s = "Hello"
for c in s:
    print(c, ord(c))
print(chr(65))

# ========== 题目3 ==========
A = [3, 4]
B = [1, 2]

# 1. 向量加法
def vector_add(a, b):
    return [x + y for x, y in zip(a, b)]

# 2. 数乘向量
def scalar_multiply(scalar, vec):
    return [scalar * x for x in vec]

# 3. 计算向量的模
def vector_norm(vec):
    return sum(x**2 for x in vec) ** 0.5

print("题目3：")
print(f"1. A + B = {vector_add(A, B)}")
print(f"2. 2 × A = {scalar_multiply(2, A)}")
print(f"3. A的模 = {vector_norm(A)}")

print("-" * 30)

# ========== 题目4 ==========
A1 = [1, 2, 3]
B1 = [4, 5, 6]
A2 = [1, 0]
B2 = [0, 1]

# 1. 点积计算
def dot_product(a, b):
    return sum(x * y for x, y in zip(a, b))

# 2. 余弦相似度计算
def cosine_similarity(a, b):
    dot = dot_product(a, b)
    norm_a = vector_norm(a)
    norm_b = vector_norm(b)
    return dot / (norm_a * norm_b) if norm_a != 0 and norm_b != 0 else 0

print("题目4：")
print(f"1. A·B = {dot_product(A1, B1)}")
print(f"2. A1与B1的余弦相似度 = {cosine_similarity(A1, B1):.4f}")
print(f"3. A2与B2的余弦相似度 = {cosine_similarity(A2, B2)}")
print("   原因：两个向量正交（点积为0），方向完全垂直，所以相似度为0")