import math
from itertools import zip_longest

x = [0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3]
y = [20, 22.222222, 8, 4.081633, 2.469136, 1.652893, 0.83665]

# # z instrukcji, tylko do testu
# x = [0.6, 0.7, 0.8, 0.9, 1.0]
# y = [-0.51083, -0.35667, -0.22314, -0.10536, 0.0]

h = math.ceil(x[1] - x[0])

def print_table(*columns):
    def generate_headers(n):
        headers = ["x", "f(x)"]
        superscripts = ["\u2070", "\u00B9", "\u00B2", "\u00B3", "\u2074", "\u2075", "\u2076", "\u2077", "\u2078", "\u2079"]
        for i in range(1, n):
            exp = ''.join(superscripts[int(digit)] for digit in str(i))
            headers.append(f"∇{exp}f(x)")
        return headers
    headers = generate_headers(len(columns))

    max_widths = [
        max(len(str(cell)) for cell in [header] + list(column))
        for header, column in zip(headers, columns)
    ]

    def format_row(row):
        return " | ".join(f"{str(cell).ljust(width)}" for cell, width in zip(row, max_widths))

    print(format_row(headers))
    print("-" * (sum(max_widths) + 3 * (len(headers) - 1)))  # Separator line

    for row in zip_longest(*columns, fillvalue=" "):
        print(format_row(row))

    print("-" * (sum(max_widths) + 3 * (len(headers) - 1)))

def oblicz(array):
    result = []
    current = array
    for _ in range(len(array) - 1):
        arr = [round(current[j] - current[j - 1], 5) for j in range(len(current) - 1, 0, -1)]
        arr.reverse()
        result.append(arr)
        current = arr
    return result

def wynik(array):
    temp = []
    suma = 0
    for x in array:
        temp.append(x[-1])
    for x in temp:
        if temp.index(x) == 0:
            suma += x
        elif temp.index(x) >= 1:
            tik = 1/(temp.index(x) + 1)
            suma += x*tik
    print(f"f⁽¹⁾(x) = {round(suma*(1/h),5)}")

result = oblicz(y)
columns = [x, y] + result
print_table(*columns)
wynik(result)