类class:
>>> class Yh(): def __init__(self,n=None): self.data = [1] if n!=None: self.data=Yh()*n def __repr__(self): return f'{self.data}' def __mul__(self,n): self.data = [1] while n>1: n-=1 self.data.append(0) self.data=[sum(z) for z in zip(self.data,self.data[::-1])] return self.data __rmul__ = __mul__ def List(n): i=0 while i<n: i+=1 print(Yh(i)) >>> Yh() [1] >>> Yh(2) [1, 1] >>> Yh(3) [1, 2, 1] >>> Yh(6) [1, 5, 10, 10, 5, 1] >>> Yh(13) [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1] >>>
测试:
>>> def test(func, n, out=True): from time import time start = time() if not out: t=(func(n)) else: for i in range(1,n+1): print(f'Y({i:>2}) = {func(i)}') print(time()-start) >>> test(Yh,15) Y( 1) = [1] Y( 2) = [1, 1] Y( 3) = [1, 2, 1] Y( 4) = [1, 3, 3, 1] Y( 5) = [1, 4, 6, 4, 1] Y( 6) = [1, 5, 10, 10, 5, 1] Y( 7) = [1, 6, 15, 20, 15, 6, 1] Y( 8) = [1, 7, 21, 35, 35, 21, 7, 1] Y( 9) = [1, 8, 28, 56, 70, 56, 28, 8, 1] Y(10) = [1, 9, 36, 84, 126, 126, 84, 36, 9, 1] Y(11) = [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1] Y(12) = [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1] Y(13) = [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1] Y(14) = [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1] Y(15) = [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1] 0.1680755615234375 >>> >>> test(Yh,1000,False) 0.2420802116394043 >>> test(Yh,2000,False) 1.3822360038757324 >>> test(Yh,3000,False) 4.064407110214233 >>>
副产品
除了像函数一样使用外,还能用乘法表示项数,也可以直接列表:
>>> Yh(11) [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1] >>> Yh()*12 [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1] >>> 12*Yh() [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1] >>> >>> triangle = Yh() >>> 6 * triangle [1, 5, 10, 10, 5, 1] >>> triangle * 13 [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1] >>> triangle *= 5 >>> triangle [1, 4, 6, 4, 1] >>> >>> Yh.List(10) [1] [1, 1] [1, 2, 1] [1, 3, 3, 1] [1, 4, 6, 4, 1] [1, 5, 10, 10, 5, 1] [1, 6, 15, 20, 15, 6, 1] [1, 7, 21, 35, 35, 21, 7, 1] [1, 8, 28, 56, 70, 56, 28, 8, 1] [1, 9, 36, 84, 126, 126, 84, 36, 9, 1] >>>