print("题目1 ")

hello1 = "Hello"  
hello2 = 'Hello'  
print("双引号表示:", hello1)
print("单引号表示:", hello2)


print("\n1. 'Hello' 每个字符的ASCII码:")
for c in hello1:
    print(f"字符 '{c}' → ASCII: {ord(c)}")


print("\n2. 验证ASCII码65对应的字符:")
print(f"chr(65) → {chr(65)}")



import math


print("\n题目3")
A = [3, 4]
B = [1, 2]


A_plus_B = [A[0] + B[0], A[1] + B[1]]
print(f"1. A + B = {A_plus_B}")


two_times_A = [2 * A[0], 2 * A[1]]
print(f"2. 2 × A = {two_times_A}")


len_A = math.sqrt(A[0] ** 2 + A[1] ** 2)
print(f"3. 向量A的长度 = {len_A}")



print("\n题目4")
A3 = [1, 2, 3]
B3 = [4, 5, 6]


dot_product = A3[0]*B3[0] + A3[1]*B3[1] + A3[2]*B3[2]
print(f"1. 点积A·B = {dot_product}")


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

cos_sim = cosine_similarity(A3, B3)
print(f"2. 余弦相似度 = {cos_sim:.4f}")


A_test = [1, 0]
B_test = [0, 1]
cos_sim_test = cosine_similarity(A_test, B_test)
print(f"3. A=[1,0], B=[0,1]的余弦相似度 = {cos_sim_test}")
print("原因：两个向量正交（垂直），方向完全不同，所以余弦相似度为0")