Given a positive integer K, a circle center at (0, 0) and coordinates of some points. The task is to find minimum radius of the circle so that at-least k points lie inside the circle. Output the square of the minimum radius.
Input : (1, 1), (-1, -1), (1, -1), k = 3 Output : 2 We need a circle of radius at least 2 to include 3 points. Input : (1, 1), (0, 1), (1, -1), k = 2 Output : 1 We need a circle of radius at least 1 to include 2 points. The circle around (0, 0) of radius 1 would include (1, 1) and (0, 1).
The idea is to find square of Euclidean Distance of each point from origin (0, 0). Now, sort these distance in increasing order. Now the kth element of distance is the required minimum radius.
Below is the implementation of this approach:
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