Choose k array elements such that difference of maximum and minimum is minimized

Given an array of n integers and a positive number k. We are allowed to take any k integers from the given array. The task is to find the minimum possible value of the difference between maximum and minimum of K numbers.

Examples:

Input : arr[] = {10, 100, 300, 200, 1000, 20, 30}
        k = 3
Output : 20
20 is the minimum possible difference between any
maximum and minimum of any k numbers.
Given k = 3, we get the result 20 by selecting 
integers {10, 20, 30}.
max(10, 20, 30) - max(10, 20, 30) = 30 - 10 = 20.

Input : arr[] = {1, 2, 3, 4, 10, 20, 30, 40, 
                                   100, 200}.
        k = 4      
Output : 3


The idea is to sort the array and choose k continuous integers. Why continuous? let the chosen k integers be arr[0], arr[1],,..arr[r], arr[r+x]…, arr[k-1], all in increasing order but not continuous in the sorted array. This means there exists an integer p which lies between arr[r] and arr[r+x],. So if p is included and arr[0] is removed, then the new difference will be arr[r] – arr[1] whereas old difference was arr[r] – arr[0]. And we know arr[0] <= arr[1] <= ..<= arr[k-1] so minimum difference reduces or remain same. If we perform same procedure for other p like number, we get the minimum difference.

Algorithm to solve the problem:

  1. Sort the Array.
  2. Calculate the maximum(k numbers) – minimum(k numbers) for each group of k consecutive integers.
  3. Return minimum of all values obtained in step 2.

Below is the implementation of above idea :

C++

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// C++ program to find minimum difference of maximum
// and minimum of K number.
#include<bits/stdc++.h>
using namespace std;
  
// Return minimum difference of maximum and minimum
// of k elements of arr[0..n-1].
int minDiff(int arr[], int n, int k)
{
    int result = INT_MAX;
  
    // Sorting the array.
    sort(arr, arr + n);
  
    // Find minimum value among all K size subarray.
    for (int i=0; i<=n-k; i++)
        result = min(result, arr[i+k-1] - arr[i]);
  
    return result;
}
  
// Driven Program
int main()
{
    int arr[] = {10, 100, 300, 200, 1000, 20, 30};
    int n = sizeof(arr)/sizeof(arr[0]);
    int k = 3;
  
    cout << minDiff(arr, n, k) << endl;
    return 0;
}

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Java

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// Java program to find minimum difference 
// of maximum and minimum of K number.
import java.util.*;
  
class GFG {
      
// Return minimum difference of 
// maximum and minimum of k 
// elements of arr[0..n-1].
static int minDiff(int arr[], int n, int k) {
    int result = Integer.MAX_VALUE;
  
    // Sorting the array.
    Arrays.sort(arr);
  
    // Find minimum value among 
    // all K size subarray.
    for (int i = 0; i <= n - k; i++)
    result = Math.min(result, arr[i + k - 1] - arr[i]);
  
    return result;
}
  
// Driver code
public static void main(String[] args) {
    int arr[] = {10, 100, 300, 200, 1000, 20, 30};
    int n = arr.length;
    int k = 3;
  
    System.out.println(minDiff(arr, n, k));
}
}
  
// This code is contributed by Anant Agarwal.

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Python3

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# Python program to find minimum
# difference of maximum
# and minimum of K number.
  
# Return minimum difference
# of maximum and minimum
# of k elements of arr[0..n-1].
def minDiff(arr,n,k):
    result = +2147483647
   
    # Sorting the array.
    arr.sort()
   
    # Find minimum value among
    # all K size subarray.
    for i in range(n-k+1):
        result = int(min(result, arr[i+k-1] - arr[i]))
   
    return result
  
# Driver code
  
arr= [10, 100, 300, 200, 1000, 20, 30]
n =len(arr)
k = 3
   
print(minDiff(arr, n, k))
  
# This code is contributed
# by Anant Agarwal.

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C#

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// C# program to find minimum
// difference of maximum and 
// minimum of K number.
using System;
  
class GFG {
      
// Return minimum difference of 
// maximum and minimum of k 
// elements of arr[0..n - 1].
static int minDiff(int []arr, int n,
                   int k) 
{
    int result = int.MaxValue;
  
    // Sorting the array.
    Array.Sort(arr);
  
    // Find minimum value among 
    // all K size subarray.
    for (int i = 0; i <= n - k; i++)
    result = Math.Min(result, arr[i + k - 1] - arr[i]);
  
    return result;
}
  
// Driver code
public static void Main() {
    int []arr = {10, 100, 300, 200, 1000, 20, 30};
    int n = arr.Length;
    int k = 3;
  
    Console.WriteLine(minDiff(arr, n, k));
}
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP program to find minimum
// difference of maximum and 
// minimum of K number.
  
// Return minimum difference 
// of maximum and minimum
// of k elements of arr[0..n-1].
function minDiff($arr, $n, $k)
{
    $INT_MAX = 2147483647;
    $result = $INT_MAX ;
  
    // Sorting the array.
    sort($arr , $n);
    sort($arr); 
  
    // Find minimum value among
    // all K size subarray.
    for ($i = 0; $i <= $n - $k; $i++)
        $result = min($result, $arr[$i + $k - 1] - 
                                       $arr[$i]);
    return $result;
}
  
    // Driver Code
    $arr = array(10, 100, 300, 200, 1000, 20, 30);
    $n = sizeof($arr);
    $k = 3;
    echo minDiff($arr, $n, $k);
      
// This code is contributed by nitin mittal.
?>

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Output:

20

Time Complexity: O(nlogn).

This article is contributed by Anuj Chauhan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Improved By : vt_m, nitin mittal



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