import random

def calculate_marginal_value(goods, selected_good, valuation_function, bids, prices):
    """
    Compute the marginal value of selected_good: 
    the difference between the valuation of the bundle that includes the good and the bundle without it.
    A bidder wins a good if bid >= price.
    """
    # TODO: Implement marginal value calculation
    raise NotImplementedError("Implement marginal value calculation")

def calculate_expected_marginal_value(goods, selected_good, valuation_function, bids, price_distribution, num_samples=50):
    """
    Compute the expected marginal value of selected_good:
    the average of the marginal values over a number of samples.
    
    Algorithm 1: Estimate the expected marginal value of good gj
    INPUTS: Set of goods G, select good gj ∈ G, valuation function v, bid vector b, price distribution P
    HYPERPARAMETERS: NUM_SAMPLES
    OUTPUT: An estimate of the expected marginal value of good gj
    

    """
    # TODO: Implement expected marginal value calculation according to Algorithm 1
    raise NotImplementedError("Implement expected marginal value calculation") 