Python高级模块化算术算法

Question

我有这个程序：#!/usr/bin/python3def 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 tmpm = abs(int(input('Modulus: '))) + 1i = abs(int(input('Iterate: '))) + 1h: int = 0m2: int = 3 * mfor 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，该bounce()函数或其测试代码都没有工作。我不知道为什么。例如，如果我输入6模数和4迭代变量i，程序应该打印 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。我已经对这个bounce()功能猛烈抨击了很多次，以至于我看不到它。add参数的标牌让我绊倒了。

Answer 1

您可能不需要生成整个序列，以下是封闭形式的实现，该形式计算并返回给定大小的序列中的索引，您希望以反复循环的方式迭代：

您可以从任何时间点开始，包括过去（负时间），并获得您在序列（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()