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| 1 | +import heapq |
| 2 | + |
| 3 | +class Point: |
| 4 | + # __init__ will be used to make a Point type object |
| 5 | + def __init__(self, x, y): |
| 6 | + self.x = x |
| 7 | + self.y = y |
| 8 | + |
| 9 | + # __lt__ is used for max-heap |
| 10 | + def __lt__(self, other): |
| 11 | + return self.distance_from_origin() > other.distance_from_origin() |
| 12 | + |
| 13 | + # __str__ is used to print the x and y values |
| 14 | + def __str__(self): |
| 15 | + return '[{self.x}, {self.y}]'.format(self=self) |
| 16 | + |
| 17 | + # distance_from_origin calculates the distance using x, y coordinates |
| 18 | + def distance_from_origin(self): |
| 19 | + # ignoring sqrt to calculate the distance |
| 20 | + return (self.x * self.x) + (self.y * self.y) |
| 21 | + |
| 22 | + __repr__ = __str__ |
| 23 | + |
| 24 | + |
| 25 | + |
| 26 | +############################################################################ |
| 27 | + |
| 28 | + |
| 29 | + |
| 30 | +def k_closest(points, k): |
| 31 | + |
| 32 | + points_max_heap = [] |
| 33 | + |
| 34 | + # Put first k points in max_heap |
| 35 | + for i in range(k): |
| 36 | + heapq.heappush(points_max_heap, points[i]) |
| 37 | + |
| 38 | + # Iterate through remaining points |
| 39 | + for i in range(k, len(points)): |
| 40 | + |
| 41 | + # If closer to origin, remove top point from heap and add point |
| 42 | + if points[i].distance_from_origin() < points_max_heap[0].distance_from_origin(): |
| 43 | + heapq.heappop(points_max_heap) |
| 44 | + heapq.heappush(points_max_heap, points[i]) |
| 45 | + |
| 46 | + return list(points_max_heap) |
| 47 | + |
| 48 | + |
| 49 | +# Helper Function |
| 50 | +def lst_to_str(lst): |
| 51 | + out = "[" |
| 52 | + for i in range(len(lst)-1): |
| 53 | + out += str(lst[i]) + ", " |
| 54 | + out += str(lst[len(lst)-1]) + "]" |
| 55 | + return out |
| 56 | + |
| 57 | + |
| 58 | + |
| 59 | +# Time Complexity = O(nlogk) |
| 60 | +# Space Complexity = O(k) |
| 61 | + |
| 62 | + |
| 63 | + |
| 64 | +############################################################################ |
| 65 | + |
| 66 | + |
| 67 | + |
| 68 | +# Driver code |
| 69 | +def main(): |
| 70 | + points_one = [Point(1, 3), Point(3, 4), Point(2, -1)] |
| 71 | + points_two = [Point(1, 3), Point(2, 4), Point(2, -1), Point(-2, 2), |
| 72 | + Point(5, 3), Point(3, -2)] |
| 73 | + points_three = [Point(1, 3), Point(5, 3), Point(3, -2), Point(-2, 2)] |
| 74 | + points_four = [Point(2, -1), Point(-2, 2), Point(1, 3), Point(2, 4)] |
| 75 | + points_five = [Point(1, 3), Point(2, 4), Point(2, -1), Point(-2, 2), |
| 76 | + Point(5, 3), Point(3, -2), Point(5, 3), Point(3, -2)] |
| 77 | + |
| 78 | + k_list = [2, 3, 1, 4, 5] |
| 79 | + points = [points_one, points_two, points_three, points_four, points_five] |
| 80 | + |
| 81 | + for i in range(len(k_list)): |
| 82 | + result = k_closest(points[i], k_list[i]) |
| 83 | + print(i + 1, ".\tSet of points: ", sep="", end='') |
| 84 | + print(lst_to_str(points[i])) |
| 85 | + print("\tk:", k_list[i]) |
| 86 | + print("\tHere are the k =", k_list[i], "points closest to the", \ |
| 87 | + "origin (0, 0): ", end='') |
| 88 | + print(lst_to_str(result)) |
| 89 | + print("-"*100) |
| 90 | + |
| 91 | +if __name__ == '__main__': |
| 92 | + main() |
| 93 | + |
| 94 | + |
| 95 | + |
| 96 | + |
| 97 | + |
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