Distance formula between two points in a list

Question

I need to take a list I have created and find the closest two points and print them out. How can I go about comparing each point in the list?

There isn't any need to plot or anything, just compare the points and find the closest two in the list.

import math # 'math' needed for 'sqrt'

# Distance function
def distance(xi,xii,yi,yii):
    sq1 = (xi-xii)*(xi-xii)
    sq2 = (yi-yii)*(yi-yii)
    return math.sqrt(sq1 + sq2)

# Run through input and reorder in [(x, y), (x,y) ...] format
oInput = ["9.5 7.5", "10.2 19.1", "9.7 10.2"] # Original input list (entered by spacing the two points).
mInput = [] # Manipulated list
fList = [] # Final list
for o in oInput:
    mInput = o.split()
    x,y = float(mInput[0]), float(mInput[1])
    fList += [(x, y)] # outputs [(9.5, 7.5), (10.2, 19.1), (9.7, 10.2)]

Answer 1

It is more convenient to rewrite your distance() function to take two (x, y) tuples as parameters:

def distance(p0, p1):
    return math.sqrt((p0[0] - p1[0])**2 + (p0[1] - p1[1])**2)

Now you want to iterate over all pairs of points from your list fList. The function iterools.combinations() is handy for this purpose:

min_distance = distance(fList[0], fList[1])
for p0, p1 in itertools.combinations(fList, 2):
    min_distance = min(min_distance, distance(p0, p1))

An alternative is to define distance() to accept the pair of points in a single parameter

def distance(points):
    p0, p1 = points
    return math.sqrt((p0[0] - p1[0])**2 + (p0[1] - p1[1])**2)

and use the key parameter to the built-in min() function:

min_pair = min(itertools.combinations(fList, 2), key=distance)
min_distance = distance(min_pair)

Answer 2

I realize that there are library constraints on this question, but for completeness if you have N points in an Nx2 numpy ndarray (2D system):

from scipy.spatial.distance import pdist
x = numpy.array([[9.5,7.5],[10.2,19.1],[9.7,10.2]])
mindist = numpy.min(pdist(x))

I always try to encourage people to use numpy/scipy if they are dealing with data that is best stored in a numerical array and it's good to know that the tools are out there for future reference.