mirror of
https://github.com/TheAlgorithms/Python.git
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4d0a8f2355
* optimized recursive_bubble_sort
* Fixed doctest error due whitespace
* reduce loop times for optimization
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
144 lines
4.2 KiB
Python
144 lines
4.2 KiB
Python
"""
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The algorithm finds distance between closest pair of points
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in the given n points.
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Approach used -> Divide and conquer
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The points are sorted based on Xco-ords and
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then based on Yco-ords separately.
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And by applying divide and conquer approach,
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minimum distance is obtained recursively.
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>> Closest points can lie on different sides of partition.
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This case handled by forming a strip of points
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whose Xco-ords distance is less than closest_pair_dis
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from mid-point's Xco-ords. Points sorted based on Yco-ords
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are used in this step to reduce sorting time.
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Closest pair distance is found in the strip of points. (closest_in_strip)
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min(closest_pair_dis, closest_in_strip) would be the final answer.
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Time complexity: O(n * log n)
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"""
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def euclidean_distance_sqr(point1, point2):
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"""
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>>> euclidean_distance_sqr([1,2],[2,4])
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5
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"""
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return (point1[0] - point2[0]) ** 2 + (point1[1] - point2[1]) ** 2
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def column_based_sort(array, column=0):
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"""
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>>> column_based_sort([(5, 1), (4, 2), (3, 0)], 1)
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[(3, 0), (5, 1), (4, 2)]
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"""
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return sorted(array, key=lambda x: x[column])
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def dis_between_closest_pair(points, points_counts, min_dis=float("inf")):
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"""
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brute force approach to find distance between closest pair points
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Parameters :
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points, points_count, min_dis (list(tuple(int, int)), int, int)
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Returns :
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min_dis (float): distance between closest pair of points
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>>> dis_between_closest_pair([[1,2],[2,4],[5,7],[8,9],[11,0]],5)
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5
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"""
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for i in range(points_counts - 1):
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for j in range(i + 1, points_counts):
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current_dis = euclidean_distance_sqr(points[i], points[j])
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if current_dis < min_dis:
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min_dis = current_dis
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return min_dis
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def dis_between_closest_in_strip(points, points_counts, min_dis=float("inf")):
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"""
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closest pair of points in strip
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Parameters :
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points, points_count, min_dis (list(tuple(int, int)), int, int)
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Returns :
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min_dis (float): distance btw closest pair of points in the strip (< min_dis)
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>>> dis_between_closest_in_strip([[1,2],[2,4],[5,7],[8,9],[11,0]],5)
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85
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"""
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for i in range(min(6, points_counts - 1), points_counts):
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for j in range(max(0, i - 6), i):
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current_dis = euclidean_distance_sqr(points[i], points[j])
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if current_dis < min_dis:
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min_dis = current_dis
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return min_dis
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def closest_pair_of_points_sqr(points_sorted_on_x, points_sorted_on_y, points_counts):
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"""divide and conquer approach
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Parameters :
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points, points_count (list(tuple(int, int)), int)
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Returns :
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(float): distance btw closest pair of points
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>>> closest_pair_of_points_sqr([(1, 2), (3, 4)], [(5, 6), (7, 8)], 2)
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8
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"""
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# base case
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if points_counts <= 3:
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return dis_between_closest_pair(points_sorted_on_x, points_counts)
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# recursion
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mid = points_counts // 2
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closest_in_left = closest_pair_of_points_sqr(
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points_sorted_on_x, points_sorted_on_y[:mid], mid
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)
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closest_in_right = closest_pair_of_points_sqr(
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points_sorted_on_y, points_sorted_on_y[mid:], points_counts - mid
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)
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closest_pair_dis = min(closest_in_left, closest_in_right)
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"""
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cross_strip contains the points, whose Xcoords are at a
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distance(< closest_pair_dis) from mid's Xcoord
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"""
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cross_strip = []
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for point in points_sorted_on_x:
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if abs(point[0] - points_sorted_on_x[mid][0]) < closest_pair_dis:
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cross_strip.append(point)
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closest_in_strip = dis_between_closest_in_strip(
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cross_strip, len(cross_strip), closest_pair_dis
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)
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return min(closest_pair_dis, closest_in_strip)
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def closest_pair_of_points(points, points_counts):
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"""
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>>> closest_pair_of_points([(2, 3), (12, 30)], len([(2, 3), (12, 30)]))
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28.792360097775937
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"""
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points_sorted_on_x = column_based_sort(points, column=0)
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points_sorted_on_y = column_based_sort(points, column=1)
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return (
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closest_pair_of_points_sqr(
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points_sorted_on_x, points_sorted_on_y, points_counts
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)
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) ** 0.5
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if __name__ == "__main__":
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points = [(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
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print("Distance:", closest_pair_of_points(points, len(points)))
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