Farthest Insertion源码

以下是Python实现Farthest Insertion算法的代码：

import math

# 计算两点之间的欧几里得距离
def euclidean_distance(point1, point2):
    x1, y1 = point1
    x2, y2 = point2
    return math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)

# 找到距离所有已选择点最远的点
def farthest_point(points, selected_points):
    max_distance = 0
    farthest_point = None
    for point in points:
        if point in selected_points:
            continue
        distance = min([euclidean_distance(point, selected) for selected in selected_points])
        if distance > max_distance:
            max_distance = distance
            farthest_point = point
    return farthest_point

# Farthest Insertion算法实现
def farthest_insertion(points):
    # 选择最远的两个点作为初始路径
    start = points[0]
    end = farthest_point(points, [start])
    path = [start, end]
    # 选择剩余的点，直到所有点都被添加到路径中
    while len(path) < len(points):
        # 找到距离已选择点最远的点
        farthest = farthest_point(points, path)
        # 找到距离已选择点最近的点
        min_distance = math.inf
        for i in range(len(path)):
            for j in range(i + 1, len(path)):
                distance = euclidean_distance(farthest, path[i]) + euclidean_distance(farthest, path[j]) - euclidean_distance(path[i], path[j])
                if distance < min_distance:
                    min_distance = distance
                    insert_index = j
                    insert_point = farthest
        # 将新点插入到路径中
        path.insert(insert_index, insert_point)
    return path

其中，`points`为输入的点集，每个点表示为二元组`(x, y)`；`farthest_insertion`函数返回最终的路径，以列表形式存储每个点的坐标。