Find perfect numbers in a given range

The problem at hand involves finding perfect numbers within a given range. A perfect number is a positive integer that is equal to the sum of its proper divisors (excluding itself). For instance, 6 is a perfect number because its divisors are 1, 2, and 3, and 1 + 2 + 3 = 6.

Problem Statement

Given a range of numbers from x to y, the objective is to identify and display all the perfect numbers within this range.

Example

Let's take an example to illustrate the problem:

Example

• Given range: x = 1, y = 200
• We need to identify and display the perfect numbers within this range.

Idea to Solve

1. Loop through the range from x to y.
2. For each number in the range, calculate its sum of proper divisors.
3. If the sum of proper divisors equals the number itself, it is a perfect number.

Pseudocode

function isPerfectNumber(num):
    if num < 0:
        return false
    sumOfDivisors = 0
    for i in range(1, num):
        if num % i == 0:
            sumOfDivisors += i
    if sumOfDivisors == num:
        return true
    else:
        return false

function findPerfectNumbersInRange(x, y):
    result = []
    for num in range(x, y + 1):
        if isPerfectNumber(num):
            result.append(num)
    return result

# Example usage
x = 1
y = 200
perfectNumbers = findPerfectNumbersInRange(x, y)
print(perfectNumbers)

Algorithm Explanation

1. The isPerfectNumber function checks whether a given number is perfect or not.
2. It iterates through all the numbers from 1 to num - 1, calculating the sum of proper divisors.
3. If the sum of proper divisors equals the number itself, the function returns true (indicating a perfect number).
4. The findPerfectNumbersInRange function iterates through the range from x to y, checking each number using the isPerfectNumber function.
5. If a perfect number is found, it's added to the result list.
6. Finally, the result list is returned, containing all perfect numbers within the specified range.

Code Solution

• Java
• C++
• C#
• Go
• Php
• Node Js
• Python
• Ruby
• Scala
• Swift 4
• Kotlin

/*
    Java program for
    Find perfect numbers in a given range
*/
public class PerfectNumber
{
	// Check given number is perfect or not
	public boolean isPerfectNo(int n)
	{
		if (n < 0)
		{
			return false;
		}
		int sum = 0;
		for (int i = (n / 2); i >= 1; i--)
		{
			if (n % i == 0)
			{
				sum += i;
			}
		}
		if (sum == n)
		{
			return true;
		}
		else
		{
			return false;
		}
	}
	public void findPerfectNo(int x, int y)
	{
		// Result indicator
		// Initial false
		boolean result = false;
		System.out.print(" Perfect number in range of (" + 
                         x + "," + y + ") is \n");
		for (int i = x; i <= y; ++i)
		{
			if (isPerfectNo(i))
			{
				// When number is perfect number
				System.out.print("  " + i);
				// Change result status
				result = true;
			}
		}
		if (result == false)
		{
			System.out.print("\n None \n");
		}
	}
	public static void main(String[] args)
	{
		PerfectNumber task = new PerfectNumber();
		// Test A
		int x = 1;
		int y = 200;
		task.findPerfectNo(x, y);
	}
}

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// Include header file
#include <iostream>
using namespace std;
/*
    C++ program for
    Find perfect numbers in a given range
*/
class PerfectNumber
{
	public:
		// Check given number is perfect or not
		bool isPerfectNo(int n)
		{
			if (n < 0)
			{
				return false;
			}
			int sum = 0;
			for (int i = (n / 2); i >= 1; i--)
			{
				if (n % i == 0)
				{
					sum += i;
				}
			}
			if (sum == n)
			{
				return true;
			}
			else
			{
				return false;
			}
		}
	void findPerfectNo(int x, int y)
	{
		// Result indicator
		// Initial false
		bool result = false;
		cout << " Perfect number in range of (" 
      		 << x << "," << y << ") is \n";
		for (int i = x; i <= y; ++i)
		{
			if (this->isPerfectNo(i))
			{
				// When number is perfect number
				cout << "  " << i;
				// Change result status
				result = true;
			}
		}
		if (result == false)
		{
			cout << "\n None \n";
		}
	}
};
int main()
{
	PerfectNumber *task = new PerfectNumber();
	// Test A
	int x = 1;
	int y = 200;
	task->findPerfectNo(x, y);
	return 0;
}

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// Include namespace system
using System;
/*
    Csharp program for
    Find perfect numbers in a given range
*/
public class PerfectNumber
{
	// Check given number is perfect or not
	public Boolean isPerfectNo(int n)
	{
		if (n < 0)
		{
			return false;
		}
		int sum = 0;
		for (int i = (n / 2); i >= 1; i--)
		{
			if (n % i == 0)
			{
				sum += i;
			}
		}
		if (sum == n)
		{
			return true;
		}
		else
		{
			return false;
		}
	}
	public void findPerfectNo(int x, int y)
	{
		// Result indicator
		// Initial false
		Boolean result = false;
		Console.Write(" Perfect number in range of (" + 
                      x + "," + y + ") is \n");
		for (int i = x; i <= y; ++i)
		{
			if (this.isPerfectNo(i))
			{
				// When number is perfect number
				Console.Write("  " + i);
				// Change result status
				result = true;
			}
		}
		if (result == false)
		{
			Console.Write("\n None \n");
		}
	}
	public static void Main(String[] args)
	{
		PerfectNumber task = new PerfectNumber();
		// Test A
		int x = 1;
		int y = 200;
		task.findPerfectNo(x, y);
	}
}

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package main
import "fmt"
/*
    Go program for
    Find perfect numbers in a given range
*/

// Check given number is perfect or not
func isPerfectNo(n int) bool {
	if n < 0 {
		return false
	}
	var sum int = 0
	for i :=(n / 2) ; i >= 1 ; i-- {
		if n % i == 0 {
			sum += i
		}
	}
	if sum == n {
		return true
	} else {
		return false
	}
}
func findPerfectNo(x, y int) {
	// Result indicator
	// Initial false
	var result bool = false
	fmt.Print(" Perfect number in range of (", 
		x, ",", y, ") is \n")
	for i := x ; i <= y ; i++ {
		if isPerfectNo(i) {
			// When number is perfect number
			fmt.Print("  ", i)
			// Change result status
			result = true
		}
	}
	if result == false {
		fmt.Print("\n None \n")
	}
}
func main() {
	// Test A
	var x int = 1
	var y int = 200
	findPerfectNo(x, y)
}

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<?php
/*
    Php program for
    Find perfect numbers in a given range
*/
class PerfectNumber
{
	// Check given number is perfect or not
	public	function isPerfectNo($n)
	{
		if ($n < 0)
		{
			return false;
		}
		$sum = 0;
		for ($i = ((int)($n / 2)); $i >= 1; $i--)
		{
			if ($n % $i == 0)
			{
				$sum += $i;
			}
		}
		if ($sum == $n)
		{
			return true;
		}
		else
		{
			return false;
		}
	}
	public	function findPerfectNo($x, $y)
	{
		// Result indicator
		// Initial false
		$result = false;
		echo(" Perfect number in range of (".$x.
			",".$y.
			") is \n");
		for ($i = $x; $i <= $y; ++$i)
		{
			if ($this->isPerfectNo($i))
			{
				// When number is perfect number
				echo("  ".$i);
				// Change result status
				$result = true;
			}
		}
		if ($result == false)
		{
			echo("\n None \n");
		}
	}
}

function main()
{
	$task = new PerfectNumber();
	// Test A
	$x = 1;
	$y = 200;
	$task->findPerfectNo($x, $y);
}
main();

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/*
    Node JS program for
    Find perfect numbers in a given range
*/
class PerfectNumber
{
	// Check given number is perfect or not
	isPerfectNo(n)
	{
		if (n < 0)
		{
			return false;
		}
		var sum = 0;
		for (var i = (parseInt(n / 2)); i >= 1; i--)
		{
			if (n % i == 0)
			{
				sum += i;
			}
		}
		if (sum == n)
		{
			return true;
		}
		else
		{
			return false;
		}
	}
	findPerfectNo(x, y)
	{
		// Result indicator
		// Initial false
		var result = false;
		process.stdout.write(" Perfect number in range of (" + 
                             x + "," + y + ") is \n");
		for (var i = x; i <= y; ++i)
		{
			if (this.isPerfectNo(i))
			{
				// When number is perfect number
				process.stdout.write("  " + i);
				// Change result status
				result = true;
			}
		}
		if (result == false)
		{
			process.stdout.write("\n None \n");
		}
	}
}

function main()
{
	var task = new PerfectNumber();
	// Test A
	var x = 1;
	var y = 200;
	task.findPerfectNo(x, y);
}
main();

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#    Python 3 program for
#    Find perfect numbers in a given range
class PerfectNumber :
	#  Check given number is perfect or not
	def isPerfectNo(self, n) :
		if (n < 0) :
			return False
		
		sum = 0
		i = (int(n / 2))
		while (i >= 1) :
			if (n % i == 0) :
				sum += i
			
			i -= 1
		
		if (sum == n) :
			return True
		else :
			return False
		
	
	def findPerfectNo(self, x, y) :
		#  Result indicator
		#  Initial false
		result = False
		print(" Perfect number in range of (", x ,",", y ,") is ")
		i = x
		while (i <= y) :
			if (self.isPerfectNo(i)) :
				#  When number is perfect number
				print("  ", i, end = "")
				#  Change result status
				result = True
			
			i += 1
		
		if (result == False) :
			print("\n None ")
		
	

def main() :
	task = PerfectNumber()
	#  Test A
	x = 1
	y = 200
	task.findPerfectNo(x, y)

if __name__ == "__main__": main()

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#    Ruby program for
#    Find perfect numbers in a given range
class PerfectNumber 
	#  Check given number is perfect or not
	def isPerfectNo(n) 
		if (n < 0) 
			return false
		end

		sum = 0
		i = (n / 2)
		while (i >= 1) 
			if (n % i == 0) 
				sum += i
			end

			i -= 1
		end

		if (sum == n) 
			return true
		else
 
			return false
		end

	end

	def findPerfectNo(x, y) 
		#  Result indicator
		#  Initial false
		result = false
		print(" Perfect number in range of (", 
              x ,",", y ,") is \n")
		i = x
		while (i <= y) 
			if (self.isPerfectNo(i)) 
				#  When number is perfect number
				print("  ", i)
				#  Change result status
				result = true
			end

			i += 1
		end

		if (result == false) 
			print("\n None \n")
		end

	end

end

def main() 
	task = PerfectNumber.new()
	#  Test A
	x = 1
	y = 200
	task.findPerfectNo(x, y)
end

main()

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/*
    Scala program for
    Find perfect numbers in a given range
*/
class PerfectNumber()
{
	// Check given number is perfect or not
	def isPerfectNo(n: Int): Boolean = {
		if (n < 0)
		{
			return false;
		}
		var sum: Int = 0;
		var i: Int = (n / 2);
		while (i >= 1)
		{
			if (n % i == 0)
			{
				sum += i;
			}
			i -= 1;
		}
		if (sum == n)
		{
			return true;
		}
		else
		{
			return false;
		}
	}
	def findPerfectNo(x: Int, y: Int): Unit = {
		// Result indicator
		// Initial false
		var result: Boolean = false;
		print(" Perfect number in range of (" + 
      	x + "," + y + ") is \n");
		var i: Int = x;
		while (i <= y)
		{
			if (isPerfectNo(i))
			{
				// When number is perfect number
				print("  " + i);
				// Change result status
				result = true;
			}
			i += 1;
		}
		if (result == false)
		{
			print("\n None \n");
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: PerfectNumber = new PerfectNumber();
		// Test A
		var x: Int = 1;
		var y: Int = 200;
		task.findPerfectNo(x, y);
	}
}

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/*
    Swift 4 program for
    Find perfect numbers in a given range
*/
class PerfectNumber
{
	// Check given number is perfect or not
	func isPerfectNo(_ n: Int) -> Bool
	{
		if (n < 0)
		{
			return false;
		}
		var sum: Int = 0;
		var i: Int = (n / 2);
		while (i >= 1)
		{
			if (n % i == 0)
			{
				sum += i;
			}
			i -= 1;
		}
		if (sum == n)
		{
			return true;
		}
		else
		{
			return false;
		}
	}
	func findPerfectNo(_ x: Int, _ y: Int)
	{
		// Result indicator
		// Initial false
		var result: Bool = false;
		print(" Perfect number in range of (", 
              x ,",", y ,") is ");
		var i: Int = x;
		while (i <= y)
		{
			if (self.isPerfectNo(i))
			{
				// When number is perfect number
				print("  ", i, terminator: "");
				// Change result status
				result = true;
			}
			i += 1;
		}
		if (result == false)
		{
			print("\n None ");
		}
	}
}
func main()
{
	let task: PerfectNumber = PerfectNumber();
	// Test A
	let x: Int = 1;
	let y: Int = 200;
	task.findPerfectNo(x, y);
}
main();

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/*
    Kotlin program for
    Find perfect numbers in a given range
*/
class PerfectNumber
{
	// Check given number is perfect or not
	fun isPerfectNo(n: Int): Boolean
	{
		if (n < 0)
		{
			return false;
		}
		var sum: Int = 0;
		var i: Int = (n / 2);
		while (i >= 1)
		{
			if (n % i == 0)
			{
				sum += i;
			}
			i -= 1;
		}
		if (sum == n)
		{
			return true;
		}
		else
		{
			return false;
		}
	}
	fun findPerfectNo(x: Int, y: Int): Unit
	{
		// Result indicator
		// Initial false
		var result: Boolean = false;
		print(" Perfect number in range of (" + 
              x + "," + y + ") is \n");
		var i: Int = x;
		while (i <= y)
		{
			if (this.isPerfectNo(i))
			{
				// When number is perfect number
				print("  " + i);
				// Change result status
				result = true;
			}
			i += 1;
		}
		if (result == false)
		{
			print("\n None \n");
		}
	}
}
fun main(args: Array < String > ): Unit
{
	val task: PerfectNumber = PerfectNumber();
	// Test A
	val x: Int = 1;
	val y: Int = 200;
	task.findPerfectNo(x, y);
}

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Time Complexity

• For each number in the range, the isPerfectNumber function takes O(num) time.
• Since we're iterating through the range of (y - x + 1) numbers, the overall time complexity is O((y - x + 1) * num).

The time complexity can be improved by employing more advanced techniques, but this simple approach is acceptable for most practical cases.