import math
A = [1, 2, 3]
B = [4, 5, 6]
def dot_product(v1, v2):
    return sum(x * y for x, y in zip(v1, v2))
A_dot_B = dot_product(A, B)
print("1. A · B =", A_dot_B)
def vector_norm(v):
    return math.sqrt(sum(x ** 2 for x in v))
def cosine_similarity(v1, v2):
    dot = dot_product(v1, v2)
    norm1 = vector_norm(v1)
    norm2 = vector_norm(v2)
    if norm1 == 0 or norm2 == 0:
        return 0.0
    return dot / (norm1 * norm2)
cos_sim = cosine_similarity(A, B)
print("2. 余弦相似度 =", round(cos_sim, 4))  
A2 = [1, 0]
B2 = [0, 1]
cos_sim2 = cosine_similarity(A2, B2)
print("3. A=[1,0], B=[0,1] 的余弦相似度 =", cos_sim2)
print("   原因：点积为 0，说明两向量正交，夹角为 90°，所以余弦相似度为 0。")