import numpy as np


def fft(x: np.array) -> np.array:
    N = len(x)

    if N == 1:
        return x
    else:
        even_fft = fft(x[::2])
        odd_fft = fft(x[1::2])

        factors = np.exp(-2j * np.pi * np.arange(N) / N)

        result = np.concatenate([even_fft + factors[:N // 2] * odd_fft,
                                 even_fft + factors[N // 2:] * odd_fft])

        return result


def main():
    x = np.arange(8)
    fft(x)
    # # x = np.random.normal(size=4)
    # x = np.array([1, 0, 1, 0, 0, 0, 0, 0])
    # print(f"own:\t{fft(x)}")
    # print(f"numpy:\t{np.fft.fft(x)}")


if __name__ == "__main__":
    main()