在二维平面上寻找与一组点的最大距离为最小的点

def weiszfeld_algorithm(points, tolerance=1e-6, max_iterations=1000):
    # 初始化权重
    weights = [1.0 / sum([distance(p, q) for q in points if q != p]) for p in points]
    for _ in range(max_iterations):
        new_weights = []
        new_center = [0, 0]
        for i, p in enumerate(points):
            distance_sum = sum([weights[j] * distance(p, points[j]) for j in range(len(points)) if j != i])
            new_weights.append(1.0 / distance_sum)
            new_center[0] += new_weights[i] * p[0]
            new_center[1] += new_weights[i] * p[1]
        new_center = [c / sum(new_weights) for c in new_center]
        
        # 检查收敛
        if all(abs(new_center[i] - center[i]) < tolerance for i in range(2)):
            break
        center = new_center
        weights = new_weights
    
    return center

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