def pre(points):
'''Pre-process for closest pair problem, 'points' being a list of 2-tuples.
return two ordered list based on x and y coordinates using merge sort.'''
px = merge_sort_2d(points, 0)
py = merge_sort_2d(points, 1)
return px, py
def closest_pair(Px, Py):
'''Divide the points into 2 halves, left and right, for each sorted copies of
the original data, find the closest pair in each half, compare with the possible
closest pairs, of which each point in different halves, return the minimum.'''
mid = int(len(Px)/2)
left_x = Px[:mid]
right_x = Px[mid:]
left_y = Py[:mid]
right_y = Py[mid:]
pair_dist = []
#base case
if len(Px) == 1:
return None
elif len(Px) == 2:
return Px
else:
left = closest_pair(left_x, left_y) #left is a list of two points
right = closest_pair(right_x, right_y)
#if None is in (left, right), it has to be left
if left == None:
delta = dist(right)
else:
delta = min(dist(left), dist(right))
split = closest_split_pair(Px, Py, delta)
pair_dist = [(x, dist(x)) for x in (left, right, split) if x]
return merge_sort_2d(pair_dist, 1)[0][0]
