pyUdemy-FurthestPoints

# A udemy Python course task
# Given a list of tuples, holding the x and y coordinates of a series of points,
# return the 2 tuples of the points which are furthest apart


def find_farthest_points(pointlist):

    # Initialise an empty list which will contain all our calculation results
    reslist = []

    # pointlist is a list of tuples containing x,y coords of a series of points
    # Here we will use nested loops, to pick up ALL combinations of points,
    # although this will produce some duplicates, and each point will get compared
    # with itself as well as with all other points. but this doesn't matter

    for pos1 in pointlist:
        for pos2 in pointlist:
            # Compute the square of the distance between 2 points

            dsq = (pos1[0] - pos2[0]) ** 2 + (pos1[1] - pos2[1]) ** 2

            # The actual distance is the square root of dsq, but as we are only asked
            # to find which points are farthest apart, and not the actual distance,
            # there is no point in actually computing the square root

            # Now we add the distance-squared and the 2 points, to a results list
            # With dsq as the first item in each list entry, as that's what we will sort on

            reslist.append((dsq, pos1, pos2))

    # Now we have built a list of distance-squared and points.
    # Sort it in reverse sequence, then return the two points from the first entry
    # (which corresponds to the furthest distance)

    sorted_list = sorted(reslist, reverse=True)

    return sorted_list[0][1], sorted_list[0][2]


pl = [(1, 2), (2, 4), (3, 7), (4, 5)]

point1, point2 = find_farthest_points(pl)

print("The furthest apart points are", point1, "and", point2)


# Output:
# The furthest apart points are (3, 7) and (1, 2)