Sort a list of candidates according to a metric - Python?

Question

I have a list of 2-D points

candidates = [(x1, y1), (x2, y2), (x3, y3), ...]

and a reference point ref = (x0, y0).

I now wish to sort the list candidates according to their euclidean distances from the reference point ref, in ascending order.

What is the most Pythonic way of doing so?

Answer 1

Euclidean distance between two points (x1, y1) and (x2, y2) is given by:

sqrt((x1 - y1)^2 + (x2 - y2)^2))

To sort the list, you can use the formula, and also you can skip the sqrt part, as you are just doing comparison, and not calculating the actual distance. i.e:

if x > y then sqrt(x) > sqrt(y)

So, following would work:

ref = (x0, y0)
candidates = [(x1, y1), (x2, y2), (x3, y3), ...]

candidates.sort(key=lambda x: (x[0] - ref[0]) ** 2 + (x[1] - ref[1]) ** 2)

Answer 2

Write a function to calculate euclidean distance and use that function with the key parameter of the list.sort function.

ref = (x0, y0)
def euclidean(coords):
    xx, yy = ref
    x, y = coords
    return ((x-xx)**2 + (y-yy)**2)**0.5

candidates = [(x1, y1), (x2, y2), (x3, y3), ...]
candidates.sort(key=euclidean)