python动态规划之旅行商问题

以下是Python中解决旅行商问题的动态规划算法：

def tsp_dp(dist):
    n = len(dist)
    all_points_set = set(range(n))
    memo = {}
    # 预处理，将所有只包含起点的情况都计算出来
    for i in range(n):
        memo[(frozenset([i]), i)] = (dist[i][0], 0)

    for r in range(2, n+1):
        for subset in itertools.combinations(all_points_set - {0}, r-1):
            subset = frozenset(subset)
            for k in subset:
                memo[(subset, k)] = min(
                    (dist[i][k] + memo[(subset - {k}, i)][0], i) for i in subset if i != 0 and i != k)

    # 找到最小的回路
    res, _ = min((dist[i][0] + memo[(all_points_set - {0}, i)][0], i) for i in range(1, n))
    path = [0]
    last = _
    all_points_set = all_points_set - {0}
    for i in range(n-2):
        next_node = memo[(all_points_set, last)][1]
        path.append(next_node)
        all_points_set = all_points_set - {next_node}
        last = next_node
    path.append(_)
    return res, list(map(int, path))

其中，dist是一个n*n的矩阵，表示每个城市之间的距离。函数返回的是最小的车费花销和路径。