unit_eighteen.py

"""recursive functions"""

"""def display_a():
    print('start a')
    display_c()
    print('c executed')
    print('end a')

def display_b():
    print('start b')
    display_a()
    print('a executed')
    print('end b')

def display_c():
    print('start c')
    display_b()
    print('b executed')
    print('end c')

display_c()
"""
"""
n = int(input('Enter: `'))

def fact(n):
    if n == 0:
        return 1
    else:
        return n + fact(n - 1)

print(fact(n))"""

"""def fibonacci(n):   # A recursive implementation of the Fibonacci function
    if n <= 1:
        return n
    else:
        return (fibonacci(n - 1) + fibonacci(n - 2))    # F_n = F_(n-1) + F_(n-2)
    
nterms = int(input('How many Fibonacci numbers do you want?'))

# Cannot find Fibonacci number if it is negative
if nterms <= 0:
    print('Error : Enter a positive number.')
else:
    print('Fibonacci sequence:', end = ' ')
    for i in range(nterms):
        print(fibonacci(i), end = ' ')"""
        
def fibonacci(n, memo={}):
    if n in memo:
        return memo[n]  # Return cached result if available
    
    if n == 0:
        return 0
    elif n == 1:
        return 1
    else:
        memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo)
        return memo[n]

nterms = int(input('How many Fibonacci numbers do you want? '))

if nterms <= 0:
    print('Error: Enter a positive number.')
else:
    print('Fibonacci sequence:', end=' ')
    for i in range(nterms):
        print(fibonacci(i), end=' ')

"""Paper Coding 1"""
print()
def sum(n):
    if n == 1:
        return 1
    else:
        return n + sum(n - 1)
    
n = int(input('Enter a number: '))
print(sum(n))

"""PAper Coding 2"""
def sum_pow(x, n):
    if n == 0:
        return 1
    else:
        return x * sum_pow(x, n - 1)
    
x = int(input('Enter a x : '))
n = int(input('Enter a n : '))
print(sum_pow(x, n))

"""Pair Programming"""
def factorial(k):
    if k == 0:
        return 1   
    else:
        return k * factorial(k - 1)

def euler(n):
    if n == 0:
        return 1
    return 1 / factorial(n) + euler(n - 1)

print('eular(20) =', round(euler(20), 5))