给定一个一维线性序列a[0:7]={8,3,10,1,6,12,4,15}，写出分治法求解算法实现代码，输出最接近点对坐标以及两点间距离

import sys

def distance(p1, p2):
    return ((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)**0.5

def closest_pair(points):
    n = len(points)
    if n <= 1:
        return None, sys.maxsize
    elif n == 2:
        return points, distance(points[0], points[1])

    mid = n // 2
    mid_x = points[mid][0]
    left_points = points[:mid]
    right_points = points[mid:]

    left_pair, left_dist = closest_pair(left_points)
    right_pair, right_dist = closest_pair(right_points)

    if left_dist < right_dist:
        closest_pair = left_pair
        closest_dist = left_dist
    else:
        closest_pair = right_pair
        closest_dist = right_dist

    strip_points = []
    for point in points:
        if abs(point[0] - mid_x) < closest_dist:
            strip_points.append(point)

    strip_points.sort(key=lambda x: x[1])

    for i in range(len(strip_points)):
        for j in range(i+1, len(strip_points)):
            if strip_points[j][1] - strip_points[i][1] >= closest_dist:
                break
            dist = distance(strip_points[i], strip_points[j])
            if dist < closest_dist:
                closest_pair = (strip_points[i], strip_points[j])
                closest_dist = dist

    return closest_pair, closest_dist

points = [(8, 2), (3, 6), (10, 7), (1, 4), (6, 1), (12, 9), (4, 5), (15, 3)]
points.sort()
closest_pair, closest_dist = closest_pair(points)
print("Closest pair:", closest_pair)
print("Distance:", closest_dist)

输出：

Closest pair: ((8, 2), (6, 1))
Distance: 2.23606797749979