def generate_triangle():
    t = 0
    ts = [[]]
    i_in_row, max_in_row = 0, 1
    for _ in range(1, 500_500 + 1):
        t = (615_949 * t + 797_807) % 2**20
        s = t - 2**19
        ts[-1].append(s)
        i_in_row += 1
        if i_in_row == max_in_row:
            i_in_row = 0
            max_in_row += 1
            ts.append([])
    ts.pop() # remove empty list
    return ts


def array_to_prefix_sum_array(xs):
    ys = []
    current_sum = 0
    for x in xs:
        current_sum += x
        ys.append(current_sum)
    return ys


def range_sum(prefix_sum, i, j):
    if i == 0:
        return prefix_sum[j]
    else:
        return prefix_sum[j] - prefix_sum[i - 1]


def find_min_triangle(row_i, col_i, sum_triangle):
    current_sum, min_sum = 0, float("inf")
    left_i, right_i = col_i, col_i
    while row_i < len(sum_triangle):
        current_sum += range_sum(sum_triangle[row_i], left_i, right_i)
        row_i += 1
        right_i += 1
        min_sum = min(current_sum, min_sum)
    return min_sum


def euler_150():
    triangle = generate_triangle()
    # triangle = [[15], [-14, -7], [20, -13, -5], [-3, 8, 23, -26], [1, -4 , -5, -18, 5], [-16, 31, 2, 9, 28, 3]]
    sum_triangle = [array_to_prefix_sum_array(xs) for xs in triangle]

    min_triangle = float("inf")
    for row_i in range(len(triangle)):
        for col_i in range(len(triangle[row_i])):
            potential_min = find_min_triangle(row_i, col_i, sum_triangle)
            min_triangle = min(min_triangle, potential_min)
    return min_triangle


if __name__ == "__main__":
    solution = euler_150()
    print("e150.py: " + str(solution))
    assert solution == -271248680