Length of Longest Perfect number Subsequence in an Array

Last Updated : 12 Jul, 2025

Given an array arr[] containing non-negative integers of length N, the task is to print the length of the longest subsequence of the Perfect number in the array.

A number is a perfect number if it is equal to the sum of its proper divisors, that is, the sum of its positive divisors excluding the number itself.

Examples:

Input: arr[] = { 3, 6, 11, 2, 28, 21, 8128 }
Output: 3
Explanation:
The 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:
The 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 the 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;
}

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# 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

JavaScript

<script>

// Javascript program to find the length of
// Longest Perfect number Subsequence in an Array

// Function to check if
// the number is a Perfect number
function isPerfect(n)
{
    // To store sum of divisors
    var sum = 1;

    // Find all divisors and add them
    for (var 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
function longestPerfectSubsequence(arr, n)
{
    var answer = 0;

    // Find the length of longest
    // Perfect number subsequence
    for (var i = 0; i < n; i++) {
        if (isPerfect(arr[i]))
            answer++;
    }

    return answer;
}

// Driver code
var arr = [3, 6, 11, 2, 28, 21, 8128];
var n = arr.length;
document.write( longestPerfectSubsequence(arr, n));


</script>

Output:

Time Complexity: O(N×?N)
Auxiliary Space Complexity: O(1)

Analysis of Algorithms

saurabhshadow

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Length of Longest Perfect number Subsequence in an Array

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