How far away is the closest alien civilisation in our galaxy?

galaxy.py

import math
import random


# Pick a random location that is uniformly distributed in a disk of radius r.
def random_point(r):
  r = random.uniform(0, 1)
  t = random.uniform(0, 2 * math.pi)
  x = math.sqrt(r) * math.cos(t) * r
  y = math.sqrt(r) * math.sin(t) * r
  return [x, y]


# Find the distance between two points.
def distance(a, b):
  dx = a[0] - b[0]
  dy = a[1] - b[1]
  return math.sqrt(dx * dx + dy * dy)


# Find the average shotest distance between n points in a disk of radius r.
# This function in O(n^2), but there are more efficient alternatives!
def average_distance(n, r):
  points = [random_point(r) for _ in range(n)]
  distances = [min([distance(p, q) for q in points if q != p]) for p in points]
  return reduce(lambda x, y: x + y, distances) / len(distances)


NUMBER_OF_CIVILISATIONS = 1000
RADIUS_OF_GALAXY = 70  # thousand light years

print(average_distance(NUMBER_OF_CIVILISATIONS, RADIUS_OF_GALAXY))