# Largest sub-set possible for an array satisfying the given condition

Given an array arr[] and an integer K. The task is to find the size of the maximum sub-set such that every pair from the sub-set (X, Y) is of the form Y != (X * K) where X < Y.

Examples:

Input: arr[] = {2, 3, 6, 5, 4, 10}, K = 2
Output:
{2, 3, 5} is the required sub-set

Input: arr[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, K = 2
Output:

Approach:

• Sort all the array elements.
• Create an empty set of integers S, which will hold the elements for the sub-set.
• Traverse the sorted array, and for each integer x in the array:
• If x % k = 0 or x / k is not already present in S then insert x into S.
• Else discard x and check the next element.
• Print the size of the set S in the end.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function to return the size of the required sub-set` `int` `sizeSubSet(``int` `a[], ``int` `k, ``int` `n)` `{` `    ``// Sort the array` `    ``sort(a, a + n);`   `    ``// Set to store the contents of the required sub-set` `    ``unordered_set<``int``> s;`   `    ``// Insert the elements satisfying the conditions` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``if` `(a[i] % k != 0 || s.count(a[i] / k) == 0)` `            ``s.insert(a[i]);` `    ``}`   `    ``// Return the size of the set` `    ``return` `s.size();` `}`   `// Driver code` `int` `main()` `{` `    ``int` `a[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };` `    ``int` `n = ``sizeof``(a) / ``sizeof``(a[0]);` `    ``int` `k = 2;`   `    ``cout << sizeSubSet(a, k, n);` `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach` `import` `java.util.*;`   `class` `GFG` `{` `    `  `// Function to return the size of the required sub-set` `static` `int` `sizeSubSet(``int` `a[], ``int` `k, ``int` `n)` `{` `    ``// Sort the array` `    ``Arrays.sort(a);`   `    ``// HashMap to store the contents` `    ``// of the required sub-set` `    ``HashMap< Integer, Integer> s = ``new` `HashMap< Integer, Integer>();` `    `  `    ``// Insert the elements satisfying the conditions` `    ``for` `(``int` `i = ``0``; i < n; i++)` `    ``{` `        ``if` `(a[i] % k != ``0` `|| s.get(a[i] / k) == ``null``)` `            ``s.put(a[i], s.get(a[i]) == ``null` `? ``1` `: s.get(a[i]) + ``1``);` `    ``}`   `    ``// Return the size of the set` `    ``return` `s.size();` `}`   `// Driver code` `public` `static` `void` `main(String args[])` `{` `    ``int` `a[] = { ``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``, ``8``, ``9``, ``10` `};` `    ``int` `n = a.length;` `    ``int` `k = ``2``;` `    ``System.out.println( sizeSubSet(a, k, n));` `}` `}` `// This code is contributed by Arnab Kundu`

## Python3

 `# Python3 implementation of the approach`   `import` `math as mt ` `# Function to return the size of the required sub-set` `def` `sizeSubSet(a, k, n):`   `    ``# Sort the array` `    ``a.sort()` ` `  `    ``# Set to store the contents of the required sub-set` `    ``s``=``set``()` ` `  `    ``# Insert the elements satisfying the conditions` `    ``for` `i ``in` `range``(n):` `        ``if` `(a[i] ``%` `k !``=` `0` `or` `a[i] ``/``/` `k ``not` `in` `s):` `            ``s.add(a[i])` `    `  ` `  `    ``# Return the size of the set` `    ``return` `len``(s)`   ` `  `# Driver code` `a``=``[``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``, ``8``, ``9``, ``10` `]` `n ``=` `len``(a)` `k ``=` `2`   `print``(sizeSubSet(a, k, n))`   `# This is contributed by Mohit kumar 29`

## C#

 `// C# implementation of the approach` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG` `{` `    `  `// Function to return the size of ` `// the required sub-set` `static` `int` `sizeSubSet(``int` `[]a, ``int` `k, ``int` `n)` `{` `    ``// Sort the array` `    ``Array.Sort(a);`   `    ``// HashMap to store the contents` `    ``// of the required sub-set` `    ``Dictionary<``int``,` `               ``int``> s = ``new` `Dictionary<``int``, ` `                                       ``int``>();` `    `  `    ``// Insert the elements satisfying the conditions` `    ``for` `(``int` `i = 0; i < n; i++)` `    ``{` `        ``if` `(a[i] % k != 0 || !s.ContainsKey(a[i] / k))` `        ``{` `            ``if``(s.ContainsKey(a[i]))` `            ``{` `                ``var` `val = s[a[i]];` `                ``s.Remove(a[i]);` `                ``s.Add(a[i], val + 1); ` `            ``}` `            ``else` `            ``{` `                ``s.Add(a[i], 1);` `            ``}` `        ``}` `    ``}`   `    ``// Return the size of the set` `    ``return` `s.Count;` `}`   `// Driver code` `public` `static` `void` `Main(String []args)` `{` `    ``int` `[]a = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };` `    ``int` `n = a.Length;` `    ``int` `k = 2;` `    ``Console.WriteLine(sizeSubSet(a, k, n));` `}` `}`   `// This code is contributed by PrinciRaj1992`

## PHP

 ``

## Javascript

 ``

Output:

`6`

Time Complexity: O(n*log(n)), As we are sorting the array
Auxiliary Space: O(n)

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