C++ Program to Generate Random Numbers Using Middle Square Method

The middle-square method is one of the simplest methods of generating random numbers. This method will either begin repeatedly generating the same number or cycle to a previous number in the sequence and loop indefinitely. For a generator of n-digit random numbers, the period can be no longer than the specified n(number of digits). If the middle n digits are all zeroes, the generator then generates zeroes forever.

In this article, we will implement a C++ program to generate ten 4-digits random number using the middle-square method.

Steps for Middle-Square Random Number Generation

The steps for generating random numbers using the middle-square method are as follows:

• We have defined an array a[] that is later used to remove and extract the specified number of digits from the generated number.
• The middleSquareNumber() function is used to generate a random number of specified digits based on the previous number. It takes two arguments: the number and the number of digits.
• Inside the function, using sqn = sqn/a[t], we remove the extra digits and bring the middle digits to the front.
• The for loop then extracts n number of middle digits and reconstructs the next number from them and the next_number is returned.
• In the main() function, we have used the srand(time(0)) function to ensure different results is generated on each run.
• The if/else statement checks that n(digit) is within the range of 1 to 8. A random number is generated using the rand() function in this defined range.
• The for loop calls the middleSquareNumber() function to generate 10 random numbers.

C++ Program for Middle-Square Random Number Generation

The following code implements above steps using the middle-square method to generate 4-digits random numbers.

#include <iostream>
#include <cstdlib> // For rand() and srand()
#include <ctime>   // For time() to seed rand()
using namespace std;

int a[] = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000 };

int middleSquareNumber(int number, int digit) {
    int sqn = number * number;
    int next_number = 0;
    int t = digit / 2;

    sqn = sqn / a[t]; // Shift the squared number to get middle digits

    for (int i = 0; i < digit; i++) {
        next_number += (sqn % 10) * a[digit - i - 1]; // Get the middle digits and rebuild the next number
        sqn = sqn / 10;
    }

    return next_number;
}

int main() {
    // Seed the random number generator with current time
    srand(time(0)); 

    // Set the number of digits 
    int n = 4; 

    // Ensure 'n' is within bounds of the array a[] (1 to 8 digits)
    if (n < 1 || n > 8) {
        cout << "Please set 'n' between 1 and 8." << endl;
        return 1;
    }

    // Calculate the range for the random number based on 'n'
    int start = a[n - 1];
    int end = a[n];
    
    // Generate the first random number within the desired range
    int number = (rand() % (end - start)) + start;

    cout << "The " << n << " digit random numbers are:\n" << number << ", ";
    for (int i = 1; i < 10; i++) { // Generate and print the next 9 random numbers
        number = middleSquareNumber(number, n);
        cout << number << ", ";
    }
    cout << "..." << endl;

    return 0;
}

The output of the above code is:

The 4 digit random numbers are:
5629, 6586, 3573, 3667, 8644, 7817, 4501, 952, 3609, 8420, ...