[Python] Important Algorithms

Factorial function 

 def factorial(n): #Task 1: Factorial function 

 if n==0: #Case 1: 0!

 return 1

 

 else: #Case 2: <positive_integer>!

 return n*factorial(n-1) #multiply with factorial of n-1

 

 

 Recursive arithmetic sum  

 def arithmetic_sum_2(term1,com_dif,n): #Task 2(alternative): Arithmetic Sum Function – Recursive method

 if n==1: #Case 1: last term to add(=the first term of the sequence)

 return term1

 else: #Case 2: add <positive integer>th term

 return arithmetic_sum_2(term1,com_dif,(n-1))+(n-1)*com_dif+term1

 

 

 Iterative arithmetic sum 

 def arithmetic_sum_1(term1,com_dif,n): #Task 2: Arithmetic Sum function – Formula method

 return (n/2)*(2*term1+(n-1)*com_dif)

 

 

 Recursive geometric sum 

 def geometric_sum_2(term1,com_rat,n): #Task 3: Geometric Sum function – Recursive method

 if n==1: #Case 1: last term to add(=the first term of the sequence)

 return float(term1)

 else: #Case 2: add <positive integer>th term

 return float(geometric_sum_2(term1,com_rat,(n-1))+term1*(com_rat**(n-1))) #perform nth term addition

 

 

 Iterative geometric sum 

 def geometric_sum_1(term1,com_rat,n): #Task 3: Geometric Sum function – Formula method

 return (term1-(com_rat**n))/(1-com_rat)

 

 

 Fibonacci function 

 def fibonacci(term1,term2,n): #Task 4: Fibonacci function

 if n == 0:

 return term1

 elif n == 1:

 return term2

 else:

 return fibonacci(term1,term2,(n-1))+fibonacci(term1,term2,(n-2))

 

 

 Compound Interest 

 def compound_interest(initial,inc,n):

 return initial*((1+(inc/100))**n) 

 

 PIN, deposit & withdraw 

 correct_pin=1111

enter_pin=0

attempt=0

balance=100.00

option=0

save=0.00

password=True

while attempt<3 and password:

 while True:

 try:

 enter_pin=str(input("Enter PIN (4 digits)"))

 if len(str(enter_pin))==4 and int(enter_pin)>=0 and int(enter_pin)<=9999:

 break

 else:

 print("invalid format")

 except ValueError:

 print("invalid format")

 if int(enter_pin)==int(correct_pin):

 password=False

 else:

 attempt+=1

 print("wrong")

def deposit():

 global balance

 while True:

 try:

 save=float(input("How much you save"))

 if save>0:

 break

 else:

 print("can't save that amount")

 except ValueError:

 print("invalid format")

 balance+=save

def withdraw():

 global balance

 while True:

 try:

 take=float(input("How much you withdraw"))

 if take>0 and take<=balance:

 break

 else:

 print("can't withdraw that amount")

 except ValueError:

 print("invalid format")

 balance-=take

def change_pin():

 global correct_pin

 while True:

 try:

 new=str(input("Enter new PIN(4digits)"))

 if len(str(new))==4 and int(new)>=0 and int(new)<=9999 and new!=correct_pin:

 break

 elif new==correct_pin:

 print("there is no change")

 else:

 print("invalid password")

 except ValueError:

 print("invalid format")

 correct_pin=new

 print("Change successful")

 

if not(password):

 Out=False

 while not(Out):

 print("MENU")

 print(f"Balance: {balance}")

 print("Deposit[1]")

 print("Withdraw[2]")

 print("Change PIN[3]")

 print("Exit[4]")

 while True:

 try:

 option=int(input("Enter Option(number key)"))

 if option>=1 and option<=4:

 break

 else:

 print("no such option")

 except ValueError:

 print("invalid format")

 if option==1:

 deposit()

 elif option==2:

 withdraw()

 elif option==3:

 change_pin()

 else:

 Out=True

 

else:

 print("Max attempt reached")

if Out==True:

 print("End.")