import math

def distance_between_points(p1, p2):
    """計(jì)算兩點(diǎn)之間的歐幾里得距離"""
    x1, y1 = p1
    x2, y2 = p2
    
    # 計(jì)算距離
    distance = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
    return distance

# 示例
point1 = (1, 2)
point2 = (4, 6)

dist = distance_between_points(point1, point2)
print(f"兩點(diǎn) {point1} 和 {point2} 之間的距離是: {dist}")
# 輸出: 5.0

import math

point1 = (1, 2)
point2 = (4, 6)

# 直接計(jì)算
distance = math.dist(point1, point2)
print(f"距離: {distance}")
# 輸出: 5.0

import numpy as np

# 方法 3.1: 使用 np.linalg.norm
point1 = np.array([1, 2])
point2 = np.array([4, 6])

distance = np.linalg.norm(point2 - point1)
print(f"距離: {distance}")
# 輸出: 5.0

# 方法 3.2: 手動(dòng)計(jì)算
distance = np.sqrt(np.sum((point2 - point1)**2))
print(f"距離: {distance}")
# 輸出: 5.0

# 方法 3.3: 批量計(jì)算多個(gè)點(diǎn)
points1 = np.array([[1, 2], [3, 4], [5, 6]])
points2 = np.array([[4, 6], [7, 8], [9, 10]])

distances = np.linalg.norm(points2 - points1, axis=1)
print(f"多個(gè)距離: {distances}")
# 輸出: [5. 5.65685425 5.65685425]

from scipy.spatial import distance

point1 = (1, 2)
point2 = (4, 6)

# 歐幾里得距離
euclidean_dist = distance.euclidean(point1, point2)
print(f"歐幾里得距離: {euclidean_dist}")

# 曼哈頓距離 (|x2-x1| + |y2-y1|)
manhattan_dist = distance.cityblock(point1, point2)
print(f"曼哈頓距離: {manhattan_dist}")

# 切比雪夫距離 (max(|x2-x1|, |y2-y1|))
chebyshev_dist = distance.chebyshev(point1, point2)
print(f"切比雪夫距離: {chebyshev_dist}")

def distance_squared(p1, p2):
    """計(jì)算距離的平方（不開(kāi)方）"""
    x1, y1 = p1
    x2, y2 = p2
    return (x2 - x1)**2 + (y2 - y1)**2

point1 = (1, 2)
point2 = (4, 6)
point3 = (5, 5)

dist2_1 = distance_squared(point1, point2)  # 25
dist2_2 = distance_squared(point1, point3)  # 25

# 比較時(shí)不需要開(kāi)方
if dist2_1 < dist2_2:
    print("point2 更近")
elif dist2_1 > dist2_2:
    print("point3 更近")
else:
    print("距離相等")

import math

def calculate_distance(p1, p2):
    """支持任意維度的點(diǎn)"""
    if len(p1) != len(p2):
        raise ValueError("兩點(diǎn)維度必須相同")
    
    # 計(jì)算各維度差值的平方和
    sum_of_squares = sum((a - b)**2 for a, b in zip(p1, p2))
    
    # 開(kāi)方
    return math.sqrt(sum_of_squares)

# 2D 點(diǎn)
p1_2d = (1, 2)
p2_2d = (4, 6)
print(f"2D 距離: {calculate_distance(p1_2d, p2_2d)}")

# 3D 點(diǎn)
p1_3d = (1, 2, 3)
p2_3d = (4, 6, 8)
print(f"3D 距離: {calculate_distance(p1_3d, p2_3d)}")

# 使用 math.dist (Python 3.8+)
print(f"3D 距離 (math.dist): {math.dist(p1_3d, p2_3d)}")