import math

def cosine_similarity(a, b):
    dot = sum(x * y for x, y in zip(a, b))
    norm_a = math.sqrt(sum(x**2 for x in a))
    norm_b = math.sqrt(sum(x**2 for x in b))
    return dot / (norm_a * norm_b)

# 题目4-1,4-2
A = [1, 2, 3]
B = [4, 5, 6]
dot_product = sum(a*b for a,b in zip(A,B))
print("点积 =", dot_product)
print("余弦相似度 =", cosine_similarity(A, B))

# 题目4-3
A2 = [1, 0]
B2 = [0, 1]
print("特殊向量余弦相似度 =", cosine_similarity(A2, B2))