Largest possible Subset from an Array such that no element is K times any other element in the Subset

Last Updated : 01 Nov, 2022

Given an array arr[] consisting of N distinct integers and an integer K, the task is to find the maximum size of a subset possible such that no element in the subset is K times any other element of the subset(i.e. no such pair {n, m} should be present in the subset such that either m = n * K or n = m * K).

Examples:

Input: arr[] = {2, 8, 6, 5, 3}, K = 2
Output: 4
Explanation:
Only possible pair existing in the array with an element being K( = 2) times the other is {6, 3}.
Hence, all possible subsets which does not contain both the elements of the pair {6, 3} together can be considered.
Therefore, the longest possible subset can be of length 4.

Input: arr[] = {1, 4, 3, 2}, K = 3
output: 3

Approach:
Follow the steps below to solve the problem:

Find the number of pairs possible such that one element is K times the other from the given array
Sort the array in increasing order of elements.
Traverse the array and store the frequency indices of array elements in Map.
Initialize an array visited to mark for every index, whether that element is included(0) or not(1) in the subset.
Traverse the array again and for every index having vis[i] = 0, check if arr[i] * K is present in the Map or not. If found, then increase the count of pairs and set vis[mp[arr[i] * K]] = 1.
Finally, print N – count of pairs as the answer.

Below is implementation of above approach:

C++

   // C++ implementation of
// the above approach
#include <bits/stdc++.h>
#define ll long long
using namespace std;
 
// Function to find the maximum
// size of the required subset
int findMaxLen(vector<ll>& a, ll k)
{
 
    // Size of the array
    int n = a.size();
 
    // Sort the array
    sort(a.begin(), a.end());
 
    // Stores which index is
    // included or excluded
    vector<bool> vis(n, 0);
 
    // Stores the indices of
    // array elements
    map<int, int> mp;
 
    for (int i = 0; i < n; i++) {
        mp[a[i]] = i;
    }
 
    // Count of pairs
    int c = 0;
 
    // Iterate through all
    // the element
    for (int i = 0; i < n; ++i) {
 
        // If element is included
        if (vis[i] == false) {
            int check = a[i] * k;
 
            // Check if a[i] * k is present
            // in the array or not
            if (mp.find(check) != mp.end()) {
 
                // Increase count of pair
                c++;
 
                // Exclude the pair
                vis[mp[check]] = true;
            }
        }
    }
 
    return n - c;
}
 
// Driver code
int main()
{
 
    int K = 3;
    vector<ll> arr = { 1, 4, 3, 2 };
 
    cout << findMaxLen(arr, K);
}
 
  

Java

   // Java implementation of
// the above approach
import java.util.*;
 
class GFG{
 
// Function to find the maximum
// size of the required subset
static int findMaxLen(int[] a, int k)
{
 
    // Size of the array
    int n = a.length;
 
    // Sort the array
    Arrays.sort(a);
 
    // Stores which index is
    // included or excluded
    boolean []vis = new boolean[n];
 
    // Stores the indices of
    // array elements
    HashMap<Integer,
            Integer> mp = new HashMap<Integer,
                                      Integer>();
                                       
    for(int i = 0; i < n; i++)
    {
        mp.put(a[i], i);
    }
 
    // Count of pairs
    int c = 0;
 
    // Iterate through all
    // the element
    for(int i = 0; i < n; ++i)
    {
 
        // If element is included
        if (vis[i] == false) 
        {
            int check = a[i] * k;
 
            // Check if a[i] * k is present
            // in the array or not
            if (mp.containsKey(check))
            {
 
                // Increase count of pair
                c++;
 
                // Exclude the pair
                vis[mp.get(check)] = true;
            }
        }
    }
    return n - c;
}
 
// Driver code
public static void main(String[] args)
{
    int K = 3;
    int []arr = { 1, 4, 3, 2 };
 
    System.out.print(findMaxLen(arr, K));
}
}
 
// This code is contributed by amal kumar choubey 
 
  

Python3

   # Python3 implementation of
# the above approach
 
# Function to find the maximum
# size of the required subset
def findMaxLen(a, k):
 
    # Size of the array
    n = len(a)
 
    # Sort the array
    a.sort()
 
    # Stores which index is
    # included or excluded
    vis = [0] * n
 
    # Stores the indices of
    # array elements
    mp = {}
 
    for i in range(n):
        mp[a[i]] = i
 
    # Count of pairs
    c = 0
 
    # Iterate through all
    # the element
    for i in range(n):
 
        # If element is included
        if(vis[i] == False):
            check = a[i] * k
 
            # Check if a[i] * k is present
            # in the array or not
            if(check in mp.keys()):
 
                # Increase count of pair
                c += 1
 
                # Exclude the pair 
                vis[mp[check]] = True
 
    return n - c
 
# Driver Code
if __name__ == '__main__':
 
    K = 3
    arr = [ 1, 4, 3, 2 ]
 
    print(findMaxLen(arr, K))
 
# This code is contributed by Shivam Singh
 
  

C#

   // C# implementation of
// the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Function to find the maximum
// size of the required subset
static int findMaxLen(int[] a, int k)
{
 
    // Size of the array
    int n = a.Length;
 
    // Sort the array
    Array.Sort(a);
 
    // Stores which index is
    // included or excluded
    bool []vis = new bool[n];
 
    // Stores the indices of
    // array elements
    Dictionary<int,
               int> mp = new Dictionary<int,
                                        int>();
                                     
    for(int i = 0; i < n; i++)
    {
        mp.Add(a[i], i);
    }
 
    // Count of pairs
    int c = 0;
 
    // Iterate through all
    // the element
    for(int i = 0; i < n; ++i)
    {
 
        // If element is included
        if (vis[i] == false) 
        {
            int check = a[i] * k;
 
            // Check if a[i] * k is present
            // in the array or not
            if (mp.ContainsKey(check))
            {
 
                // Increase count of pair
                c++;
 
                // Exclude the pair
                vis[mp[check]] = true;
            }
        }
    }
    return n - c;
}
 
// Driver code
public static void Main(String[] args)
{
    int K = 3;
    int []arr = { 1, 4, 3, 2 };
 
    Console.Write(findMaxLen(arr, K));
}
}
 
// This code is contributed by gauravrajput1
 
  

Javascript

   <script>
 
// Javascript implementation of
// the above approach
 
// Function to find the maximum
// size of the required subset
function findMaxLen(a, k)
{
  
    // Size of the array
    let n = a.length;
  
    // Sort the array
    a.sort();
  
    // Stores which index is
    // included or excluded
    let vis = Array.from({length: n}, (_, i) => 0);
  
    // Stores the indices of
    // array elements
    let mp = new Map();
                                        
    for(let i = 0; i < n; i++)
    {
        mp.set(a[i], i);
    }
  
    // Count of pairs
    let c = 0;
  
    // Iterate through all
    // the element
    for(let i = 0; i < n; ++i)
    {
  
        // If element is included
        if (vis[i] == false)
        {
            let check = a[i] * k;
  
            // Check if a[i] * k is present
            // in the array or not
            if (mp.has(check))
            {
  
                // Increase count of pair
                c++;
  
                // Exclude the pair
                vis[mp.get(check)] = true;
            }
        }
    }
    return n - c;
}
 
// Driver code
 
    let K = 3;
    let arr = [ 1, 4, 3, 2 ];
  
    document.write(findMaxLen(arr, K));
 
// This code is contributed by souravghosh0416.
</script>
 
  

Output:

Time Complexity: O(N*log(N))
Auxiliary Space: O(N)

Largest element in the array that is repeated exactly k times

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Practice Tags :

Largest possible Subset from an Array such that no element is K times any other element in the Subset

C++

Java

Python3

C#

Javascript

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