// Q3

public static double[] findShortestDistance

(double[] x, double[] y)

 

One of the most basic classification algorithms in data science is the K-Nearest-Neighbor (KNN) algorithm, which forms clusters and categorizes data into K groups. For each cluster, you identify the position by averaging all coordinates within the cluster. This coordinate unique to each cluster is known as the centroid C. Then, for a given point P, you calculate the distance from the current point to each centroid C_i  , where i represents the ith cluster. The given point P is categorized to the cluster having its centroid C_i closest to P. For this problem, instead of finding the closest distance from Point P to each centroid, you'll find the closest distance from Point P to the remaining data points. In other words, you'll iterate through each point in the data and find the distance between that point and its nearest neighboring point. 

 

You are given two arrays, an array of x-coordinates and an array of y-coordinates, where (x[i], y[i]) forms a point in the Cartesian coordinate. You then return a double array, where the value at index i yields the distance between (x[i], y[i]) and its nearest neighbor. Below is an example of the algorithm:

 

Input : x=[0, 3, 0, 4], y=[0, 0, 4, 4]

 

Output: [3.0, 3.0, 4.0, 4.0]

A brief explanation of the output:

 

Index i	Point P1 at index i (x[i], y[i])	Nearest Point P2 from P1	Distance between P1 and P2
0	(0,0)	(3,0)	3.0
1	(3,0)	(0,0)	3.0
2	(0,4)	(4,4)	4.0
3	(4,4)	(0,4)	4.0

 

Note: You are guaranteed that the length of array x will be equal to the length of array y, and the length of the array will be greater than 1, implying that there will be at least two points.