Additive Congruential Method is a type of linear congruential generator for generating pseudorandom numbers in a specific range. This method can be defined as:
where,
X, the sequence of pseudo-random numbers
m ( > 0), the modulus
c [0, m), the increment
X0 [0, m), initial value of the sequence – termed as seedm, c, X0 should be chosen appropriately to get a period almost equal to m.
Approach:
- Choose the seed value X0, modulus parameter m, 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, vector is considered) of size noOfRandomNums.
- Initialize the 0th index of the vector with the seed value.
- For rest of indexes follow the Additive Congruential Method to generate the random numbers.
randomNums[i] = (randomNums[i – 1] + c) % m
Finally, return the generated 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 numbersvoid additiveCongruentialMethod( int Xo, int m, 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 additive // congruential method randomNums[i] = (randomNums[i - 1] + c) % m; }}// Driver Codeint main(){ int Xo = 3; // seed value int m = 15; // modulus parameter int c = 2; // increment term // Number of Random numbers // to be generated int noOfRandomNums = 20; // To store random numbers vector<int> randomNums(noOfRandomNums); // Function Call additiveCongruentialMethod(Xo, m, 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 approachclass GFG{// Function to generate random numbersstatic void additiveCongruentialMethod( int Xo, int m, 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 additive // congruential method randomNums[i] = (randomNums[i - 1] + c) % m; }}// Driver Codepublic static void main(String[] args){ // Seed value int Xo = 3; // Modulus parameter int m = 15; // Increment term int c = 2; // Number of Random numbers // to be generated int noOfRandomNums = 20; // To store random numbers int []randomNums = new int[noOfRandomNums]; // Function Call additiveCongruentialMethod(Xo, m, 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 PrinciRaj1992 |
Python3
# Python3 implementation of the# above approach# Function to generate random numbersdef additiveCongruentialMethod(Xo, m, 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] + c) % m# Driver Codeif __name__ == '__main__': # Seed value Xo = 3 # Modulus parameter m = 15 # Multiplier term c = 2 # Number of Random numbers # to be generated noOfRandomNums = 20 # To store random numbers randomNums=[0] * (noOfRandomNums) # Function Call additiveCongruentialMethod(Xo, m, 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 approachusing System;class GFG{// Function to generate random numbersstatic void additiveCongruentialMethod( int Xo, int m, 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 additive // congruential method randomNums[i] = (randomNums[i - 1] + c) % m; }}// Driver Codepublic static void Main(String[] args){ // Seed value int Xo = 3; // Modulus parameter int m = 15; // Increment term int c = 2; // Number of Random numbers // to be generated int noOfRandomNums = 20; // To store random numbers int []randomNums = new int[noOfRandomNums]; // Function call additiveCongruentialMethod(Xo, m, c, randomNums, noOfRandomNums); // Print the generated random numbers for(int i = 0; i < noOfRandomNums; i++) { Console.Write(randomNums[i] + " "); }}}// This code is contributed by PrinciRaj1992 |
Javascript
<script>// Javascript program to implement// the above approach// Function to generate random numbersfunction additiveCongruentialMethod( Xo, m, 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 additive // congruential method randomNums[i] = (randomNums[i - 1] + c) % m; }} // Driver Code // Seed value let Xo = 3; // Modulus parameter let m = 15; // Increment term let c = 2; // Number of Random numbers // to be generated let noOfRandomNums = 20; // To store random numbers let randomNums = new Array(noOfRandomNums).fill(0); // Function Call additiveCongruentialMethod(Xo, m, c, randomNums, noOfRandomNums); // Print the generated random numbers for(let i = 0; i < noOfRandomNums; i++) { document.write(randomNums[i] + " "); }</script> |
Output:
3 5 7 9 11 13 0 2 4 6 8 10 12 14 1 3 5 7 9 11
Time complexity: O(N) where N is the count of random numbers to be generated.
Auxiliary space: O(N)
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.
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