Optimum location of point to minimize total distance

import math

class Optimum_distance:

class Point:

def __init__(self, x, y):

self.x = x

self.y = y

class Line:

def __init__(self, a, b, c):

self.a = a

self.b = b

self.c = c

def dist(self, x, y, p):

return math.sqrt((x - p.x) ** 2 +

(y - p.y) ** 2)

def compute(self, p, n, l, x):

res = 0

y = -1 * (l.a*x + l.c) / l.b

for i in range(n):

res += self.dist(x, y, p[i])

return res

def find_Optimum_cost_untill(self, p, n, l):

low = -1e6

high = 1e6

eps = 1e-6 + 1

while((high - low) > eps):

mid1 = low + (high - low) / 3

mid2 = high - (high - low) / 3

dist1 = self.compute(p, n, l, mid1)

dist2 = self.compute(p, n, l, mid2)

if (dist1 < dist2):

high = mid2

else:

low = mid1

return self.compute(p, n, l, (low + high) / 2)

def find_Optimum_cost(self, p, l):

n = len(p)

p_arr = [None] * n

for i in range(n):

p_obj = self.Point(p[i][0], p[i][1])

p_arr[i] = p_obj

return self.find_Optimum_cost_untill(p_arr, n, l)

if __name__ == "__main__":

obj = Optimum_distance()

l = obj.Line(1, -1, -3)

p = [ [ -3, -2 ], [ -1, 0 ],

[ -1, 2 ], [ 1, 2 ],

[ 3, 4 ] ]

print(obj.find_Optimum_cost(p, l))