A full cycle is a mathematical term that represents a traversal over a set of non-random numbers. A full cycle implies that every number in the set was chosen exactly once before repeating.

Full cycles are useful in Pseudorandom number generators.

Example 1 (in C++)

Given a random number seed that is greater or equal to zero.
Given a total sample size greater than 1.
Given a prime number that cannot be evenly divided into the total sample size.

A full cycle can be generated with the following logic. Each number in the sample_size should occur once.

unsigned int random_seed = 0;

unsigned int sample_size = 3000;

unsigned int generated_number = random_seed % sample_size;

unsigned int prime_number = 7;

unsigned int increment = prime_number;

for(unsigned int iterator = 0; iterator < sample_size; ++iterator)

{

   generated_number = (generated_number + increment) % sample_size;

}

Example 2 (in C++)

// PseudoRandomTest1.cpp : Defines the entry point for the console application.

include "stdafx.h"




int main(int argc, char* argv[])

{

	unsigned int random_seed = 0;

	const unsigned int sample_size = 3000;

	unsigned int generated_number = random_seed % sample_size;

	unsigned int prime_number = 1;

	unsigned int increment = prime_number;



	bool test[sample_size] = {0};



	for(unsigned int iterator = 0; iterator < sample_size; ++iterator)

	{

		generated_number = (generated_number + increment) % sample_size;

		test[generated_number] = true;



		static bool displayOnce = true;

		if (displayOnce)

		{

			printf("Predicable Random Numbers:\n");

			displayOnce = false;

		}



		printf("%d ", generated_number);

	}



	for(unsigned int iterator = 0; iterator < sample_size; ++iterator)

	{

		if (!test[iterator])

		{

			static bool displayOnce = true;

			if (displayOnce)

			{

				printf("\nYou must have not used a prime number [ERROR]\n");

				displayOnce = false;

			}

			printf("%d ", iterator);

		}

	}

}

Example 2 (in C#)

using System;

using System.Collections.Generic;

using System.Text;



namespace PseudoRandomTest1

{

    class Program

    {

        static Boolean m_DisplayOnce = false;



        static void Main(string[] args)

        {

            const UInt32 random_seed = 0;

            const UInt32 sample_size = 3000;

            UInt32 generated_number = random_seed % sample_size;

            const UInt32 prime_number = 751;

            const UInt32 increment = prime_number;

         

            Boolean[] test = new Boolean[sample_size];

         

            m_DisplayOnce = true;

            for(UInt32 iterator = 0; iterator < sample_size; ++iterator)

            {

                generated_number = (generated_number + increment) % sample_size;

                test[generated_number] = true;



                if (m_DisplayOnce)

                {

                        Console.WriteLine("Predicable Random Numbers:");

                        m_DisplayOnce = false;

                }



                Console.Write("{0} ", generated_number);

            }

         

            m_DisplayOnce = true;

            for(UInt32 iterator = 0; iterator < sample_size; ++iterator)

            {

                if (!test[iterator])

                {

                    if (m_DisplayOnce)

                    {

                        Console.WriteLine;

                        Console.WriteLine("You must have not used a prime number [ERROR]");

                        m_DisplayOnce = false;

                    }

                    Console.Write("{0} ", iterator);

                }

            }

        }

    }

}

See also

• Linear congruential generator
  Linear congruential generator
  A Linear Congruential Generator represents one of the oldest and best-known pseudorandom number generator algorithms. The theory behind them is easy to understand, and they are easily implemented and fast....
  
  
• Prime numbers
• Lists of Prime Numbers