Linear Congruence method for generating Pseudo Random Numbers

17 Jul, 2021
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: 
where,
X, is the sequence of pseudo-random numbersm, ( > 0) the modulusa, (0, m) the multiplierc, (0, m) the incrementX0,  [0, m) – Initial value of sequence known as seed
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: 
Choose the seed value X0, 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 a 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 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:
C++
Java
Python3
C#
Javascript
// C++ implementation of the// above approach #include <bits/stdc++.h>using namespace std; // Function to generate random numbersvoid linearCongruentialMethod(    int Xo, int m, int a, 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 linear congruential method        randomNums[i]            = ((randomNums[i - 1] * a) + c) % m;    }} // Driver Codeint main(){    int Xo = 5; // Seed value    int m = 7; // Modulus parameter    int a = 3; // Multiplier term    int c = 3; // Increment term     // Number of Random numbers    // to be generated    int noOfRandomNums = 10;     // To store random numbers    vector<int> randomNums(        noOfRandomNums);     // Function Call    linearCongruentialMethod(        Xo, m, a, c,        randomNums, noOfRandomNums);     // Print the generated random numbers    for (int i = 0; i < noOfRandomNums; i++) {        cout << randomNums[i] << " ";    }     return 0;}
// Java implementation of the above approachimport java.util.*; class GFG{ // Function to generate random numbersstatic void linearCongruentialMethod(int Xo, int m,                                     int a, 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 linear congruential method        randomNums[i] = ((randomNums[i - 1] * a) + c) % m;    }} // Driver codepublic static void main(String[] args){         // Seed value    int Xo = 5;         // Modulus parameter    int m = 7;         // Multiplier term    int a = 3;         // Increment term    int c = 3;         // Number of Random numbers    // to be generated    int noOfRandomNums = 10;         // To store random numbers    int[] randomNums = new int[noOfRandomNums];         // Function Call    linearCongruentialMethod(Xo, m, a, 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 offbeat
# Python3 implementation of the# above approach # Function to generate random numbersdef linearCongruentialMethod(Xo, m, a, 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] * a) +                                         c) % m # Driver Codeif __name__ == '__main__':         # Seed value    Xo = 5         # Modulus parameter    m = 7         # Multiplier term    a = 3         # Increment term    c = 3     # Number of Random numbers    # to be generated    noOfRandomNums = 10     # To store random numbers    randomNums = [0] * (noOfRandomNums)     # Function Call    linearCongruentialMethod(Xo, m, a, c,                             randomNums,                             noOfRandomNums)     # Print the generated random numbers    for i in randomNums:        print(i, end = " ") # This code is contributed by mohit kumar 29
// C# implementation of the above approachusing System; class GFG{ // Function to generate random numbersstatic void linearCongruentialMethod(int Xo, int m,                                     int a, 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 linear congruential method        randomNums[i] = ((randomNums[i - 1] * a) + c) % m;    }} // Driver codepublic static void Main(String[] args){         // Seed value    int Xo = 5;         // Modulus parameter    int m = 7;         // Multiplier term    int a = 3;         // Increment term    int c = 3;         // Number of Random numbers    // to be generated    int noOfRandomNums = 10;         // To store random numbers    int[] randomNums = new int[noOfRandomNums];         // Function call    linearCongruentialMethod(Xo, m, a, c,                             randomNums,                             noOfRandomNums);         // Print the generated random numbers    for(int i = 0; i < noOfRandomNums; i++)    {        Console.Write(randomNums[i] + " ");    }}} // This code is contributed by sapnasingh4991
<script> // Javascript program to implement// the above approach // Function to generate random numbersfunction linearCongruentialMethod(Xo, m,  a, c,                     randomNums, noOfRandomNums){           // Initialize the seed state    randomNums[0] = Xo;       // Traverse to generate required    // numbers of random numbers    for(let i = 1; i < noOfRandomNums; i++)    {                   // Follow the linear congruential method        randomNums[i] = ((randomNums[i - 1] * a) + c) % m;    }}     // Driver Code                 // Seed value    let Xo = 5;           // Modulus parameter    let m = 7;           // Multiplier term    let a = 3;           // Increment term    let c = 3;           // Number of Random numbers    // to be generated    let noOfRandomNums = 10;           // To store random numbers    let randomNums = new Array(noOfRandomNums).fill(0);           // Function Call    linearCongruentialMethod(Xo, m, a, c,                             randomNums,                             noOfRandomNums);           // Print the generated random numbers    for(let i = 0; i < noOfRandomNums; i++)    {        document.write(randomNums[i] + " ");    } </script>
5 4 1 6 0 3 5 4 1 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. 
mohit kumar 29
offbeat
sapnasingh4991
chinmoy1997pal
saurabh1990aror
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