# Additive Congruence method for generating Pseudo Random Numbers

• Last Updated : 11 Oct, 2022

Additive Congruential 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
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 storage to keep the generated 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  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

## Javascript

 

Output:

3 5 7 9 11 13 0 2 4 6 8 10 12 14 1 3 5 7 9 11

Time complexity: O(N) where N is the count of random numbers to be generated.
Auxiliary space: O(N)

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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