Program 3 BCA Madras University BCA Object Oriented Programming using C++ Practical Madras University Program 3Design and implement a class that represents a Harmonic Progression (HP). Implement functions to do the following: a. Generate the HP up to a specified number of terms b. Calculate the sum of the HP to n terms and to infinity c. Generate the nth term of the HP d. Generate the corresponding Arithmetic Progression. (Design and implement a class that encapsulates an AP, and allow the HP class to use its facilities by implementing friend functions.)

 

BCA

Object Oriented Programming using C++ Practical

Madras University 

Program 3

Design and implement a class that represents a Harmonic Progression (HP). Implement functions to do the following: a. Generate the HP up to a specified number of terms b. Calculate the sum of the HP to n terms and to infinity c. Generate the nth term of the HP d. Generate the corresponding Arithmetic Progression. (Design and implement a class that encapsulates an AP, and allow the HP class to use its facilities by implementing friend functions.)

SOURCE CODE:

#include <iostream>

#include <vector>

#include <limits>

#include <cmath> // For log and pow functions

using namespace std;

class ArithmeticProgression {

private:

    double a; // First term

    double d; // Common difference

public:

    ArithmeticProgression(double first_term, double common_difference)

        : a(first_term), d(common_difference) {}

    double nth_term(int n) const {

        return a + (n - 1) * d;

    }

    double sum_to_n_terms(int n) const {

        return n * (2 * a + (n - 1) * d) / 2;

    }

    vector<double> generate_terms(int n) const {

        vector<double> terms;

        for (int i = 1; i <= n; ++i) {

            terms.push_back(nth_term(i));

        }

        return terms;

    }

    friend class HarmonicProgression;

};

class HarmonicProgression {

private:

    ArithmeticProgression ap;

public:

    HarmonicProgression(double first_term, double common_difference)

        : ap(first_term, common_difference) {}

    double nth_term(int n) const {

        return 1.0 / ap.nth_term(n);

    }

    vector<double> generate_terms(int n) const {

        vector<double> terms;

        for (int i = 1; i <= n; ++i) {

            terms.push_back(nth_term(i));

        }

        return terms;

    }

    double sum_to_n_terms(int n) const {

        double sum = 0;

        for (int i = 1; i <= n; ++i) {

            sum += nth_term(i);

        }

        return sum;

    }

    double sum_to_infinity() const {

        if (ap.d == 0) {

            return numeric_limits<double>::infinity();

        }

        return numeric_limits<double>::infinity();

    }

    ArithmeticProgression corresponding_ap() const {

        return ap;

    }

};

int main() {

    HarmonicProgression hp(1, 1);

    int n;

    cout<<"Enter number of HP terms: ";

    cin>>n;

    cout << "First " << n << " terms of HP: ";

    vector<double> hp_terms = hp.generate_terms(n);

    for (double term : hp_terms) {

        cout << term << " ";

    }

    cout << std::endl;

    cout << "Sum of first " << n << " terms of HP: " << hp.sum_to_n_terms(n) << endl;

    cout << n << "th term of HP: " << hp.nth_term(n) << endl;

    cout << "Sum of HP to infinity: " << hp.sum_to_infinity() << endl;

    ArithmeticProgression ap = hp.corresponding_ap();

    cout << "First " << n << " terms of corresponding AP: ";

    vector<double> ap_terms = ap.generate_terms(n);

    for (double term : ap_terms) {

        cout << term << " ";

    }

    cout << endl;

    cout << "Sum of first " << n << " terms of AP: " << ap.sum_to_n_terms(n) << endl;

    cout << n << "th term of AP: " << ap.nth_term(n) << endl;

    return 0;

}

Explanation:

1. ArithmeticProgression Class:

   • Represents an arithmetic progression with the first term $a$ and common difference $d$.
   • Provides methods to calculate the nth term, sum of the first n terms, and generate the first n terms.
   • The HarmonicProgression class is declared as a friend to allow access to its private members.

2. HarmonicProgression Class:

   • Contains an instance of the ArithmeticProgression class.
   • Provides methods to calculate the nth term of the HP, generate the first n terms of the HP, calculate the sum of the first n terms of the HP, and calculate the sum of the HP to infinity.
   • Returns the corresponding AP using the corresponding_ap method.

3. Main Function:

   • Demonstrates the usage of the HarmonicProgression and ArithmeticProgression classes, including generating terms, calculating sums, and accessing corresponding AP terms.

OUTPUT:

Enter number of HP terms: 5

First 5 terms of HP: 1 0.5 0.333333 0.25 0.2 

Sum of first 5 terms of HP: 2.28333

5th term of HP: 0.2

Sum of HP to infinity: inf

First 5 terms of corresponding AP: 1 2 3 4 5

Sum of first 5 terms of AP: 15

5th term of AP: 5