Given an array A and positive integer K. The task is to find maximum number of 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:
- Sort the given Array in ascending order.
- Iterate from index i = 0 to n.
- 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 - Return Max Count
Below is the implementation of the above approach:
// 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;
// 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++;
}
maximum=max(maximum,j-i);
}
// 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;
} |
// 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 |
# 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))
|
// 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 */ |
<?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 ?> |
<script> // JavaScript 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)
{ var maximum = 0;
var i = 0, j = 0;
var start = 0;
var end = 0;
// Sort the Given array
A.sort((a,b)=> a-b)
// 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 var A = [1, 26, 17, 12, 15, 2 ];
var N = A.length;
var K = 5;
document.write( maxCount(A, N, K)); </script> |
3
Time Complexity: O(N logN), where N*logN is the time required to sort the given array
Auxiliary Space: O(1), no extra space required