生成伪随机数的线性同余方法

线性同余方法是一类伪随机数生成器(PRNG)算法，用于生成特定范围内的类随机数序列。此方法可以定义为：

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

where,

 

X, is the sequence of pseudo-random numbers
m, ( > 0) the modulus
a, (0, m) the multiplier
c, (0, m) the increment
X_0,  [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.

 

对于a = 1，这将是加法全等法。
对于c = 0，它将是乘法同余方法。

方法：

• 选择种子值X _0，模数参数m，乘数项a和增量项c。
• 初始化所需数量的随机数以生成(例如，整数变量noOfRandomNums )。
• 定义一个存储区，以保持生成的随机数(此处为vector )的大小为noOfRandomNums 。
• 用种子值初始化向量的^第0^个索引。
• 对于其余的索引，请遵循线性同余方法来生成随机数。

randomNums[i] = ((randomNums[i – 1] * a) + c) % m 

最后，返回随机数。
下面是上述方法的实现：

C++

// C++ implementation of the
// above approach
 
#include 
using namespace std;
 
// Function to generate random numbers
void linearCongruentialMethod(
    int Xo, int m, int a, int c,
    vector& 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 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

 
// 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] + " ");
    }
 

输出：

5 4 1 6 0 3 5 4 1 6

伪的字面量意思是假的。这些随机数被称为伪数，因为利用了一些已知的算术过程来生成。即使生成的序列也形成一个模式，因此生成的数字似乎是随机的，但可能不是真正的随机。