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updates in closest pair of points algorithm (#979)

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* updated closest pair of points (n*(logn)^2) to (n*logn)
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Dharni0607 2019-07-09 20:50:43 +05:30 committed by Erfan Alimohammadi
parent 8b2d1b7f50
commit c85312da89
1 changed files with 28 additions and 21 deletions
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49
divide_and_conquer/closest_pair_of_points.py
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@ -1,27 +1,27 @@
""" """
The algorithm finds distance btw closest pair of points in the given n points. The algorithm finds distance between closest pair of points
in the given n points.
Approach used -> Divide and conquer Approach used -> Divide and conquer
The points are sorted based on Xco-ords The points are sorted based on Xco-ords and
& by applying divide and conquer approach, then based on Yco-ords separately.
And by applying divide and conquer approach,
minimum distance is obtained recursively. minimum distance is obtained recursively.
>> closest points lie on different sides of partition >> Closest points can lie on different sides of partition.
This case handled by forming a strip of points This case handled by forming a strip of points
whose Xco-ords distance is less than closest_pair_dis whose Xco-ords distance is less than closest_pair_dis
from mid-point's Xco-ords. from mid-point's Xco-ords. Points sorted based on Yco-ords
are used in this step to reduce sorting time.
Closest pair distance is found in the strip of points. (closest_in_strip) Closest pair distance is found in the strip of points. (closest_in_strip)
min(closest_pair_dis, closest_in_strip) would be the final answer. min(closest_pair_dis, closest_in_strip) would be the final answer.
Time complexity: O(n * (logn)^2) Time complexity: O(n * log n)
""" """
import math
def euclidean_distance_sqr(point1, point2): def euclidean_distance_sqr(point1, point2):
return pow(point1[0] - point2[0], 2) + pow(point1[1] - point2[1], 2) return (point1[0] - point2[0]) ** 2 + (point1[1] - point2[1]) ** 2
def column_based_sort(array, column = 0): def column_based_sort(array, column = 0):
@ -66,7 +66,7 @@ def dis_between_closest_in_strip(points, points_counts, min_dis = float("inf")):
return min_dis return min_dis
def closest_pair_of_points_sqr(points, points_counts): def closest_pair_of_points_sqr(points_sorted_on_x, points_sorted_on_y, points_counts):
""" divide and conquer approach """ divide and conquer approach
Parameters : Parameters :
@ -79,12 +79,16 @@ def closest_pair_of_points_sqr(points, points_counts):
# base case # base case
if points_counts <= 3: if points_counts <= 3:
return dis_between_closest_pair(points, points_counts) return dis_between_closest_pair(points_sorted_on_x, points_counts)
# recursion # recursion
mid = points_counts//2 mid = points_counts//2
closest_in_left = closest_pair_of_points(points[:mid], mid) closest_in_left = closest_pair_of_points_sqr(points_sorted_on_x,
closest_in_right = closest_pair_of_points(points[mid:], points_counts - mid) points_sorted_on_y[:mid],
mid)
closest_in_right = closest_pair_of_points_sqr(points_sorted_on_y,
points_sorted_on_y[mid:],
points_counts - mid)
closest_pair_dis = min(closest_in_left, closest_in_right) closest_pair_dis = min(closest_in_left, closest_in_right)
""" cross_strip contains the points, whose Xcoords are at a """ cross_strip contains the points, whose Xcoords are at a
@ -92,22 +96,25 @@ def closest_pair_of_points_sqr(points, points_counts):
""" """
cross_strip = [] cross_strip = []
for point in points: for point in points_sorted_on_x:
if abs(point[0] - points[mid][0]) < closest_pair_dis: if abs(point[0] - points_sorted_on_x[mid][0]) < closest_pair_dis:
cross_strip.append(point) cross_strip.append(point)
cross_strip = column_based_sort(cross_strip, 1)
closest_in_strip = dis_between_closest_in_strip(cross_strip, closest_in_strip = dis_between_closest_in_strip(cross_strip,
len(cross_strip), closest_pair_dis) len(cross_strip), closest_pair_dis)
return min(closest_pair_dis, closest_in_strip) return min(closest_pair_dis, closest_in_strip)
def closest_pair_of_points(points, points_counts): def closest_pair_of_points(points, points_counts):
return math.sqrt(closest_pair_of_points_sqr(points, points_counts)) points_sorted_on_x = column_based_sort(points, column = 0)
points_sorted_on_y = column_based_sort(points, column = 1)
return (closest_pair_of_points_sqr(points_sorted_on_x,
points_sorted_on_y,
points_counts)) ** 0.5
points = [(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (0, 2), (5, 6), (1, 2)] if __name__ == "__main__":
points = column_based_sort(points) points = [(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
print("Distance:", closest_pair_of_points(points, len(points))) print("Distance:", closest_pair_of_points(points, len(points)))