user: Write a Python program that takes a sequence of points and returns the shortest path that goes through them all.

assistant: Here is an example of a Python program that takes a sequence of points and returns the shortest path that goes through them all using the "Traveling Salesman Problem" algorithm:

```
from itertools import permutations

def tsp(points):
    # calculate the distance between all points
    def distance(p1, p2):
        x1, y1 = p1
        x2, y2 = p2
        return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5

    # get all possible permutations of points
    all_paths = permutations(points)

    # calculate the distance of each path and keep track of the shortest one
    shortest_path = float("inf")
    shortest_path_points = []
    for path in all_paths:
        total_distance = 0
        for i in range(len(path) - 1):
            total_distance += distance(path[i], path[i + 1])
        if total_distance < shortest_path:
            shortest_path = total_distance
            shortest_path_points = path

    return shortest_path, shortest_path_points

points = [(0, 0), (1, 2), (3, 4), (5, 6)]
shortest_path, path = tsp(points)
print("Shortest path is: " + str(path))
print("Distance: " + str(shortest_path))
```

This program uses the "itertools" library to generate all possible permutations of the points, and uses a custom distance function to calculate the distance between each pair of points. It then iterates through each permutation, calculates the total distance of the path, and keeps track of the shortest one.

It's worth noting that this approach can be computationally expensive for large number of points, more efficient algorithm such as Christofides algorithm and Lin-Kernighan algorithm can also be used to solve the TSP problem.

user: Do you know any libraries for those more efficient algorithms?

assistant: The python package `networkx` contains an implementation of the Christofides algorithm. You can install `networkx` with the following command:
```console
pip install networkx
```

Here is how you could rewrite the above code using the Christofides algorithm:

```py
from networkx import Graph
from networkx.algorithms.approximation.traveling_salesman import christofides

def tsp(points):
    # calculate the distance between all points
    def distance(p1, p2):
        x1, y1 = p1
        x2, y2 = p2
        return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5

    # create the distance graph
    distance_graph = Graph()
    for i in range(len(points)):
        for j in range(len(points)):
            distance_graph.add_edge(i, j, weight=distance(points[i], points[j]))

    # find TSP path
    path = christofides(distance_graph)

    # calculate length of path
    length = 0
    for i in range(len(points)):
        length += distance_graph.get_edge_data(path[i], path[i+1])["weight"]
    return length, path

points = [(0, 0), (1, 2), (3, 4), (5, 6)]
length, path = tsp(points)
print("Shortest path is: " + str(path))
print("Distance: " + str(length))
```

Be careful as this algorithm is not guaranteed to give the optimal solution. The Christofides algorithm sacrifices accuracy for speed, running in $O(n^3)$ time (rather than $O(n!)$), but only guaranteeing a 3/2 approximation.