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Additive Congruence method for generating Pseudo Random Numbers
  • Last Updated : 05 Aug, 2020

Additive Congruential Method is a type of linear congruential generator for generating pseudorandom numbers in a specific range. This method can be defined as: 

X_{i + 1} = X_{i} + c \hspace{0.2cm} mod \hspace{0.2cm} m

where,  

X, the sequence of pseudo-random numbers
m ( > 0), the modulus
c [0, m), the increment
X0 [0, m), initial value of the sequence – termed as seed

m, c, X0 should be chosen appropriately to get a period almost equal to m.



 

Approach: 

  • Choose the seed value X0, modulus parameter m, and increment term c.
  • Initialize the required amount of random numbers to generate (say, an integer variable noOfRandomNums).
  • Define a storage to keep the genrated random numbers (here, vector is considered) of size noOfRandomNums.
  • Initialize the 0th index of the vector with the seed value.
  • For rest of indexes follow the Additive Congruential Method to generate the random numbers.

randomNums[i] = (randomNums[i – 1] + c) % m 

Finally, return the generated random numbers.

Below is the implementation of the above approach: 

C++




// C++ implementation of the
// above approach
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to generate random numbers
void additiveCongruentialMethod(
    int Xo, int m, int c,
    vector<int>& randomNums,
    int noOfRandomNums)
{
  
    // Initialize the seed state
    randomNums[0] = Xo;
  
    // Traverse to generate required
    // numbers of random numbers
    for (int i = 1; i < noOfRandomNums; i++) {
  
        // Follow the additive
        // congruential method
        randomNums[i]
            = (randomNums[i - 1] + c)
              % m;
    }
}
  
// Driver Code
int main()
{
    int Xo = 3; // seed value
    int m = 15; // modulus parameter
    int c = 2; // increment term
  
    // Number of Random numbers
    // to be generated
    int noOfRandomNums = 20;
  
    // To store random numbers
    vector<int> randomNums(noOfRandomNums);
  
    // Function Call
    additiveCongruentialMethod(
Xo, m, c,
                               randomNums,
 noOfRandomNums);
  
    // Print the generated random numbers
    for (int i = 0; i < noOfRandomNums; i++) {
        cout << randomNums[i] << " ";
    }
  
    return 0;
}

Java




// Java implementation of the
// above approach
class GFG{
  
// Function to generate random numbers
static void additiveCongruentialMethod(
    int Xo, int m, int c,
    int []randomNums,
    int noOfRandomNums)
{
  
    // Initialize the seed state
    randomNums[0] = Xo;
  
    // Traverse to generate required
    // numbers of random numbers
    for(int i = 1; i < noOfRandomNums; i++) 
    {
  
        // Follow the additive
        // congruential method
        randomNums[i] = (randomNums[i - 1] + c) % m;
    }
}
  
// Driver Code
public static void main(String[] args)
{
      
    // Seed value
    int Xo = 3
      
    // Modulus parameter
    int m = 15
      
    // Increment term
    int c = 2
  
    // Number of Random numbers
    // to be generated
    int noOfRandomNums = 20;
  
    // To store random numbers
    int []randomNums = new int[noOfRandomNums];
  
    // Function Call
    additiveCongruentialMethod(Xo, m, c,
                               randomNums,
                               noOfRandomNums);
  
    // Print the generated random numbers
    for(int i = 0; i < noOfRandomNums; i++)
    {
        System.out.print(randomNums[i] + " ");
    }
}
}
  
// This code is contributed by PrinciRaj1992

Python3




# Python3 implementation of the
# above approach
  
# Function to generate random numbers
def additiveCongruentialMethod(Xo, m, c, 
                               randomNums, 
                               noOfRandomNums):
  
    # Initialize the seed state
    randomNums[0] = Xo
  
    # Traverse to generate required
    # numbers of random numbers
    for i in range(1, noOfRandomNums):
          
        # Follow the linear congruential method
        randomNums[i] = (randomNums[i - 1] + c) % m
  
# Driver Code
if __name__ == '__main__':
      
    # Seed value
    Xo = 3
      
    # Modulus parameter
    m = 15 
      
    # Multiplier term
    c = 2 
  
    # Number of Random numbers
    # to be generated
    noOfRandomNums = 20
  
    # To store random numbers
    randomNums=[0] * (noOfRandomNums)
  
    # Function Call
    additiveCongruentialMethod(Xo, m, c, 
                               randomNums, 
                               noOfRandomNums)
  
    # Print the generated random numbers
    for i in randomNums:
        print(i, end = " ")
  
# This code is contributed by mohit kumar 29

C#




// C# implementation of the
// above approach
using System;
  
class GFG{
  
// Function to generate random numbers
static void additiveCongruentialMethod(
    int Xo, int m, int c,
    int []randomNums,
    int noOfRandomNums)
{
  
    // Initialize the seed state
    randomNums[0] = Xo;
  
    // Traverse to generate required
    // numbers of random numbers
    for(int i = 1; i < noOfRandomNums; i++) 
    {
  
        // Follow the additive
        // congruential method
        randomNums[i] = (randomNums[i - 1] + c) % m;
    }
}
  
// Driver Code
public static void Main(String[] args)
{
      
    // Seed value
    int Xo = 3; 
      
    // Modulus parameter
    int m = 15; 
      
    // Increment term
    int c = 2; 
  
    // Number of Random numbers
    // to be generated
    int noOfRandomNums = 20;
  
    // To store random numbers
    int []randomNums = new int[noOfRandomNums];
  
    // Function call
    additiveCongruentialMethod(Xo, m, c,
                               randomNums,
                               noOfRandomNums);
  
    // Print the generated random numbers
    for(int i = 0; i < noOfRandomNums; i++)
    {
        Console.Write(randomNums[i] + " ");
    }
}
}
  
// This code is contributed by PrinciRaj1992
Output: 
3 5 7 9 11 13 0 2 4 6 8 10 12 14 1 3 5 7 9 11

The literal meaning of pseudo is false. These random numbers are called pseudo because some known arithmetic procedure is utilized to generate. Even the generated sequence forms a pattern hence the generated number seems to be random but may not be truly random.
 

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