Count maximum elements of an array whose absolute difference does not exceed K

Given an array A and positive integer K. The task is to find maximum number elements for which the absolute difference of any of the pair does not exceed K.

Examples:

Input: A[] = {1, 26, 17, 12, 15, 2}, K = 5
Output: 3
There are maximum 3 values so that the absolute difference of each pair
does not exceed K(K=5) ie., {12, 15, 17}



Input: A[] = {1, 2, 5, 10, 8, 3}, K = 4
Output: 4
There are maximum 4 values so that the absolute difference of each pair
does not exceed K(K=4) ie., {1, 2, 3, 5}

Approach:

  1. Sort the given Array in ascending order.
  2. Iterate from index i = 0 to n.
  3. For every A[i] count how many values which are in range A[i] to A[i] + K
    ie., A[i]<= A[j] <= A[i]+K
  4. Return Max Count

Below is the implementation of the above approach:

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// C++ implementation of the above approach
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the maximum elements
// in which absolute difference of any pair
// does not exceed K
int maxCount(int A[], int N, int K)
{
    int maximum = 0;
    int i = 0, j = 0;
    int start = 0;
    int end = 0;
  
    // Sort the Given array
    sort(A, A + N);
  
    // Find max elements
    for (i = 0; i < N; i++) {
  
        // Count all elements which are in range
        // A[i] to A[i] + K
        while (j < N && A[j] <= A[i] + K)
            j++;
        if (maximum < (j - i)) {
            maximum = (j - i);
            start = i;
            end = j;
        }
    }
  
    // Return the max count
    return maximum;
}
  
// Driver code
int main()
{
    int A[] = { 1, 26, 17, 12, 15, 2 };
    int N = sizeof(A) / sizeof(A[0]);
    int K = 5;
    cout << maxCount(A, N, K);
  
    return 0;
}
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// Java implementation of the approach 
import java.util.*;
  
class GFG 
{
      
// Function to return the maximum elements 
// in which absolute difference of any pair 
// does not exceed K 
static int maxCount(int A[], int N, int K) 
    int maximum = 0
    int i = 0, j = 0
    int start = 0
    int end = 0
  
    // Sort the Given array 
    Arrays.sort(A); 
  
    // Find max elements 
    for (i = 0; i < N; i++)
    
  
        // Count all elements which are in range 
        // A[i] to A[i] + K 
        while (j < N && A[j] <= A[i] + K) 
            j++; 
        if (maximum < (j - i)) 
        
            maximum = (j - i); 
            start = i; 
            end = j; 
        
    
  
    // Return the max count 
    return maximum; 
  
// Driver code 
public static void main(String[] args)
{
    int A[] = { 1, 26, 17, 12, 15, 2 }; 
    int N = A.length; 
    int K = 5
    System.out.println(maxCount(A, N, K));
}
}
  
// This code has been contributed by 29AjayKumar
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# Python3 implementation of the approach
  
def maxCount(A, N, K):
  
    maximum = 0
    start = 0
    end = 0
    j = 0
      
    # Sort the Array
    A.sort()
      
    # Find max elements
    for i in range(0, N):
        while(j < N and A[j] <= A[i] + K):
            j += 1
        if maximum < (j - i ):
            maximum = (j - i)
            start = i;
            end = j; 
  
    # Return the maximum
    return maximum
  
# Driver code
A = [1, 26, 17, 12, 15, 2
N = len(A)
K = 5
  
print(maxCount(A, N, K))
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// C# implementation of the approach
using System;
  
class GFG 
{
      
// Function to return the maximum elements 
// in which absolute difference of any pair 
// does not exceed K 
static int maxCount(int []A, int N, int K) 
    int maximum = 0; 
    int i = 0, j = 0; 
    int start = 0; 
    int end = 0; 
  
    // Sort the Given array 
    Array.Sort(A); 
  
    // Find max elements 
    for (i = 0; i < N; i++)
    
  
        // Count all elements which are in range 
        // A[i] to A[i] + K 
        while (j < N && A[j] <= A[i] + K) 
            j++; 
        if (maximum < (j - i)) 
        
            maximum = (j - i); 
            start = i; 
            end = j; 
        
    
  
    // Return the max count 
    return maximum; 
  
// Driver code 
public static void Main()
{
    int []A = { 1, 26, 17, 12, 15, 2 }; 
    int N = A.Length; 
    int K = 5; 
    Console.Write(maxCount(A, N, K));
}
}
  
/* This code contributed by PrinciRaj1992 */
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<?php
// PHP implementation of the above approach 
  
// Function to return the maximum 
// elements in which absolute difference 
// of any pair does not exceed K 
function maxCount($A, $N, $K
    $maximum = 0; 
    $i = 0;
    $j = 0; 
    $start = 0; 
    $end = 0; 
  
    // Sort the Given array 
    sort($A); 
  
    // Find max elements 
    for ($i = 0; $i < $N; $i++)
    
  
        // Count all elements which 
        // are in range A[i] to A[i] + K 
        while ($j < $N && 
               $A[$j] <= $A[$i] + $K
            $j++; 
        if ($maximum < ($j - $i)) 
        
            $maximum = ($j - $i); 
            $start = $i
            $end = $j
        
    
  
    // Return the max count 
    return $maximum
  
// Driver code 
$A = array( 1, 26, 17, 12, 15, 2 ); 
$N = Count($A); 
$K = 5; 
echo maxCount($A, $N, $K); 
  
// This code is contributed 
// by Arnab Kundu
?>
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Output:
3



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