https://community.topcoder.com/stat?c=problem_statement&pm=3543&rd=6538 brute force

ATaleOfThreeCities.py

from math import sqrt, pow

class ATaleOfThreeCities:

    AB = 1
    BC = 2
    CA = 3

    def __init__(self, min1=999, min2=999):
        self.min1 = min1
        self.min2 = min2
        self.links = [0, 0]

    def set_min_dist(self, x1, y1, x2, y2, link):
        dist = sqrt( pow(x2 - x1, 2) + pow(y2 - y1, 2) )
        if dist < self.min1:
            if self.links[0] != link:
                self.min2 = self.min1
                self.links[1] = self.links[0]
            self.min1 = dist
            self.links[0] = link
        elif dist < self.min2 and link != self.links[0]:
            self.min2 = dist
            self.links[1] = link

    def connect(self, ax, ay, bx, by, cx, cy):
        self.__init__()

        La = len(ax)
        Lb = len(bx)
        Lc = len(cx)

        for i in range(La):
            Ax = ax[i]
            Ay = ay[i]
            for j in range(Lb):
                Bx = bx[j]
                By = by[j]
                for k in range(Lc):
                    Cx = cx[k]
                    Cy = cy[k]
                    self.set_min_dist(Ax, Ay, Cx, Cy, self.CA)
                    self.set_min_dist(Bx, By, Cx, Cy, self.BC)
                self.set_min_dist(Ax, Ay, Bx, By, self.AB)
        return self.min1 + self.min2

Q = ATaleOfThreeCities()
print(Q.connect([0,0,0],
       [0,1,2],
       [2,3],
       [1,1],
       [1,5],
       [3,28]))
print(Q.connect([-2,-1,0,1,2],
       [0,0,0,0,0],
       [-2,-1,0,1,2],
       [1,1,1,1,1],
       [-2,-1,0,1,2],
       [2,2,2,2,2]))
print(Q.connect([4,5,11,21,8,10,3,9,5,6],
       [12,8,9,12,2,3,5,7,10,13],
       [34,35,36,41,32,39,41,37,39,50],
       [51,33,41,45,48,22,33,51,41,40],
       [86,75,78,81,89,77,83,88,99,77],
       [10,20,30,40,50,60,70,80,90,100]))