Find K Closest Points to the Origin

Given a list of points on the 2-D plane and an integer K. The task is to find K closest points to the origin and print them.

Note: The distance between two points on a plane is the Euclidean distance.

Examples:



Input : point = [[3, 3], [5, -1], [-2, 4]], K = 2
Output : [[3, 3], [-2, 4]]
Square of Distance of origin from this point is 
(3, 3) = 18
(5, -1) = 26
(-2, 4) = 20
So rhe closest two points are [3, 3], [-2, 4].

Input : point = [[1, 3], [-2, 2]], K  = 1
Output : [[-2, 2]]
Square of Distance of origin from this point is
(1, 3) = 10
(-2, 2) = 8 
So the closest point to origin is (-2, 2)

Approach : The idea is to calculate the euclidean distance from the origin for every given point and sort the array according to the euclidean distance found. Print the first k closest points from the list.

Algorithm :
Consider two points with coordinates as (x1, y1) and (x2, y2) respectively. The euclidean distance between these two points will be:

√{(x2-x1)2 + (y2-y1)2}
  1. Sort the points by distance using Euclidean distance formula.
  2. Select first K points form the list
  3. Print the points obtained in any order.

Below is the implementation of the above approach:

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# Python program for implementation of 
# above approach
  
# Function to return required answer
def pClosest(points, K):
  
    points.sort(key = lambda K: K[0]**2 + K[1]**2)
  
    return points[:K]
  
# Driver program
points = [[3, 3], [5, -1], [-2, 4]]
  
K = 2
  
print(pClosest(points, K))

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Output:


[[3, 3], [-2, 4]]





Complexity Analysis:


    

  • Time Complexity: O(n log n).
    
Time complexity to find the distance from origin for every point is O(n) and to sort the array is O(n log n)
    • 

  • Space Complexity: O(1).
    
As no extra space is required.
    • 





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