# Multiplicative Congruence method for generating Pseudo Random Numbers

Multiplicative Congruential Method (Lehmer Method) is a type of linear congruential generator for generating pseudorandom numbers in a specific range. This method can be defined as: where,
X, the sequence of pseudo-random numbers
m ( > 0), the modulus
a (0, m), the multiplier
X0 [0, m), initial value of the sequence – termed as seed

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

Approach:

• Choose the seed value ( X0 ), modulus parameter ( m ), and multiplier term ( a ).
• 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 the indexes follow the Multiplicative Congruential Method to generate the random numbers.

randomNums[i] = (randomNums[i – 1] * a) % m

Finally, return the random numbers.
Below is the implementation of the above approach:

## C++

 // C++ implementation of the   // above approach   #include    using namespace std;      // Function to generate random numbers   void multiplicativeCongruentialMethod(       int Xo, int m, int a,       vector<int>& randomNums,       int noOfRandomNums)   {          // Initialize the seed state       randomNums = Xo;          // Traverse to generate required       // numbers of random numbers       for (int i = 1; i < noOfRandomNums; i++) {              // Follow the multiplicative           // congruential method           randomNums[i]               = (randomNums[i - 1] * a) % m;       }   }      // Driver Code   int main()   {       int Xo = 3; // seed value       int m = 15; // modulus parameter       int a = 7; // multiplier term          // Number of Random numbers       // to be generated       int noOfRandomNums = 10;          // To store random numbers       vector<int> randomNums(noOfRandomNums);          // Function Call       multiplicativeCongruentialMethod(           Xo, m, a, 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  import java.util.*;     class GFG{     // Function to generate random numbers  static void multiplicativeCongruentialMethod(      int Xo, int m, int a,      int[] randomNums,      int noOfRandomNums)  {             // Initialize the seed state      randomNums = Xo;             // Traverse to generate required      // numbers of random numbers      for(int i = 1; i < noOfRandomNums; i++)      {                     // Follow the multiplicative          // congruential method          randomNums[i] = (randomNums[i - 1] * a) % m;      }  }     // Driver code  public static void main(String[] args)  {             // Seed value      int Xo = 3;              // Modulus parameter      int m = 15;              // Multiplier term      int a = 7;              // Number of Random numbers      // to be generated      int noOfRandomNums = 10;             // To store random numbers      int[] randomNums = new int[noOfRandomNums];             // Function Call      multiplicativeCongruentialMethod(Xo, m, a,                                        randomNums,                                       noOfRandomNums);             // Print the generated random numbers      for(int i = 0; i < noOfRandomNums; i++)      {          System.out.print(randomNums[i] + " ");      }  }  }     // This code is contributed by offbeat

## Python3

 # Python3 implementation of the  # above approach     # Function to generate random numbers  def multiplicativeCongruentialMethod(Xo, m, a,                                       randomNums,                                       noOfRandomNums):         # Initialize the seed state      randomNums = 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] * a) % m     # Driver Code  if __name__ == '__main__':             # Seed value      Xo = 3             # Modulus parameter      m = 15             # Multiplier term      a = 7         # Number of Random numbers      # to be generated      noOfRandomNums = 10        # To store random numbers      randomNums =  * (noOfRandomNums)         # Function Call      multiplicativeCongruentialMethod(Xo, m, a,                                       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 multiplicativeCongruentialMethod(      int Xo, int m, int a,      int[] randomNums,      int noOfRandomNums)  {             // Initialize the seed state      randomNums = Xo;             // Traverse to generate required      // numbers of random numbers      for(int i = 1; i < noOfRandomNums; i++)      {                     // Follow the multiplicative          // congruential method          randomNums[i] = (randomNums[i - 1] * a) % m;      }  }     // Driver code  public static void Main(String[] args)  {             // Seed value      int Xo = 3;              // Modulus parameter      int m = 15;              // Multiplier term      int a = 7;              // Number of Random numbers      // to be generated      int noOfRandomNums = 10;             // To store random numbers      int[] randomNums = new int[noOfRandomNums];             // Function call      multiplicativeCongruentialMethod(Xo, m, a,                                        randomNums,                                       noOfRandomNums);             // Print the generated random numbers      for(int i = 0; i < noOfRandomNums; i++)      {          Console.Write(randomNums[i] + " ");      }  }  }     // This code is contributed by sapnasingh4991

Output:

3 6 12 9 3 6 12 9 3 6


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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