problems(S)

# # Total budget and allocation step
# B = 1000  # Total budget (e.g., seconds of CPU time)
# delta_b = 1  # Allocation step (e.g., 1 second)

# # Initialize allocation
# allocation = {solver: 0 for solver in solvers}

# # Greedy allocation
# while sum(allocation.values()) < B:
#     best_solver = None
#     best_gain = -float('inf')

#     for solver in solvers:
#         # Test marginal gain for allocating delta_b to this solver
#         current_allocation = allocation.copy()
#         current_allocation[solver] += delta_b
#         gain = (submodular_function(current_allocation) - submodular_function(allocation)) / delta_b

#         if gain > best_gain:
#             best_gain = gain
#             best_solver = solver

#     # Allocate delta_b to the best solver
#     allocation[best_solver] += delta_b

# # Output the allocation
# print("Final Allocation:", allocation)
