# 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.

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

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 ` `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; ` `} `

## 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 `

## 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))  `

## 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 `

Output:

```3
```

Time Complexity: O(N×√N)

Auxiliary Space Complexity: O(1)

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