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:
Xi+1 = aXi + 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 approachimport 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.
