Java Program to Implement the Linear Congruential Generator for Pseudo Random Number Generation

Linear Congruential Method is a class of Pseudo-Random Number Generator (PRNG) algorithms used for generating sequences of random-like numbers in a specific range. This method can be defined as: 

                                                  X_i+1 = aX_i + c mod m

where,

X, is the sequence of pseudo-random numbers

m, ( > 0) the modulus

a, (0, m) the multiplier

c, (0, m) the increment

X0,  [0, m) – Initial value of sequence known as seed

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

• For a = 1, it will be the additive congruence method.
• For c = 0, it will be the multiplicative congruence method.

Approach:  

• The seed value X0 is chosen, Modulus parameter m, Multiplier term a, 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, the vector is considered) of size noOfRandomNums.
• Initialize the 0th index of the vector with the seed value.
• For the rest of the indexes follow the Linear Congruential Method to generate the random numbers.

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

• Finally, return the random numbers.

Below is the implementation of the above approach:

// Java implementation of the above approach
import java.util.*;

class GFG {

    // Function to generate random numbers
    static void lcm(int seed, int mod, int multiplier,
                    int inc, int[] randomNums,
                    int noOfRandomNum)
    {

        // Initialize the seed state
        randomNums[0] = seed;

        // Traverse to generate required
        // numbers of random numbers
        for (int i = 1; i < noOfRandomNum; i++) {

            // Follow the linear congruential method
            randomNums[i]
                = ((randomNums[i - 1] * multiplier) + inc)
                  % m;
        }
    }

    // Driver code
    public static void main(String[] args)
    {

        // Seed value
        int seed = 5;

        // Modulus parameter
        int mod = 7;

        // Multiplier term
        int multiplier = 3;

        // Increment term
        int inc = 3;

        // Number of Random numbers
        // to be generated
        int noOfRandomNum = 10;

        // To store random numbers
        int[] randomNums = new int[noOfRandomNum];

        // Function Call
        lcm(seed, mod, multiplier, inc, randomNums,
            noOfRandomNum);

        // Print the generated random numbers
        for (int i = 0; i < noOfRandomNum; i++) {
            System.out.print(randomNums[i] + " ");
        }
    }
}

5 4 1 6 0 3 5 4 1 6

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