Multiplicative Congruence method for generating Pseudo Random Numbers
Last Updated :
08 Feb, 2022
Multiplicative Congruential Method (Lehmer 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
a (0, m), the multiplier
X0 [0, m), initial value of the sequence – termed as seed
m, a, and X0 should be chosen appropriately to get a period almost equal to m.
Approach:
- Choose the seed value ( X0 ), modulus parameter ( m ), and multiplier term ( a ).
- 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 Multiplicative Congruential Method to generate the random numbers.
randomNums[i] = (randomNums[i – 1] * a) % m
Finally, return the random numbers.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
void multiplicativeCongruentialMethod(
int Xo, int m, int a,
vector< int >& randomNums,
int noOfRandomNums)
{
randomNums[0] = Xo;
for ( int i = 1; i < noOfRandomNums; i++) {
randomNums[i]
= (randomNums[i - 1] * a) % m;
}
}
int main()
{
int Xo = 3;
int m = 15;
int a = 7;
int noOfRandomNums = 10;
vector< int > randomNums(noOfRandomNums);
multiplicativeCongruentialMethod(
Xo, m, a, randomNums,
noOfRandomNums);
for ( int i = 0; i < noOfRandomNums; i++) {
cout << randomNums[i] << " " ;
}
return 0;
}
|
Java
import java.util.*;
class GFG{
static void multiplicativeCongruentialMethod(
int Xo, int m, int a,
int [] randomNums,
int noOfRandomNums)
{
randomNums[ 0 ] = Xo;
for ( int i = 1 ; i < noOfRandomNums; i++)
{
randomNums[i] = (randomNums[i - 1 ] * a) % m;
}
}
public static void main(String[] args)
{
int Xo = 3 ;
int m = 15 ;
int a = 7 ;
int noOfRandomNums = 10 ;
int [] randomNums = new int [noOfRandomNums];
multiplicativeCongruentialMethod(Xo, m, a,
randomNums,
noOfRandomNums);
for ( int i = 0 ; i < noOfRandomNums; i++)
{
System.out.print(randomNums[i] + " " );
}
}
}
|
Python3
def multiplicativeCongruentialMethod(Xo, m, a,
randomNums,
noOfRandomNums):
randomNums[ 0 ] = Xo
for i in range ( 1 , noOfRandomNums):
randomNums[i] = (randomNums[i - 1 ] * a) % m
if __name__ = = '__main__' :
Xo = 3
m = 15
a = 7
noOfRandomNums = 10
randomNums = [ 0 ] * (noOfRandomNums)
multiplicativeCongruentialMethod(Xo, m, a,
randomNums,
noOfRandomNums)
for i in randomNums:
print (i, end = " " )
|
C#
using System;
class GFG{
static void multiplicativeCongruentialMethod(
int Xo, int m, int a,
int [] randomNums,
int noOfRandomNums)
{
randomNums[0] = Xo;
for ( int i = 1; i < noOfRandomNums; i++)
{
randomNums[i] = (randomNums[i - 1] * a) % m;
}
}
public static void Main(String[] args)
{
int Xo = 3;
int m = 15;
int a = 7;
int noOfRandomNums = 10;
int [] randomNums = new int [noOfRandomNums];
multiplicativeCongruentialMethod(Xo, m, a,
randomNums,
noOfRandomNums);
for ( int i = 0; i < noOfRandomNums; i++)
{
Console.Write(randomNums[i] + " " );
}
}
}
|
Javascript
<script>
function multiplicativeCongruentialMethod(
Xo, m, a,
randomNums, noOfRandomNums)
{
randomNums[0] = Xo;
for (let i = 1; i < noOfRandomNums; i++)
{
randomNums[i] = (randomNums[i - 1] * a) % m;
}
}
let Xo = 3;
let m = 15;
let a = 7;
let noOfRandomNums = 10;
let randomNums = new Array(noOfRandomNums).fill(0);
multiplicativeCongruentialMethod(Xo, m, a,
randomNums,
noOfRandomNums);
for (let i = 0; i < noOfRandomNums; i++)
{
document.write(randomNums[i] + " " );
}
</script>
|
Output: 3 6 12 9 3 6 12 9 3 6
Time Complexity: O(N), where N is the total number of random numbers we need to generate.
Auxiliary Space: O(1)
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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