1）求一个矩阵的转置
matrix_before = [[1, 4], [2, 5], [3, 6]]
matrix_trans = []
length = len(matrix_before[0])
for j in range(length):
vectors = []
for i in matrix_before:
vectors.append(i[j])
matrix_trans.append(vectors)
print(matrix_trans)
2）推算任意层的杨辉三角
此题可以用填1法，补0法，置换法，对称法等求解。
以下我用的是置换法：
layer = int(input("input the layer number >>>"))
before = [[1], [1, 1]]
for i in range(2, layer + 1):
current_sub = [1] * (i + 1)
before_sub = before[-1]
for j in range(i - 1):
val = before_sub[j] + before_sub[j + 1]
current_sub[j + 1] = val
before.append(current_sub)
num = len(before[-1]) * len(str(before[-1][6])) + (len(before[-1]) - 1) * 2
for i in before:
print('{:^{}}'.format(i, num))
3）生成15个0-15的随机数，分别列出不重复的数与重复的数有哪些，且统计重复的数出现几次。
import random
repeat = {}
unique = []
l = []
for _ in range(10):
l.append(random.randint(1, 10))
k = [0] * len(l)
for i in range(10):
k[i] = l.count(l[i])
if k[i] == 1:
unique.append(l[i])
else:
repeat.fromkeys([l[i]])
repeat[l[i]] = k[i]
print("random num: ", l)
print("unique num: {}".format(unique))
print("repeat num: {}".format(repeat))
