Length of Longest Perfect number Subsequence in an Array
Given an array arr[] containing non-negative integers of length N, the task is to print the length of the longest subsequence of Perfect numbers in the array.
A number is a perfect number if it is equal to the sum of its proper divisors, that is, sum of its positive divisors excluding the number itself.
Examples:
Input: arr[] = { 3, 6, 11, 2, 28, 21, 8128 }
Output: 3
Explanation:
Longest Perfect number subsequence is {6, 28, 8128} and hence the answer is 3.Input:arr[] = { 6, 4, 10, 13, 9, 25 }
Output: 1
Explanation:
Longest Perfect number subsequence is {6} and hence the answer is 1.
Approach:
To solve the problem mentioned above follow the steps given below:
- Traverse the given array and for each element in the array, check if it is a perfect number or not.
- If the element is a perfect number, it will be in the Longest Perfect number Subsequence. Hence increment the required length of Longest Perfect number Subsequence by 1
Below is the implementation of the above approach:
C++
// C++ program to find the length of // Longest Perfect number Subsequence in an Array #include <bits/stdc++.h> using namespace std; // Function to check if // the number is a Perfect number bool isPerfect(long long int n) { // To store sum of divisors long long int sum = 1; // Find all divisors and add them for (long long int i = 2; i * i <= n; i++) { if (n % i == 0) { if (i * i != n) sum = sum + i + n / i; else sum = sum + i; } } // Check if sum of divisors is equal to // n, then n is a perfect number if (sum == n && n != 1) return true; return false; } // Function to find the longest subsequence // which contain all Perfect numbers int longestPerfectSubsequence(int arr[], int n) { int answer = 0; // Find the length of longest // Perfect number subsequence for (int i = 0; i < n; i++) { if (isPerfect(arr[i])) answer++; } return answer; } // Driver code int main() { int arr[] = { 3, 6, 11, 2, 28, 21, 8128 }; int n = sizeof(arr) / sizeof(arr[0]); cout << longestPerfectSubsequence(arr, n) << endl; return 0; } |
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Java
// Java program to find the length of // longest perfect number subsequence // in an array class GFG { // Function to check if the // number is a perfect number static boolean isPerfect(long n) { // To store sum of divisors long sum = 1; // Find all divisors and add them for(long i = 2; i * i <= n; i++) { if (n % i == 0) { if (i * i != n) sum = sum + i + n / i; else sum = sum + i; } } // Check if sum of divisors is equal // to n, then n is a perfect number if (sum == n && n != 1) { return true; } return false; } // Function to find the longest subsequence // which contain all Perfect numbers static int longestPerfectSubsequence(int arr[], int n) { int answer = 0; // Find the length of longest // perfect number subsequence for(int i = 0; i < n; i++) { if (isPerfect(arr[i]) == true) answer++; } return answer; } // Driver code public static void main (String[] args) { int arr[] = { 3, 6, 11, 2, 28, 21, 8128 }; int n = arr.length; System.out.println(longestPerfectSubsequence(arr, n)); } } // This code is contributed by AnkitRai01 |
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Python3
# Python3 program to find the length of # Longest Perfect number Subsequence in an Array # Function to check if # the number is Perfect number def isPerfect( n ): # To store sum of divisors sum = 1 # Find all divisors and add them i = 2 while i * i <= n: if n % i == 0: sum = sum + i + n / i i += 1 # Check if sum of divisors is equal to # n, then n is a perfect number return (True if sum == n and n != 1 else False) # Function to find the longest subsequence # which contain all Perfect numbers def longestPerfectSubsequence( arr, n): answer = 0 # Find the length of longest # Perfect number subsequence for i in range (n): if (isPerfect(arr[i])): answer += 1 return answer # Driver code if __name__ == "__main__": arr = [ 3, 6, 11, 2, 28, 21, 8128 ] n = len(arr) print (longestPerfectSubsequence(arr, n)) |
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C#
// C# program to find the length of // longest perfect number subsequence // in an array using System; class GFG { // Function to check if the // number is a perfect number static bool isPerfect(long n) { // To store sum of divisors long sum = 1; // Find all divisors and add them for(long i = 2; i * i <= n; i++) { if (n % i == 0) { if (i * i != n) sum = sum + i + n / i; else sum = sum + i; } } // Check if sum of divisors is equal // to n, then n is a perfect number if (sum == n && n != 1) { return true; } return false; } // Function to find the longest subsequence // which contain all perfect numbers static int longestPerfectSubsequence(int []arr, int n) { int answer = 0; // Find the length of longest // perfect number subsequence for(int i = 0; i < n; i++) { if (isPerfect(arr[i]) == true) answer++; } return answer; } // Driver code public static void Main (string[] args) { int []arr = { 3, 6, 11, 2, 28, 21, 8128 }; int n = arr.Length; Console.WriteLine(longestPerfectSubsequence(arr, n)); } } // This code is contributed by AnkitRai01 |
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Output:
3
Time Complexity: O(N×√N)
Auxiliary Space Complexity: O(1)
