python3练习-杨辉三角/帕斯卡三角形

杨辉三角形式如下：
          1
        1   1
      1   2   1
    1   3   3   1
  1   4   6   4   1
1   5   10  10  5   1    

# 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
for t in triangles():
    print(t)
    n = n + 1
    if n == 10:
        break

思路：
1、第i-1行最后补0，将长度与第i行保持一致；
2、第i行第n个元素值为L(i)[n] = L(i-1)[n-1]+L(i-1)[n]
例如：
1、i=3时，此时集合为[1,3,3,1]；
2、i-1行集合补0后，集合为[1,2,1,0]
3、L(3)[0]=L(2)[-1]+L(2)[0]=0+1=1
     L(3)[1]=L(2)[0]+L(2)[1]=1+2=3
     .....

代码如下：
def triangles():
    L = [1]
    while True:
        yield L
        L.append(0)
        L = [L[i - 1] + L[i] for i in range(len(L))]

n=0
for t in triangles():
    print(t)
    n = n + 1
    if n == 10:
        break