Question

The is a Python code, if possible add comments .

Use recursions to solve the following problems. If you can find prove a closed-form formula for each, implement the closed-form solution, then compare the performance of two implementations. 1. GDC function 2. Fibonacci numbers 3. Relation: - T(1) = 1 - T(n) = T(n-1) + 3 Implement a function for the following summation. Find the closed-form formula for the following summation and compare the performance of your implementations. (k − 1)2 3+1 t=2

Answer 1

Code:-

def gcd(a,b):
if (b == 0):
return a
return gcd(b, a%b)

def Fibonacci(n):
if n==0:
return 0
elif n==1:
return 1
else:
return Fibonacci(n-1)+Fibonacci(n-2)

def T(n):
if n == 1:
return 1
return T(n-1) + 3

Screenshot:-

def ged(a,b): if (b == 0): return a return ged(b, a b) def Fibonacci(n): if no: return 0 elit n=1: return 1 else: return Fibonacci(n-1)-Fibonaccin 2) def Tin): if n == 1: return 1 return T(n-1) + 3