Python高级模数算法

Question

我有这个程序:

#!/usr/bin/python3
def bounce(modulo: int, here: int, add: int) -> int:
    # additive version
    # modulo = 2n > 0, 0 <= here < n, add is any integer
    # cycle {
    #   {0, 1, 2, 3, ..., n - 1, n - 2, n - 3, ...,
    #    0, 1, 2, 3, ..., n - 1, n - 2, n - 3, ...},
    #   {0, 1, 2, 3, ..., n - 1, n - 2, n - 3, ...,
    #    0, 1, 2, 3, ..., n - 1, n - 2, n - 3, ...},
    #   ...
    # }
    tmp = abs(here + add) % (2 * modulo)
    if tmp <= modulo:
        tmp *= -1
        tmp -= 1
    tmp %= modulo
    return tmp


m = abs(int(input('Modulus: '))) + 1
i = abs(int(input('Iterate: '))) + 1

h: int = 0
m2: int = 3 * m

for x in range(1, 1 + i):
    print(h, end = ('\n' if x % m2 == 0 else ', '))
    h = bounce(m, h, 1)

input('Done.')

由于某种原因，bounce() 函数或其测试代码均无法正常工作。我不知道为什么。例如，如果我输入 6 作为模数，输入 4 作为迭代变量 i，则程序应打印 5 行 0 , 1, 2, 3, 4, 5, 4, 3, 2, 1, 0。相反，我会看到 2 行 6, 0, 6, 0, ...。答案可能很简单。我刚刚绞尽脑汁地反对这个 bounce() 函数很多次，以至于我看不到它。 add 参数的标志让我很困惑。

Answer 1

您可能不需要生成整个序列，以下是封闭形式的实现，它计算并返回您希望以往返循环方式迭代的给定大小的序列中的索引:

您可以从任何时间点开始，包括过去(负时间)，并获取您在序列(索引)中的位置，而无需迭代或构建整个序列。

def bounce_back_and_forth(size: int, start_t: int=0)->int:
    """returns the index position in a sequence at time t=t, when the index starts
    at position zero at time t=0, and walks the list from end to end, and and bounces
    back and forth.
    returns the index for all t in Z

    @param size: int, the size of the sequence to iterate over
    @param start_t: int, the starting indice (usually time), zero by default
    :return: the index in the sequence corresponding to the start_t provided

    closed form, no iteration necessary --> O(1) time & space complexity

       size=5                     size=5                    size=5
       start at t=0               start at t=6              start at t=-1 and decreases
     0 [0, _, _, _, _]         6 [_, _, 2, _, _]        -1 [_, _, _, _, 4]
     1 [_, 1, _, _, _]         7 [_, 1, _, _, _]        -2 [_, _, _, 3, _]
     2 [_, _, 2, _, _]         8 [0, _, _, _, _]        -3 [_, _, 2, _, _]
     3 [_, _, _, 3, _]         9 [_, 1, _, _, _]        -4 [_, 1, _, _, _]
     4 [_, _, _, _, 4]        10 [_, _, 2, _, _]        -5 [0, _, _, _, _]
     5 [_, _, _, 3, _]        11 [_, _, _, 3, _]        -6 [_, 1, _, _, _]
     6 [_, _, 2, _, _]        12 [_, _, _, _, 4]        -7 [_, _, 2, _, _]
     7 [_, 1, _, _, _]        13 [_, _, _, 3, _]        -8 [_, _, _, 3, _]
     8 [0, _, _, _, _]        14 [_, _, 2, _, _]        -9 [_, _, _, _, 4]
     9 [_, 1, _, _, _]        15 [_, 1, _, _, _]       -10 [_, _, _, 3, _]
    10 [_, _, 2, _, _]        16 [0, _, _, _, _]       -11 [_, _, 2, _, _]
    """

    go_and_back = size * 2 - 2

    if start_t < 0:
        start_t = size - abs(start_t) % go_and_back

    tdx_at_start_t = start_t % go_and_back
    if tdx_at_start_t >= size:
        tdx_at_start_t = go_and_back - tdx_at_start_t

    return tdx_at_start_t


if __name__ == '__main__':

    # tests
    res = [0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1]
    for idx in range(18):
        actual, expected = bounce_back_and_forth(5, start_t=idx), res[idx]
        assert actual == expected

    stride = 0
    for _ in range(5):
        mod = 8  # the size of the sequence to iterate over
        start = 0
        stride += 1
        print(f'size: {mod}, stride: {stride} -> ', end='')
        for tdx in range(start, 20, stride):  # <-- get indices for 20 time steps ahead
            print(bounce_back_and_forth(mod, tdx), end=' ')
        print()

输出:

size: 8, step: 1 -> 0 1 2 3 4 5 6 7 6 5 4 3 2 1 0 1 2 3 4 5 
size: 8, step: 2 -> 0 2 4 6 6 4 2 0 2 4 
size: 8, step: 3 -> 0 3 6 5 2 1 4 
size: 8, step: 4 -> 0 4 6 2 2 
size: 8, step: 5 -> 0 5 4 1 

测试:

class TestBounceBackAndForth(unittest.TestCase):

    def test_size5_t0(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=0), 0)

    def test_size5_t3(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=3), 3)

    def test_size5_t4(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=4), 4)

    def test_size5_t5(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=5), 3)

    def test_size5_t6(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=6), 2)

    def test_size5_t7(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=7), 1)

    def test_size5_t8(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=8), 0)

    def test_size5_t9(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=9), 1)

    def test_size5_t10(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=10), 2)

    def test_size5_t11(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=11), 3)

    def test_size2_t0(self):
        self.assertEqual(bounce_back_and_forth(size=2, start_t=0), 0)

    def test_size2_t1(self):
        self.assertEqual(bounce_back_and_forth(size=2, start_t=1), 1)

    def test_size2_t2(self):
        self.assertEqual(bounce_back_and_forth(size=2, start_t=2), 0)

    def test_size2_t3(self):
        self.assertEqual(bounce_back_and_forth(size=2, start_t=3), 1)

    def test_size2_t4(self):
        self.assertEqual(bounce_back_and_forth(size=2, start_t=4), 0)

    def test_size15_t7(self):
        self.assertEqual(bounce_back_and_forth(size=15, start_t=7), 7)

    def test_size15_t8(self):
        self.assertEqual(bounce_back_and_forth(size=15, start_t=97), 13)

    # --- Negative Indices ------------
    def test_size5_t_m1(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-1), 4)

    def test_size5_t_m2(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-2), 3)

    def test_size5_t_m3(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-3), 2)

    def test_size5_t_m4(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-4), 1)

    def test_size5_t_m5(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-5), 0)

    def test_size5_t_m6(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-6), 1)

    def test_size5_t_m7(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-7), 2)

    def test_size5_t_m8(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-8), 3)

    def test_size5_t_m9(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-9), 4)

    def test_size5_t_m10(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-10), 3)

    def test_size5_t_m11(self):
        self.assertEqual(bounce_back_and_forth(size=5, start_t=-11), 2)

    def test_size2_t_m1(self):
        self.assertEqual(bounce_back_and_forth(size=2, start_t=-1), 1)

    def test_size2_t_m2(self):
        self.assertEqual(bounce_back_and_forth(size=2, start_t=-2), 0)

    def test_size2_t_m3(self):
        self.assertEqual(bounce_back_and_forth(size=2, start_t=-3), 1)

    def test_size2_t_m4(self):
        self.assertEqual(bounce_back_and_forth(size=2, start_t=-4), 0)

    def test_size15_t_m7(self):
        self.assertEqual(bounce_back_and_forth(size=15, start_t=-7), 8)

    def test_size15_t_m8(self):
        self.assertEqual(bounce_back_and_forth(size=15, start_t=-8), 7)

    def test_size15_t_m97(self):
        self.assertEqual(bounce_back_and_forth(size=15, start_t=-97), 2)


if __name__ == '__main__':
    unittest.main()