C++ Exercises: Create the first twenty Hamming numbers

Last update on December 20 2024 12:24:37 (UTC/GMT +8 hours)

Write a C++ program to create the first twenty Hamming numbers.

Sample Solution:

C++ Code:

#include <iostream>
#include <cmath>
using namespace std;

// Function to check if a number is a Hamming number
bool chkHhamming(int n) {
    if (n == 1) return true; // Hamming number condition for 1

    // Checking divisibility by 2, 3, or 5, the prime factors of Hamming numbers
    if (n % 2 == 0 or n % 3 == 0 or n % 5 == 0) {
        for (int i = 2; i * i < n; ++i) {
            // Check for divisibility by prime factors
            if (n % i == 0) {
                if (i % 2 != 0 and i % 3 != 0 and i % 5 != 0) return false;
            }
            // Check for divisibility by the other factor
            if (n % (n / i) == 0) {
                if ((n / i) % 2 != 0 and (n / i) % 3 != 0 and (n / i) % 5 != 0) return false;
            }
        }
        return true; // If no issues, it's a Hamming number
    }
    return false; // If not divisible by 2, 3, or 5, it's not a Hamming number
}

int main() {
    int n, j;
    cout << "\n\n Find first twenty Hamming numbers: \n";
    cout << " ---------------------------------------\n";
    cout << " Input the upper limit of Hamming numbers: ";
    cin >> n; // Input the upper limit of Hamming numbers
    cout << " The Hamming numbers are: " << endl;

    // Loop to find and print the first 'n' Hamming numbers
    while (j <= n) {
        int count = 0;
        int i = 1;
        bool first = true;

        // Loop to find 'n' Hamming numbers
        while (count < n) {
            if (chkHhamming(i)) { // If 'i' is a Hamming number
                if (not first) cout << ","; // Display ',' for separation
                cout << i; // Display the Hamming number
                ++count; // Increment count of Hamming numbers found
                first = false;
            }
            ++i; // Move to the next number
        }
        j++; // Increment j to control the while loop
    }
    cout << endl; // End of the program
}

Sample Output:

 Find first twenty Hamming numbers:                                    
 ---------------------------------------                               
 Input the upper limit of Hamming numbers: 20                          
 The Hamming numbers are:                                              
1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10,1
2,15,16,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,
27,30,32,361,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,361,2,3,4,5
,6,8,9,10,12,15,16,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10,12,15,16,1
8,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,
361,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10
,12,15,16,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10,12,15,16,18,20,24,2
5,27,30,32,361,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,361,2,3,4
,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10,12,15,16
,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,3
2,361,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,
10,12,15,16,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10,12,15,16,18,20,24
,25,27,30,32,361,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,361,2,3
,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10,12,15,
16,18,20,24,25,27,30,32,361,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30
,32,36

Flowchart:

C++ Code Editor:

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