import numpy as np


def resolve_up(A: np.array, b: np.array) -> np.array:
    x = np.zeros(len(b))
    for i in range(len(A) - 1, -1, -1):
        right_of_diagonal = 0.0
        for k in range(i+1, len(A)):
            right_of_diagonal += A[i, k] * x[k]
        x[i] = (b[i] - right_of_diagonal) / A[i,i]
    return x


def resolve_down(A: np.array, b: np.array) -> np.array:
    x = np.zeros(len(b))
    for i in range(len(A)):
        sum = 0.0
        for k in range(i):
            sum += A[i,k] * x[k]
        x[i] = (b[i] - sum) / A[i, i]
    return x


if __name__ == '__main__':
    A = np.array([
        [2, 4, -6],
        [0, -1, 1],
        [0, 0, -2],
    ], dtype=float)

    b = np.array([2, 3, -7], dtype=float)

    A_down = np.array([
        [2, 0, 0],
        [4, -1, 0],
        [-6, 1, -2],
    ])

    b_down = np.array([2, 3, -7])

    print(resolve_up(A, b))
    print(resolve_down(A_down, b_down))