Max Min


Problem Statement :


You will be given a list of integers,  arr , and a single integer k. You must create an array of length k from elements of arr such that its unfairness is minimized. Call that array arr' . Unfairness of an array is calculated as

                max( arr' ) -  min( arr ' )

Where:
- max denotes the largest integer in arr' .
- min denotes the smallest integer in arr'.


Note: Integers in  may not be unique.

Function Description

Complete the maxMin function in the editor below.
maxMin has the following parameter(s):

int k: the number of elements to select
int arr[n]:: an array of integers
Returns

int: the minimum possible unfairness


Input Format

The first line contains an integer n, the number of elements in array arr.
The second line contains an integer k .
Each of the next n lines contains an integer arr[ i ] where 0  <=  i  < n.

Constraints

2  <=  n  <=  10^5
2  <=  k  <=  n
0   < =   arr[ i ]   <=  10^9


Sample Input 0

7
3
10
100
300
200
1000
20
30
Sample Output 0

20


Solution :



title-img


                            Solution in C :

In  C :





#include <stdio.h>
#include<stdlib.h>
int compare(int *a,int *b)
{
	return *(int*)a-*(int*)b;
}
int main(void)
{
	int n,k,i,j,min,a[100010];
	scanf("%d",&n);
	scanf("%d",&k);
	for(i=0;i<n;i++)
		scanf("%d",&a[i]);
	qsort(a,n,sizeof(int),compare);

	min=a[k-1]-a[0];
	for(i=0;i<=n-k;i++)	
	{
		if( (j=(a[i+k-1]-a[i]) ) <min)
			min=j;
	}
	printf("%d",min);
	return 0;
}
                        

                        Solution in C++ :

In  C ++ :





#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int arr[100010];

int main() {
   
    int n,k;
    cin>>n>>k;
    for(int i=0;i<n;i++)cin>>arr[i];
    sort(arr,arr+n);
    int ans=1e9;
    for(int i=k-1;i<n;i++){
        ans=min(arr[i]-arr[i-k+1],ans);
    }
    cout<<ans<<endl;
    return 0;
}
                    

                        Solution in Java :

In  Java :




import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt(), k = in.nextInt();
        int[] x = new int[n];
        for(int i = 0; i < n; i++) x[i] = in.nextInt();
        Arrays.sort(x);
        System.out.println(f(n, k, x));
    }
    
    private static int f(int n, int k, int[] x){
        int min = 100000000;
        for(int i = 0; i + k-1 < x.length; i++){
            if(x[i+k-1] - x[i] < min) min = x[i+k-1]-x[i];
        }
        return min;
    }
}
                    

                        Solution in Python : 
                            
In  Python3 :




def unfairness(candies, i, j):
    res = candies[j-1] - candies[i]
    return res

n = int(input())
kids = int(input())
candies = []

for i in range(n):
    candies.append(int(input()))

candies = sorted(candies)

min_uf = unfairness(candies, 0, kids)

for i in range(1, len(candies)-kids):
    this_uf = unfairness(candies, i, i+kids)
    min_uf = min(min_uf, this_uf) 
    
    
print(min_uf)
                    

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