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

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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

// 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] + " ");
        }
    }
}

Output

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.