import math

# 定义向量x和y
x = (0, 1, 0, 1)
y = (1, 0, 1, 0)

# 计算余弦相似度
def cosine(x, y):
    numerator = sum([x[i] * y[i] for i in range(len(x))])
    denominator = math.sqrt(sum([x[i] ** 2 for i in range(len(x))])) * math.sqrt(sum([y[i] ** 2 for i in range(len(y))]))
    return numerator / denominator

# 计算相关系数
def correlation(x, y):
    n = len(x)
    sum_x = sum(x)
    sum_y = sum(y)
    sum_xy = sum([x[i] * y[i] for i in range(n)])
    sum_x2 = sum([x[i] ** 2 for i in range(n)])
    sum_y2 = sum([y[i] ** 2 for i in range(n)])
    numerator = n * sum_xy - sum_x * sum_y
    denominator = math.sqrt((n * sum_x2 - sum_x ** 2) * (n * sum_y2 - sum_y ** 2))
    return numerator / denominator

# 计算Jaccard系数
def jaccard(x, y):
    intersection = sum([x[i] and y[i] for i in range(len(x))])
    union = sum([x[i] or y[i] for i in range(len(x))])
    return intersection / union

# 输出结果
print('余弦相似度:', cosine(x, y))
print('相关系数:', correlation(x, y))
print('Jaccard系数:', jaccard(x, y))