Print all Perfect Numbers from an array whose sum of digits is also a Perfect Number

Given an array arr[] of size N, the task is to print all the perfect numbers from an array whose sum of digits is also a perfect number.

Examples:

Input: arr[] = { 3, 8, 12, 28, 6 }
Output: 6
Explanation: The array element arr[4] (= 6) is a perfect number. The array element arr[3] (= 28) is a perfect number but its sum of digits (= 10) is not a perfect number.

Input: arr[] = { 1, 2, 3 }
Output: 1

Approach: Follow the steps below to solve the problem:

1. Declare a function, isPerfect() to check if the number is a perfect number or not.
2. Declare another function, sumOfDigits() to calculate the sum of all the digits of a number.
3. Traverse the array arr[]:
   • If arr[i] is a perfect number:
     • Initialize a variable, say digitSum, to store the sum of digits of the current array element.
     • If digitSum is also a perfect number, print that number.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to check if a number
// is perfect number or not
int isPerfect(int N)
{
    // Stores sum of proper divisors
    int sumOfDivisors = 1;
    for (int i = 2; i <= N / 2; ++i) {

        if (N % i == 0) {
            sumOfDivisors += i;
        }
    }

    // If sum of digits is equal to N,
    // then it's a perfect number
    if (sumOfDivisors == N) {
        return 1;
    }

    // Otherwise, not a perfect number
    else
        return 0;
}

// Function to find the
// sum of digits of a number
int sumOfDigits(int N)
{
    // Stores sum of digits
    int sum = 0;

    while (N != 0) {
        sum += (N % 10);
        N = N / 10;
    }

    // Return sum of digits
    return sum;
}

// Function to count perfect numbers from
// an array whose sum of digits is also perfect
void countPerfectNumbers(int arr[], int N)
{
    // Traverse the array
    for (int i = 0; i < N; ++i) {

        // If number is perfect
        if (isPerfect(arr[i])) {

            // Stores sum of digits
            // of the number
            int sum = sumOfDigits(arr[i]);

            // If that is also perfect number
            if (isPerfect(sum)) {

                // Print that number
                cout << arr[i] << " ";
            }
        }
    }
}

// Driver Code
int main()
{
    // Given array
    int arr[] = { 3, 8, 12, 28, 6 };

    // Size of the array
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function call to count perfect numbers
    // having sum of digits also perfect
    countPerfectNumbers(arr, N);

    return 0;
}

Java

// Java Program to implement
// the above approach

import java.io.*;
import java.util.*;

class GFG {

  // Function to check if a number
  // is perfect number or not
  static boolean isPerfect(int N)
  {
    // Stores sum of proper divisors
    int sumOfDivisors = 1;
    for (int i = 2; i <= N / 2; ++i) {

      if (N % i == 0) {
        sumOfDivisors += i;
      }
    }

    // If sum of digits is equal to N,
    // then it's a perfect number
    if (sumOfDivisors == N) {
      return true;
    }

    // Otherwise, not a perfect number
    else
      return false;
  }

  // Function to find the
  // sum of digits of a number
  static int sumOfDigits(int N)
  {
    // Stores sum of digits
    int sum = 0;

    while (N != 0) {
      sum += (N % 10);
      N = N / 10;
    }

    // Return sum of digits
    return sum;
  }

  // Function to count perfect numbers from
  // an array whose sum of digits is also perfect
  static void countPerfectNumbers(int arr[], int N)
  {
    // Traverse the array
    for (int i = 0; i < N; ++i) {

      // If number is perfect
      if (isPerfect(arr[i])) {

        // Stores sum of digits
        // of the number
        int sum = sumOfDigits(arr[i]);

        // If that is also perfect number
        if (isPerfect(sum)) {

          // Print that number
          System.out.print(arr[i] + " ");
        }
      }
    }
  }

  // Driver Code
  public static void main(String[] args)
  {

    // Given array
    int arr[] = { 3, 8, 12, 28, 6 };

    // Size of the array
    int N = arr.length;

    // Function call to count perfect numbers
    // having sum of digits also perfect
    countPerfectNumbers(arr, N);
  }
}

// This code is contributed by Kingash.

Python3

# Python Program to implement
# the above approach

# Function to check if a number
# is perfect number or not
def isPerfect(N):

    # Stores sum of proper divisors
    sumOfDivisors = 1;
    for i in range(2, int(N / 2) + 1):

        if (N % i == 0):
            sumOfDivisors += i;

    # If sum of digits is equal to N,
    # then it's a perfect number
    if (sumOfDivisors == N):
        return True;

    # Otherwise, not a perfect number
    else:
        return False;

# Function to find the
# sum of digits of a number
def sumOfDigits(N):

    # Stores sum of digits
    sum = 0;

    while (N != 0):
        sum += (N % 10);
        N = N // 10;

    # Return sum of digits
    return sum;

# Function to count perfect numbers from
# an array whose sum of digits is also perfect
def countPerfectNumbers(arr, N):

    # Traverse the array
    for i in range(N):

        # If number is perfect
        if (isPerfect(arr[i])):

            # Stores sum of digits
            # of the number
            sum = sumOfDigits(arr[i]);

            # If that is also perfect number
            if (isPerfect(sum)):

                # Print that number
                print(arr[i], end=" ");

# Driver Code
if __name__ == '__main__':

    # Given array
    arr = [3, 8, 12, 28, 6];

    # Size of the array
    N = len(arr);

    # Function call to count perfect numbers
    # having sum of digits also perfect
    countPerfectNumbers(arr, N);

    # This code is contributed by 29AjayKumar

C#

// C# program for the above approach
using System;
class GFG
{

  // Function to check if a number
  // is perfect number or not
  static bool isPerfect(int N)
  {

    // Stores sum of proper divisors
    int sumOfDivisors = 1;
    for (int i = 2; i <= N / 2; ++i) {

      if (N % i == 0) {
        sumOfDivisors += i;
      }
    }

    // If sum of digits is equal to N,
    // then it's a perfect number
    if (sumOfDivisors == N) {
      return true;
    }

    // Otherwise, not a perfect number
    else
      return false;
  }

  // Function to find the
  // sum of digits of a number
  static int sumOfDigits(int N)
  {

    // Stores sum of digits
    int sum = 0;

    while (N != 0) {
      sum += (N % 10);
      N = N / 10;
    }

    // Return sum of digits
    return sum;
  }

  // Function to count perfect numbers from
  // an array whose sum of digits is also perfect
  static void countPerfectNumbers(int []arr, int N)
  {

    // Traverse the array
    for (int i = 0; i < N; ++i) {

      // If number is perfect
      if (isPerfect(arr[i])) {

        // Stores sum of digits
        // of the number
        int sum = sumOfDigits(arr[i]);

        // If that is also perfect number
        if (isPerfect(sum)) {

          // Print that number
          Console.Write(arr[i] + " ");
        }
      }
    }
  }

// Driver Code
static public void Main()
{

    // Given array
    int []arr = { 3, 8, 12, 28, 6 };

    // Size of the array
    int N = arr.Length;

    // Function call to count perfect numbers
    // having sum of digits also perfect
    countPerfectNumbers(arr, N);
}
}

// This code is contributed by jana_sayantan.

Javascript

<script>
// JavaScript program for the above approach

// Function to check if a number
// is perfect number or not
function isPerfect(N)
{

    // Stores sum of proper divisors
    let sumOfDivisors = 1;
    for (let i = 2; i <= Math.floor(N / 2); ++i)
    {

        if (N % i === 0)
        {
            sumOfDivisors += i;
        }
    }

    // If sum of digits is equal to N,
    // then it's a perfect number
    if (sumOfDivisors === N) {
        return 1;
    }

    // Otherwise, not a perfect number
    else
        return 0;
}

// Function to find the
// sum of digits of a number
function sumOfDigits(N)
{
    // Stores sum of digits
    let sum = 0;

    while (N != 0) {
        sum += (N % 10);
        N = Math.floor(N / 10);
    }

    // Return sum of digits
    return sum;
}

// Function to count perfect numbers from
// an array whose sum of digits is also perfect
function countPerfectNumbers(arr, N)
{
    // Traverse the array
    for (let i = 0; i < N; ++i) {

        // If number is perfect
        if (isPerfect(arr[i])) {

            // Stores sum of digits
            // of the number
            let sum = sumOfDigits(arr[i]);

            // If that is also perfect number
            if (isPerfect(sum)) {

                // Print that number
                document.write(arr[i] + " ");
            }
        }
    }
}

// Driver Code

    // Given array
    let arr = [ 3, 8, 12, 28, 6 ];

    // Size of the array
    let N = arr.length;

    // Function call to count perfect numbers
    // having sum of digits also perfect
    countPerfectNumbers(arr, N);

// This code is contributed by Surbhi Tyagi.
</script>

Output:

6

Time Complexity: O(N³ * log N)
Auxiliary Space: O(1)