Skip to content
Related Articles

Related Articles

Linear Congruence method for generating Pseudo Random Numbers
  • Last Updated : 11 May, 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: 
 

X_{i + 1} = aX_{i} + c \hspace{0.2cm} mod \hspace{0.2cm} 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



 

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

 

For a = 1, it will be 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++




// C++ implementation of the
// above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to generate random numbers
void 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 Code
int 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




// Java implementation of the above appraoch
import java.util.*;
 
class GFG{
 
// Function to generate random numbers
static 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 code
public 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




# Python3 implementation of the
# above approach
 
# Function to generate random numbers
def 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 Code
if __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#




// C# implementation of the above appraoch
using System;
 
class GFG{
 
// Function to generate random numbers
static 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 code
public 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

Javascript




<script>
 
// Javascript program to implement
// the above approach
 
// Function to generate random numbers
function 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>
Output: 
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.
 

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

My Personal Notes arrow_drop_up
Recommended Articles
Page :