# 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}

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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:

 `// C++ implementation of the above approach ` ` `  `#include ` `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); ` `    ``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 */`

 ` `

Output:
```3
```

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