50. Magnetic Force Between Two Balls

Topic :

binary search

Difficulty :

medium

Problem Link :

problem statement

In the universe Earth C-137, Rick discovered a special form of magnetic force between two balls if they are put in his newly invented basket. Rick has n empty baskets, the ith basket is at position[i], Morty has m balls and needs to distribute the balls into the baskets such that the minimum magnetic force between any two balls is maximum.

Rick stated that magnetic force between two different balls at positions x and y is |x - y|.

Given the integer array position and the integer m. Return the required force.

Example 1:

Input: position = [1,2,3,4,7], m = 3
Output: 3
Explanation: Distributing the 3 balls into baskets 1, 4 and 7 will make the 
magnetic force between ball pairs [3, 3, 6]. 
The minimum magnetic force is 3. 
We cannot achieve a larger minimum magnetic force than 3.

Example 2:

Input: position = [5,4,3,2,1,1000000000], m = 2
Output: 999999999
Explanation: We can use baskets 1 and 1000000000.

Constraints:

n == position.length
2 <= n <= 105
1 <= position[i] <= 109
All integers in position are distinct.
2 <= m <= position.length

solution

import java.io.*;
import java.util.*; 
class MagneticForce_BetweenTwoBalls
{
  public static void main (String args[]){
    int position[] = {1,2,3,4,7}; int m = 3;
    System.out.println(maxDistance( position,m));
   }
  static boolean isPossible(int []position,int m, int curr_magneticForce)
    {
        int countBalls=1;
        int indexOfLastBall=position[0];
        
        for(int i=1;i<position.length;i++)
        {
            if(position[i]-indexOfLastBall>=curr_magneticForce)
            {
                countBalls++;
                indexOfLastBall=position[i];
            }
        }
        
        if(countBalls>=m)
            return true;
        else
            return false;
    }
    
  static int maxDistance(int[] position, int m) {
     Arrays.sort(position);
        int low=1 ;// minimum magnetic force b/w two balls
        int high=position[position.length-1]-position[0]; // maximum magnetic force b/w 2 balls
        
        while(low<=high)
        {
            int mid=low+(high-low)/2;
            int curr_magneticForce=mid;
            
            if(isPossible(position,m,curr_magneticForce))
            {
                low=mid+1;
            }
            else{
               high=mid-1;             
            }
        }
        
        return high;
    }
}