Full cycle

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: "); 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(" You must have not used a prime number [ERROR] "); 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); } } }

ee also

* Linear congruential generator
* Prime numbers
* [http://primes.utm.edu/lists/small/millions/ Lists of Prime Numbers]