Step by Step solution about How to resolve the algorithm Pseudo-random numbers/Middle-square method step by step in the C++ programming language

The provided code is a C++ implementation of the Middle Square Method, a pseudorandom number generator (PRNG). Let's break down the code step by step:

1. Class Definition:

   • There is a class named MiddleSquare that encapsulates the necessary operations to generate pseudorandom numbers using the Middle Square Method.

2. Private Members:

   • state: An unsigned long variable that represents the current state of the PRNG. It holds the previously generated random number.
   • div and mod: These are also unsigned long variables used for mathematical operations within the Middle Square Method.

3. Constructors:

   • The default constructor is deleted using delete.
   • There is a parameterized constructor that takes two arguments:
     • start: The initial random number used to seed the PRNG.
     • length: The length of the squared number (in digits) used for the next random number generation. It must be an even number.
     • Inside the constructor, it calculates div and mod based on the given length and initializes state with the start value.

4. next() Method:

   • This method generates the next pseudorandom number using the Middle Square Method.
   • It squares state, divides the result by div, and then takes the remainder by mod. This operation effectively produces a number within the range [0, mod-1].
   • The generated random number is then stored in state for the next iteration.

5. main() Function:

   • In the main function:
     • An instance of MiddleSquare is created with an initial random number 675248 and a length of 6.
     • It iterates 5 times, generating and printing the next 5 pseudorandom numbers.

#include <exception>
#include <iostream>

using ulong = unsigned long;

class MiddleSquare {
private:
    ulong state;
    ulong div, mod;
public:
    MiddleSquare() = delete;
    MiddleSquare(ulong start, ulong length) {
        if (length % 2) throw std::invalid_argument("length must be even");
        div = mod = 1;
        for (ulong i=0; i<length/2; i++) div *= 10;
        for (ulong i=0; i<length; i++) mod *= 10;
        state = start % mod;
    }
    
    ulong next() { 
        return state = state * state / div % mod;
    }
};

int main() {
    MiddleSquare msq(675248, 6);
    for (int i=0; i<5; i++)
        std::cout << msq.next() << std::endl;
    return 0;
}