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, 24 May 2002 58.3K 426 12
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Testing the c# random generator numbers

Sample Image - snap.jpg

Introduction

The goal of the application is to test the C# random generator numbers. There are three sub applications that cover all the aspects of a random generator:

  1. Testing the randomness of C# generator.
  2. A comparison between two methods of generating random numbers.
  3. A little game.

For the simplicity of the formalism let's make the following conventions:

  • RI - An ideal random numbers generator.
  • R - C# random generator.
  • P(n) - The set of permutations of n elements .

Details

  1. Assume we want to want to apply the test on a permutation of n numbers: We generate the permutation using the brute method. We call the R even it can generate a number that we already have. We retain the number of the calls(NC) of G . It's quite simple to demonstrate that RI will generate our sequence calling [n*(1+1/2+.....1/n)] times his generator. So we can calculate the error of G:abs(n*(1+1/2+.....1/n)-NC) / ([n*(1+1+1/2+......1/n)]. The rest you can see in the application...
  2. The brute method spent quiet a lot of time for generating a permutation. Take a lock at the following method that calls only n times R.A. The method is called replace method.
    public void  generate()    // the algorithm is verry simple
            {
                int k,count;   // fist i initiliaze an array of
                // n number with the value:x[i]=i(i>0;i<n)
                        
                                         
                for(int i=1;i<=n;i++)
                    etalon[i]=i;
    
                count=n;
                while (count!=0)  //i call the generator only n times
                {   // each time i generate a number(k)
                    // i move the last number of the initial
                    // array on the k position , i retain the value
                    // that i have found here and then 
                    // i remove the last element
                    k=gen.Next(count)+1;
                    a[n-count+1]=etalon[k];
                    etalon[k]=etalon[count];
                    count--;
                }
    
            }
    
    But what interests us is the efficatity of those two methods (brute and replace) The efficatity is the number of different permutation those method can generate in a imitated period of time. You can see the efficatity between those two methods running the application. For counting the number of different permutation I use a bijection between P(n) and n! (the number of permutation of n elements).

    See the bijection for n=3 lock like this :-

    1 2 3----->1
    2 3 2----->2
    2 1 3----->3
    2 3 1----->4
    3 1 2----->5
    3 2 1----->6

    Here's the code of the bijection

    private long fact(int n)   //a method for calculating n!
            {
                if (n==0) return 1;
                else return(n*fact(n-1));
            }
            public long getposition()     // the main method of the class
            {                             // it's calculate the bijection
                // from P(n) to [1..n!]
                int i,j,k,rest,cate,ii;
                long suma=0;
                for( i=1;i<=n;i++)
                {
                    
                    for(j=i;j<=n;j++)
                    {
                        cate=0;
                        for(k=i;k<=n;k++)
                            if (a[j]>a[k]) cate++;
                        a[j]=cate+1;
                    }
                    
                    suma+=fact(n-i)*(a[i]-1);
            
                }
                return suma+1;
            }
    
  3. I implemented a simple game. The user picks up an array and tells the computer the length of the array and the sum of the elements. The elements must be greater than 0 and they can repeat .The computer will put "yes/no" questions and will try to guess the array. I know that are lot's more algorithm to make the computer play better (minimum number of questions), but i use a pure random algorithm (almost all the decisions are made using a random asign). I also calculate at the begin of each game the number of the solutions, using a simple recursive method.
    public long dami(int n,int sume,int lol)
            {                                       //calculate the number
                long k1=0;                         //of solution in for 
                long k2=0;
                int j,restinpeace;                  //a given lenght
                if (n==1) if (lol<=sume) return 1;  //and a given sum
                          else return 0;            // the initial call
                //of the function will be
                // dami(n,sume,1)
                k1=dami(n-1,sume-lol,lol);
                restinpeace=sume-(lol+1)*(n-1);
                for(j=lol+1;j<=restinpeace;j++)
                    k2+=dami(n-1,sume-j,j);
                return k1+k2;
            }
    
    

Sorry for my English

License

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About the Author

Vlad Beu
Web Developer
Romania Romania
Born 1980,Romania

Comments and Discussions

 
GeneralApplying The Permutation Pin
Fairuz Azah21-Jul-04 16:27
memberFairuz Azah21-Jul-04 16:27 
GeneralThank you Pin
Beo&Vasti25-May-02 9:07
memberBeo&Vasti25-May-02 9:07 
GeneralRe: Huh???? Pin
Paul Barrass11-Jun-02 11:25
memberPaul Barrass11-Jun-02 11:25 
GeneralRe: Nope, you are not going crazy :-) Pin
Nishant S2-Dec-03 15:53
staffNishant S2-Dec-03 15:53 
GeneralYour English... Pin
Blake Coverett24-May-02 17:05
memberBlake Coverett24-May-02 17:05 
GeneralRe: Your English... Pin
Chris Maunder24-May-02 21:46
adminChris Maunder24-May-02 21:46 

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