Find minimum radius such that atleast k point lie inside the circle - GeeksforGeeks

01 Sep, 2021
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. 
Examples:  
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:  
C++
Java
Python3
C#
PHP
Javascript
// C++ program to find minimum radius// such that atleast k point lie inside// the circle#include<bits/stdc++.h>using namespace std; // Return minimum distance required so that// aleast k point lie inside the circle.int minRadius(int k, int x[], int y[], int n){   int dis[n];        // Finding distance between of each   // point from origin   for (int i = 0; i < n; i++)       dis[i] = x[i] * x[i] + y[i] * y[i];         // Sorting the distance    sort(dis, dis + n);         return dis[k - 1];} // Driven Programint main(){  int k = 3;  int x[] = { 1, -1, 1 };  int y[] = { 1, -1, -1 };  int n = sizeof(x)/sizeof(x[0]);       cout << minRadius(k, x, y, n) << endl;       return 0;}
// Java program to find minimum radius// such that atleast k point lie inside// the circleimport java.util.Arrays; class GFG{     // Return minimum distance required so that    // aleast k point lie inside the circle.    static int minRadius(int k, int[] x, int[] y,                                          int n)    {        int[] dis=new int[n];             // Finding distance between of each        // point from origin        for (int i = 0; i < n; i++)            dis[i] = x[i] * x[i] + y[i] * y[i];             // Sorting the distance        Arrays.sort(dis);             return dis[k - 1];    }     // Driven Program    public static void main (String[] args) {             int k = 3;    int[] x = { 1, -1, 1 };    int[] y = { 1, -1, -1 };    int n = x.length;         System.out.println(minRadius(k, x, y, n));     }} /* This code is contributed by Mr. Somesh Awasthi */
# Python3 program to find minimum radius# such that atleast k point lie inside# the circle  # Return minimum distance required so# that aleast k point lie inside the# circle.def minRadius(k, x, y, n):    dis = [0] * n     # Finding distance between of each    # point from origin     for i in range(0, n):        dis[i] = x[i] * x[i] + y[i] * y[i]     # Sorting the distance    dis.sort()     return dis[k - 1]         # Driver Programk = 3x = [1, -1, 1]y = [1, -1, -1]n = len(x) print(minRadius(k, x, y, n)) # This code is contributed by# Prasad Kshirsagar
// C# program to find minimum radius// such that atleast k point lie inside// the circleusing System; class GFG {     // Return minimum distance required    // so that aleast k point lie inside    // the circle.    static int minRadius(int k, int []x,                          int[] y, int n)    {        int[] dis = new int[n];             // Finding distance between of        // each point from origin        for (int i = 0; i < n; i++)            dis[i] = x[i] * x[i] +                       y[i] * y[i];             // Sorting the distance        Array.Sort(dis);             return dis[k - 1];    }     // Driven Program    public static void Main ()    {        int k = 3;        int[] x = { 1, -1, 1 };        int[] y = { 1, -1, -1 };        int n = x.Length;                 Console.WriteLine(              minRadius(k, x, y, n));    }} // This code is contributed by vt_m.
<?php// PHP program to find minimum radius// such that atleast k point lie inside// the circle // Return minimum distance required// so that aleast k point lie// inside the circle.function minRadius($k, $x, $y, $n){    $dis =array();             // Finding distance between    // of each point from origin    for ($i = 0; $i < $n; $i++)        $dis[$i] = $x[$i] * $x[$i] +                   $y[$i] * $y[$i];                 // Sorting the distance        sort($dis);                 return $dis[$k - 1];} // Driver Code$k = 3;$x = array(1, -1, 1);$y = array(1, -1, -1);$n = count($x);     echo minRadius($k, $x, $y, $n) ;     // This code is contributed by anuj_67.?>
<script>// Javascript program to find minimum radius// such that atleast k point lie inside// the circle     // Return minimum distance required so that    // aleast k point lie inside the circle.    function minRadius(k, x, y, n) {             let dis = Array.from({length: n}, (_, i) => 0);               // Finding distance between of each        // point from origin        for (let i = 0; i < n; i++)            dis[i] = x[i] * x[i] + y[i] * y[i];               // Sorting the distance        dis.sort();               return dis[k - 1];    }   // driver function     let k = 3;    let x = [ 1, -1, 1 ];    let y = [ 1, -1, -1 ];    let n = x.length;           document.write(minRadius(k, x, y, n));   // This code is contributed by code_hunt.</script>   
Output: 
2
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