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Code Number

Polite number

A polite number is a positive integer that can be expressed as the sum of two or more consecutive positive integers. For example, the number 6 is a polite number because it can be expressed as the sum of three consecutive positive integers: 1 + 2 + 3 = 6.

Problem Statement

The task is to write a program that prints the first 'k' polite numbers, where 'k' is a given positive integer.

For example, if 'k' is 10, the program should print the following polite numbers:

1, 3, 5, 6, 7, 9, 10, 11, 12, 13

Explanation with an Example

Let's take the example of finding the first 10 polite numbers.

To find the polite numbers, we can use the following formula:

n + (log(n + log(n)) / log(2))

Starting from 'n = 1', we iterate up to 'k' and calculate the nth polite number using the formula. We then display the calculated result.

For 'n = 1', the calculation is as follows:

n + (log(n + log(n)) / log(2)) = 1 + (log(1 + log(1)) / log(2)) = 1

Similarly, for 'n = 2', the calculation is:

n + (log(n + log(n)) / log(2)) = 2 + (log(2 + log(2)) / log(2)) = 3

By following this process for 'k' iterations, we obtain the polite numbers.

Algorithm

  1. Define a function politeNo(k) that takes the number of polite numbers to be generated as input.
  2. Initialize a loop variable 'n' from 1 to 'k'.
  3. Inside the loop, calculate the nth polite number using the formula: n + (log(n + log(n)) / log(2)).
  4. Display the calculated polite number.
  5. Repeat steps 2-4 until the desired number of polite numbers are generated.
  6. In the main function, call politeNo(k), where 'k' is the number of polite numbers to be generated.

Pseudocode

politeNo(k)
  for n = 1 to k
    result = n + (log(n + (log(n) / log(2)))) / log(2)
    print result

main()
  politeNo(k)

Code Solution

Here given code implementation process.

// C Program for
// Polite number
#include <stdio.h>
#include <math.h>

void politeNo(int k)
{
	// Print all initial k Polite number
	for (int n = 1; n <= k; ++n)
	{
		// Formula
		//    n + (log (n+log n) 
		//            ²      ²
		// Calculate nth Polite number
		int result = (int)(n + 
                           (log((n + (log(n) / log(2))))) / 
                              log(2));
		// Display calculated result
		printf("  %d", result);
	}
}
int main()
{
	//  Polite number are
	// —————————————————————————————————————————————
	//  1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
	//  18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
	//  30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
	//  43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56 etc.
	// k = 10
	politeNo(10);
	return 0;
}

Output

  1  3  5  6  7  9  10  11  12  13
// Java program for
// Polite number
public class PoliteNumber
{
	public void politeNo(int k)
	{
		// Print all initial k Polite number
		for (int n = 1; n <= k; ++n)
		{
			// Formula
			//    n + (log (n+log n) 
			//            ²      ²
			// Calculate nth Polite number
			int result = (int)(n + 
                               (Math.log((n + (Math.log(n) / 
                                               Math.log(2))))) /
                               Math.log(2));
			// Display calculated result
			System.out.print(" " + result);
		}
	}
	public static void main(String[] args)
	{
		PoliteNumber task = new PoliteNumber();
		//  Polite number are
		// —————————————————————————————————————————————
		//  1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
		//  18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
		//  30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
		//  43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
		//  53, 54, 55, 56 etc.
		// k = 10
		task.politeNo(10);
	}
}

Output

 1 3 5 6 7 9 10 11 12 13
// Include header file
#include <iostream>
#include <math.h>

using namespace std;
// C++ program for
// Polite number
class PoliteNumber
{
	public: void politeNo(int k)
	{
		// Print all initial k Polite number
		for (int n = 1; n <= k; ++n)
		{
			// Formula
			//    n + (log (n+log n) 
			//            ²      ²
			// Calculate nth Polite number
			int result = (int)(n + 
                               (log((n + (log(n) / 
                                          log(2))))) / 
                               log(2));
			// Display calculated result
			cout << " " << result;
		}
	}
};
int main()
{
	PoliteNumber *task = new PoliteNumber();
	//  Polite number are
	// —————————————————————————————————————————————
	//  1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
	//  18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
	//  30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
	//  43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
	//  53, 54, 55, 56 etc.
	// k = 10
	task->politeNo(10);
	return 0;
}

Output

 1 3 5 6 7 9 10 11 12 13
// Include namespace system
using System;
// Csharp program for
// Polite number
public class PoliteNumber
{
	public void politeNo(int k)
	{
		// Print all initial k Polite number
		for (int n = 1; n <= k; ++n)
		{
			// Formula
			//    n + (log (n+log n) 
			//            ²      ²
          
			// Calculate nth Polite number
			int result = (int)(n + 
                               (Math.Log((n + 
                                          (Math.Log(n) /
                                           Math.Log(2))))) / 
                               Math.Log(2));
			// Display calculated result
			Console.Write(" " + result);
		}
	}
	public static void Main(String[] args)
	{
		PoliteNumber task = new PoliteNumber();
		//  Polite number are
		// —————————————————————————————————————————————
		//  1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
		//  18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
		//  30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
		//  43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
		//  53, 54, 55, 56 etc.
      
		// k = 10
		task.politeNo(10);
	}
}

Output

 1 3 5 6 7 9 10 11 12 13
package main
import "math"
import "fmt"
// Go program for
// Polite number

func politeNo(k int) {
	// Print all initial k Polite number
	for n := 1 ; n <= k ; n++ {
		// Formula
		//    n + (log (n+log n) 
		//            ²      ²

		// Calculate nth Polite number
		var result int = (int)(float64(n) + 
			(math.Log((float64(n) + 
				(math.Log(float64(n)) / 
					math.Log(2.0))))) /
					 math.Log(2.0))
		
		// Display calculated result
		fmt.Print(" ", result)
	}
}
func main() {

	//  Polite number are
	// —————————————————————————————————————————————
	//  1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
	//  18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
	//  30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
	//  43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
	//  53, 54, 55, 56 etc.
  
	// k = 10
	politeNo(10)
}

Output

 1 3 5 6 7 9 10 11 12 13
<?php
// Php program for
// Polite number
class PoliteNumber
{
	public	function politeNo($k)
	{
		// Print all initial k Polite number
		for ($n = 1; $n <= $k; ++$n)
		{
			// Formula
			//    n + (log (n+log n) 
			//            ²      ²
          
			// Calculate nth Polite number
			$result = (int)($n + 
                            (log(($n + (log($n) / log(2))))) / 
                            log(2));
			// Display calculated result
			echo(" ".$result);
		}
	}
}

function main()
{
	$task = new PoliteNumber();
	//  Polite number are
	// —————————————————————————————————————————————
	//  1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
	//  18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
	//  30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
	//  43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
	//  53, 54, 55, 56 etc.
	// k = 10
	$task->politeNo(10);
}
main();

Output

 1 3 5 6 7 9 10 11 12 13
// Node JS program for
// Polite number
class PoliteNumber
{
	politeNo(k)
	{
		// Print all initial k Polite number
		for (var n = 1; n <= k; ++n)
		{
			// Formula
			//    n + (log (n+log n) 
			//            ²      ²
			// Calculate nth Polite number
			var result = parseInt(n + 
                               (Math.log((n + (Math.log(n) / 
                                               Math.log(2))))) / 
                               Math.log(2));
			// Display calculated result
			process.stdout.write(" " + result);
		}
	}
}

function main()
{
	var task = new PoliteNumber();
	//  Polite number are
	// —————————————————————————————————————————————
	//  1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
	//  18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
	//  30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
	//  43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
	//  53, 54, 55, 56 etc.
	// k = 10
	task.politeNo(10);
}
main();

Output

 1 3 5 6 7 9 10 11 12 13
import math
#  Python 3 program for
#  Polite number
class PoliteNumber :
	def politeNo(self, k) :
		n = 1
		#  Print all initial k Polite number
		while (n <= k) :
			#  Formula
			#     n + (log (n+log n) 
			#             ²      ²
            
			#  Calculate nth Polite number
			result = (int)(n + 
                           (math.log((n + 
                                      (math.log(n) / 
                                       math.log(2))))) / 
                           math.log(2))

			#  Display calculated result
			print(" ", result, end = "")
			n += 1
		
	

def main() :
	task = PoliteNumber()
	#   Polite number are
	#  —————————————————————————————————————————————
	#   1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
	#   18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
	#   30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
	#   43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
	#   53, 54, 55, 56 etc.
    
	#  k = 10
	task.politeNo(10)

if __name__ == "__main__": main()

Output

  1  3  5  6  7  9  10  11  12  13
#  Ruby program for
#  Polite number
class PoliteNumber 
	def politeNo(k) 
		n = 1
		#  Print all initial k Polite number
		while (n <= k) 
			#  Formula
			#     n + (log (n+log n) 
			#             ²      ²
            
			#  Calculate nth Polite number
			result = (n + 
                           (Math.log((n + 
                                      (Math.log(n) /
                                       Math.log(2))))) / 
                           Math.log(2)).to_i
			#  Display calculated result
			print(" ", result)
			n += 1
		end

	end

end

def main() 
	task = PoliteNumber.new()
	#   Polite number are
	#  —————————————————————————————————————————————
	#   1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
	#   18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
	#   30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
	#   43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
	#   53, 54, 55, 56 etc.
	#  k = 10
	task.politeNo(10)
end

main()

Output

 1 3 5 6 7 9 10 11 12 13
// Scala program for
// Polite number
class PoliteNumber()
{
	def politeNo(k: Int): Unit = {
		var n: Int = 1;
		// Print all initial k Polite number
		while (n <= k)
		{
			// Formula
			//    n + (log (n+log n) 
			//            ²      ²
          
			// Calculate nth Polite number
			var result: Int = (n + 
                               (Math.log((n + 
                                          (Math.log(n) / 
                                           Math.log(2))))) / 
                               Math.log(2)).toInt;
          
			// Display calculated result
			print(" " + result);
			n += 1;
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: PoliteNumber = new PoliteNumber();
		//  Polite number are
		// —————————————————————————————————————————————
		//  1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
		//  18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
		//  30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
		//  43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
		//  53, 54, 55, 56 etc.
  
		// k = 10
		task.politeNo(10);
	}
}

Output

 1 3 5 6 7 9 10 11 12 13
import Foundation;
// Swift 4 program for
// Polite number
class PoliteNumber
{
	func politeNo(_ k: Int)
	{
		var n: Int = 1;
		// Print all initial k Polite number
		while (n <= k)
		{
			// Formula
			//    n + (log (n+log n) 
			//            ²      ²
			// Calculate nth Polite number
			let result: Int = 
              Int((Double(n) + 
                   (log((Double(n) + 
                         (log(Double(n)) / log(2.0))))) / 
                   log(2.0)));
			// Display calculated result
			print(" ", result, terminator: "");
			n += 1;
		}
	}
}
func main()
{
	let task: PoliteNumber = PoliteNumber();
	//  Polite number are
	// —————————————————————————————————————————————
	//  1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
	//  18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
	//  30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
	//  43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
	//  53, 54, 55, 56 etc.
	// k = 10
	task.politeNo(10);
}
main();

Output

  1  3  5  6  7  9  10  11  12  13
// Kotlin program for
// Polite number
class PoliteNumber
{
	fun politeNo(k: Int): Unit
	{
		var n: Int = 1;
		// Print all initial k Polite number
		while (n <= k)
		{
			// Formula
			//    n + (log (n+log n) 
			//            ²      ²
			// Calculate nth Polite number
			val result: Int = 
              (n + (Math.log((n.toDouble() + 
                              (Math.log(n.toDouble()) / 
                               Math.log(2.0))))) / 
               Math.log(2.0)).toInt();
			// Display calculated result
			print(" " + result);
			n += 1;
		}
	}
}
fun main(args: Array < String > ): Unit
{
	val task: PoliteNumber = PoliteNumber();
	//  Polite number are
	// —————————————————————————————————————————————
	//  1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 
	//  18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
	//  30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 
	//  43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 
	//  53, 54, 55, 56 etc.
	// k = 10
	task.politeNo(10);
}

Output

 1 3 5 6 7 9 10 11 12 13

Time Complexity

The time complexity of the program depends on the value of 'k', which represents the number of polite numbers to be generated.

Since we iterate from 'n = 1' to 'k' and perform constant time operations inside the loop, the time complexity can be approximated as O(k).

Output

The output of the program is a list of the first 'k' polite numbers.

For example, if 'k' is 10, the output will be:

1 3 5 6 7 9 10 11 12 13

This indicates that the first 10 polite numbers are 1, 3, 5, 6, 7, 9, 10, 11, 12, and 13.

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