Question

Please C++ create a program that will do one of two functions using a menu, like so: 1. Do Catalan numbers 2. Do Fibonacci numbers (recursive) 0. Quit Enter selection: 1 Enter Catalan number to calculate: 3 Catalan number at 3 is 5 1. Do Catalan numbers 2. Do Fibonacci numbers (recursive) 0. Quit Enter selection: 2 Enter Fibonacci number to calculate: 6 Fibonacci number 6 is 8 Create a function of catalan that will take a parameter and return the Catalan number. Also create a function of Fibonacci that will take a parameter, calculate using recursion the Fibonacci number and return the number. Main will have a do/while loop that will print the menu, enter the selection, and call the functions. Have it quit on 0. Fibonacci are the sequence 1 1 2 3 5 8 13 21 Catalan numbers follow the sequence defined in Chapter 5 of the text. Also, the formula for the Catalan sequence is given here: https://en.wikipedia.org/wiki/Catalan_number (Links to an external site.)

Answer 1

C++ program:

#include<iostream>
using namespace std;
// Function to find the catalan number
unsigned long int catalan(unsigned int n)
{
    // Base case
    if (n <= 1) return 1;
 
    // catalan(n) is sum of catalan(i)*catalan(n-i-1)
    unsigned long int res = 0;
    for (int i=0; i<n; i++)
        res += catalan(i)*catalan(n-i-1);
    // Returning the calculated result
    return res;
}

// Function to calculate the nth Fibonacci number
int fib(int n) 
{ 
    // base conditions at n=1 and n=0
    if (n == 1) 
        return 1;
    else if (n == 0)
        return 0;
    // recursive call for n-1 and n-2 
    return fib(n-1) + fib(n-2); 
} 
  

// main Function
int main()
{
    //  while loop till  user presses 0 to quit
    while (1)
    {
        // printing the menu for user
        int choice;
        cout<<"1. Do Catalan numbers "<<endl;
        cout<<"2. Do Fibonacci numbers (recursive)"<<endl;
        cout<<"0. Quit"<<endl;
        cout<<"Enter selection: ";
        // taking user choice 
        cin>>choice;
        // if choice is 1 calculating Catalan number
        if (choice==1)
        {
            int num;
            cout<<"Enter Catalan number to calculate: ";
            cin>>num;
            cout<<"Catalan number at "<<num<<" is "<<catalan(num)<<endl;
        }
        // if choice is 2 calculating Fibonacci number
        else if (choice==2)
        {
            int num;
            cout<<"Enter Fibonacci number to calculate: ";
            cin>>num;
            cout<<"Fibonacci number "<<num<<" is "<<fib(num)<<endl;
        }
        // if choice is 0 ending the program
        else
        {
            break;
        }
    }
    return 0;
}

Screenshot of code for reference:

Screenshot of output: