Finding Euclidean distance between two list

Question

list1=[(1116.7983351235232, 1311.3754027926993), (1116.7983351235232, 1218.42998120301), (1116.7983351235232, 1125.4845596133205), (1116.7983351235232, 1032.539138023631), (1116.7983351235232, 939.5937164339416)]

list2=[(1215.7983351235232, 1315.130773361976), (1215.7983351235232, 1223.1241944146077), (1215.7983351235232, 1131.1176154672394), (1215.7983351235232, 1039.111036519871), (1215.7983351235232, 947.1044575725027)]

For the above list, I want to find the Euclidean distance between a point in list1 and all the points in list2 . Here, I want to find the min distance from the point in list1 to all the points in list2. Could any one suggest what is the best way to work on it?

i tried out

for i in list1:
     for j in list2:
         list3=min(sqrt(i,j))  
            print(list3)

I am getting error as AttributeError: 'Tuple' object has no attribute '_eval_power'

Answer 1

I propose doing this step by step:

First, write a function that calculates the euclidean distance between two points. We can do this by using Pythagoras' theorem on the distance between their respective components:

from math import sqrt

def distance(x, y):
    a, b = y[0] - x[0], y[1] - x[1]
    return sqrt(a**2 + b**2)

Now you can loop over all combinations of points and return all distances. I'll use a generator to do that:

def all_distances(one, two):
    for point_a in one:
        for point_b in two:
            yield distance(point_a, point_b)

Finally, it all falls into place:

>>> min(all_distances(list1, list2))
99.07120069986327

So the minimum distance is (very close to) 99.