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035457f569
* created divide_and_conquer folder and added max_sub_array_sum.py under it (issue #817) * additional file in divide_and_conqure (closest pair of points)
114 lines
3.4 KiB
Python
114 lines
3.4 KiB
Python
"""
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The algorithm finds distance btw closest pair of points 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
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& by applying divide and conquer approach,
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minimum distance is obtained recursively.
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>> closest points 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.
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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 * (logn)^2)
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"""
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import math
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def euclidean_distance_sqr(point1, point2):
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return pow(point1[0] - point2[0], 2) + pow(point1[1] - point2[1], 2)
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def column_based_sort(array, column = 0):
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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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""" 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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"""
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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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""" 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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"""
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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, 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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"""
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# base case
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if points_counts <= 3:
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return dis_between_closest_pair(points, 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(points[:mid], mid)
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closest_in_right = closest_pair_of_points(points[mid:], points_counts - mid)
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closest_pair_dis = min(closest_in_left, closest_in_right)
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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:
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if abs(point[0] - points[mid][0]) < closest_pair_dis:
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cross_strip.append(point)
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cross_strip = column_based_sort(cross_strip, 1)
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closest_in_strip = dis_between_closest_in_strip(cross_strip,
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len(cross_strip), closest_pair_dis)
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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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return math.sqrt(closest_pair_of_points_sqr(points, points_counts))
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points = [(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (0, 2), (5, 6), (1, 2)]
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points = column_based_sort(points)
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print("Distance:", closest_pair_of_points(points, len(points)))
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