Question

1. The famous Fibonacci sequence f1, f2, f3, . . . is defined as f1 = 1, f2 = 1 fn = fn−1 + fn−2, for n > 2 So the sequence begins as 1, 1, 2, 3, 5, 8, 13, 21, 34, . . .. Define a recursive function int fibonacci(int n) which returns the n-th Fibonacci number

2. Define recursive function my_sequence(n) which returns the n-th member of the sequence a1 = 3, a2 = 5, a3 = −7, an = an−1 − 2an−2 + an−3, n > 3.

3. Define a recursive function double my_pow(double a, int n) which returns a n for integers n ≥ 0. Do not use library .

4.. It is not difficult to show that n ∑ i=1 1 i(i + 1) = 1 2 + 1 6 + 1 12 + . . . + 1 n(n + 1) = n n + 1 . So a simple C++ function which computes this sum is double f(int n) {return 1.0*n/(n+1); } Define a recursive function which computes this sum directly, without using the formula.

5.. Define recursive function void print_digits_reverse(unsigned int) which takes an unsigned int as input and prints its digits in reverse on the console (cout). (Hint: n/10 is the same as n with its ones digit removed.)

6.Define recursive function print_rectangle(m,n) which prints an m×n grid of *’s.

For example,

print_rectangle(4,3)

yields

***

***

***

***

7.Define function sequence(m,n) which prints the sequence of integers from m to n, counting up if m ≤ n, or counting down if m > n. For example, sequence(-1,3) prints

-1

0

1

2

3

while sequence(5,2) yields

5

4

3

2

USE C++ ONLY

Answer 1

#include <iostream>

using namespace std;

//Recursive method that returns the nth Fibonacci number

int fib(int n) {

if (n <= 1)

return n;

return fib(n-1) + fib(n-2);
}

//Main method that calls the recursive Fibonacci method

int main(){

int n = 0;

cout<<"Enter n: ";

cin>>n;

cout<<"Fib("<<n<<") = "<<fib(n);

return 0;
}

Output:

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