等差数列和等比数列类。功能如下：

• 模拟无穷项数
• 获取任一项的值
• 跨步取项

class GeneralSequence:

    
    def __init__(self, valueAt):
        
        self.valueAt = valueAt
    
    
    def __getitem__(self, index):

        if isinstance(index, slice):
            
            from itertools import islice
            
            return islice(iter(self), index.start,
                          index.stop, index.step)
        
        else:    
            return self.valueAt(index)
    
    
    def __iter__(self):
        from itertools import count
        return map(self.valueAt, count())
    
    
class ArithmeticSequence(GeneralSequence):
    
    def __init__(self, a, d):
        valueAt = lambda n: a + n * d
        GeneralSequence.__init__(self, valueAt)

        
class GeometricSequence(GeneralSequence):
    
    def __init__(self, a, q):
        valueAt = lambda n: a * q**n
        GeneralSequence.__init__(self, valueAt)

GeneralSequence

__init__

持有通项公式。

__genitem__

分两种情况，

• 输入的index是切片时，用itertools.islice跨步取项。
• 输入index是数字时，用通项公式算出该处的值。

__iter__

实现迭代协议，可以支持这样的用法：

for item in GeometricSequence(1, 2):
    if item > 10000:
        break
    print(item, end=' ')
>> 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 

因为itertools.count不会抛出StopIteration异常，需要手动跳出循环。

ArithmeticSequence和GeometricSequence

接收各自的参数，构造充当通项公式的valueAt函数。

用例

an = ArithmeticSequence(10, 2)

it = iter(an)
for i in range(10):
    print(next(it), end=' ')
>> 10 12 14 16 18 20 22 24 26 28 

bn = ArithmeticSequence(-5, 3)
for i in range(10):
    print(bn[i], end=' ')
>> -5 -2 1 4 7 10 13 16 19 22 

cn = GeometricSequence(1, 2)
list(cn[100:140:5])
>> 
[1267650600228229401496703205376,
 40564819207303340847894502572032,
 1298074214633706907132624082305024,
 41538374868278621028243970633760768,
 1329227995784915872903807060280344576,
 42535295865117307932921825928971026432,
 1361129467683753853853498429727072845824,
 43556142965880123323311949751266331066368]