用 Python 实现节约里程法

节约里程法是一种启发式算法，用于解决TSP问题。以下是用Python实现节约里程法的简单代码示例：

import math

def calc_distance(points, i, j):
    # 计算两个点之间的欧氏距离
    dx = points[i][0] - points[j][0]
    dy = points[i][1] - points[j][1]
    return math.sqrt(dx * dx + dy * dy)

def saving_algorithm(points):
    # 初始化边权
    n = len(points)
    edge_weight = [[0] * n for i in range(n)]
    for i in range(n):
        for j in range(n):
            if i == j:
                edge_weight[i][j] = float('inf')
            else:
                # 计算两个点之间的距离
                edge_weight[i][j] = calc_distance(points, i, j)

    # 计算节约值，存储在数组中
    saving = [[0] * n for i in range(n)]
    for i in range(n - 1):
        for j in range(i + 1, n):
            for k in range(n):
                if k != i and k != j:
                    saving[i][j] += edge_weight[i][k] + edge_weight[k][j] - edge_weight[i][j]

    # 对节约值进行排序
    savings = []
    for i in range(n - 1):
        for j in range(i + 1, n):
            savings.append((i, j, saving[i][j]))
    savings.sort(key=lambda x: -x[2])

    # 合并路径
    route = list(range(n))
    for i, j, s in savings:
        if route[i] != route[j]:
            route_j = route[j]
            for k in range(n):
                if route[k] == route_j:
                    route[k] = route[i]

    # 返回路径和长度
    res_route = [points[route[i]] for i in range(n)]
    res_length = sum(calc_distance(res_route, i, i + 1) for i in range(n - 1)) + calc_distance(res_route, n - 1, 0)

    return res_route, res_length

这个函数接受一个由点坐标构成的列表，返回一个最优路径和长度。要使用这个函数，请将点列表传递给它，例如：

points = [(0, 0), (1, 2), (3, 4), (5, 6)]
route, length = saving_algorithm(points)
print(route)
print(length)

这将输出最优路径和长度。