from itertools import product
from sympy import symbols, log, diff, exp, Product, Pow


def calc_posterior(p_c1: float, D: int, p_ij: dict[tuple[int, int], float]):
    priors = {
        1: p_c1,
        2: 1 - p_c1,
    }

    def p_x_given_Ci(xs: list[int], i: int):
        s = 1.0
        for j in range(len(xs)):
            s *= pow(p_ij[i, j], 1.0 - xs[j]) * pow(1.0 - p_ij[i, j], xs[j])
        return s

    posteriors = {}
    for i in [1, 2]:
        for xs in product([0, 1], repeat=D):
            numer = p_x_given_Ci(xs, i) * priors[i]

            def each_denom(k): return p_x_given_Ci(xs, k) * priors[k]
            denom = sum(map(each_denom, priors.keys()))
            posteriors[*xs, i] = numer / denom

    print("Priors:", priors)
    for xs in product([0, 1], repeat=D):
        print(f"{xs = }")
        for i in [1, 2]:
            prob = posteriors[*xs, i]
            print(f" * C{i}: {prob:0.3f}")
        print()


def prob_3c():
    D = 2
    p_ij = {}
    p_ij[1, 0] = 0.6
    p_ij[1, 1] = 0.1
    p_ij[2, 0] = 0.6
    p_ij[2, 1] = 0.9

    calc_posterior(0.2, D, p_ij)
    calc_posterior(0.8, D, p_ij)


def prob_2a():
    p, x, theta, k, n = symbols("p x theta k n")

    def get_mle(expr):
        likelihood_func = Product(expr, (k, 1, n))
        log_likelihood_func = log(likelihood_func)

        print(diff(log_likelihood_func, x).simplify())

    # print(diff(expr, x))
    print(get_mle(Pow(p, x) * Pow(1 - p, 1 - x)))
    print(get_mle((1 / theta) * exp(-x / theta)))


prob_2a()
prob_3c()