杨辉三角-python实现

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

把每一行看做一个list，试写一个generator，不断输出下一行的list：

代码来自https://baike.baidu.com/item/杨辉三角#4_10

第一个方法:

>>> def triangles():
...     L=[1]
...     while True:
...         yield L
...         L = [sum(i) for i in zip([0]+L,L+[0])]
... 
>>> n = 0
>>> results=[]
>>> for t in triangles():
...     print(t)
...     results.append(t)
...     n= n+1
...     if n==10:
...         break
... 
[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]

其中，zip函数的原型为：zip([iterable, …]) 参数iterable为可迭代的对象，并且可以有多个参数。该函数返回一个以元组为元素的列表，其中第 i 个元组包含每个参数序列的第 i 个元素。返回的列表长度为最短的参数序列的长度。

>>> a = [1,2,3]

>>> b = [4,5,6]

>>> c = [8,9,10,11,12]

>>> zz = zip(a,b,c)

>>> print(zz)

<zip object at 0x10340ac88>

>>> next(zz)

(1, 4, 8)

>>> next(zz)

(2, 5, 9)

>>> next(zz)

(3, 6, 10)

>>> next(zz)

Traceback (most recent call last):

  File "<stdin>", line 1, in <module>

StopIteration

该方式用到了列表生成式，理解起来较困难，下面是另一种方式：

def triangles():
    ret = [1]
    while True:
        yield ret
        for i in range(1, len(ret)):
            ret[i] = pre[i] + pre[i - 1]
        ret.append(1)
        pre = ret[:]

另一个不用生成器的版本：

def YangHui (num = 10):

LL = [[1]] #LL为全是1的矩阵

for i in range(1,num):

LL.append([(0 if j== 0 else LL[i-1][j-1])+ (0 if j ==len(LL[i-1]) else LL[i-1][j]) for j in range(i+1)])

return LL

在评论区看到了一个用生成器的方式：

def triangle():
    L=[1]
    while True:
        yield L
        G=[0]+L+[0]
        L=[G[i]+G[i+1] for i in range(len(G)-1)]
    return ('done') 
# 期待输出:
# [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]
n = 0
results = []
for t in triangles():
    print(t)
    results.append(t)
    n = n + 1
    if n == 10:
        break
if results == [
    [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]
]:
    print('测试通过!')
else:
    print('测试失败!')

杨辉三角-python实现

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