import math
import matplotlib.pyplot as plt


def do_bis(fun, a, b):
    c_bis = (a + b) / 2

    if fun(a) * fun(c_bis) < 0:
        return a, c_bis

    return c_bis, b


def do_falsi(fun, a, b):
    if fun(b) - fun(a) == 0:
        print("Division by zero\n")
    c_falsi = (a * fun(b) - b * fun(a)) / (fun(b) - fun(a))

    if fun(c_falsi) * fun(a) < 0:
        return a, c_falsi

    return c_falsi, b


def bi_reg_root(fun, a, b, err_max):
    MAX_ITER = 1000
    last_ans = (a + b) / 2
    f = []
    for i in range(MAX_ITER):
        lb, rb = do_bis(fun, a, b)
        lf, rf = do_falsi(fun, a, b)
        if abs(rf - lf) < abs(lb - rb):
            a, b = lf, rf
        else:
            a, b = lb, rb
        ans = (a + b) / 2
        err = abs((ans - last_ans) / last_ans)
        f.append(ans)
        if err < err_max:
            return f
        last_ans = (a + b) / 2
        print(i, " : ", ans)
    return last_ans


def graph(f):
    plt.plot(range(0, len(f)), f)
    plt.title("Method plot")
    plt.show()


l = 1
T = 6
g = 9.81
my_function = lambda x: (math.pi * ((x / g) ** (1 / 2)) + math.pi * (((x - l) / g) ** (1 / 2)) - T).real
graph(bi_reg_root(my_function, 1, 100, 1e-7))