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: 3
{2, 3, 5} is the required sub-setInput: arr[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, K = 2
Output: 6
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 <bits/stdc++.h>using namespace std;// Function to return the size of the required sub-setint 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 codeint 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 approachimport java.util.*;class GFG{ // Function to return the size of the required sub-setstatic 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 codepublic 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 approachimport math as mt # Function to return the size of the required sub-setdef 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 codea=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]n = len(a)k = 2print(sizeSubSet(a, k, n))# This is contributed by Mohit kumar 29 |
C#
// C# implementation of the approachusing System;using System.Collections.Generic;class GFG{ // Function to return the size of // the required sub-setstatic 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 codepublic 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
<?php// Php implementation of the approach // Function to return the size of// the required sub-set function sizeSubSet($a, $k, $n){ // Sort the array sort($a) ; // Set to store the contents of // the required sub-set $s = array(); // Insert the elements satisfying // the conditions for ($i = 0 ; $i < $n ; $i++) { if ($a[$i] % $k != 0 or !in_array(floor($a[$i] / $k), $s)) array_push($s, $a[$i]); } // Return the size of the set return sizeof($s);}// Driver code $a = array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10 );$n = sizeof($a);$k = 2;echo sizeSubSet($a, $k, $n);// This code is contributed by Ryuga?> |
Javascript
<script>// Javascript implementation of the approach// Function to return the size of the// required sub-setfunction sizeSubSet(a, k, n){ // Sort the array a.sort(function(a, b){return a - b;}); // HashMap to store the contents // of the required sub-set let s = new Map(); // Insert the elements satisfying the conditions for(let i = 0; i < n; i++) { if (a[i] % k != 0 || s.get(a[i] / k) == null) s.set(a[i], s.get(a[i]) == null ? 1 : s.get(a[i]) + 1); } // Return the size of the set return s.size;}// Driver codelet a = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];let n = a.length;let k = 2;document.write(sizeSubSet(a, k, n));// This code is contributed by patel2127</script> |
Output:
6
Time Complexity: O(n*log(n)), As we are sorting the array
Auxiliary Space: O(n)
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