Lecture Notes on 03 Mar 2014

Loop Problems

* Write a program that prompts the user to enter a postive number
  and then print the sum of its digits

* Write a program that prompts the user to enter a postive number
  and then print the reverse of that number

* Write a program that prompts the user to enter a postive number
  and then prints if it is prime or not. A prime number is divisible
  by one and itself. First prime is 2.

* Write a program that prompts the user to enter a postive number
  and then prints if it is a perfect number or not. A perfect number
  is the sum of its proper divisors.

* Write a program that prompts the user to enter a postive number n
  and then prints the nth Fibonacci number.
  n     0  1  2  3  4  5  6   7   8   9  10 
  F(n)  0  1  1  2  3  5  8  13  21  34  55

* Samuel Pepys asked Issac Newton which is more likely: getting 
  a 1 at least once when rolling a fair die six times or getting 1 
  at least twice when rolling the die twelve times. Do a simulation
  of a thousand trials to determine the answer. In the first case,
  one trial is 6 throws and in the second case, one trial is 12 throws.

* Draw the following pattern
  1
  1 2
  1 2 3
  1 2 3 4
  1 2 3 4 5

* Draw the following pattern
  1 2 3 4 5
  1 2 3 4
  1 2 3
  1 2
  1

* Draw the following pattern
      1
     2 2
    3 3 3
   4 4 4 4
  5 5 5 5 5


def main():
  # prompt user to enter a positive number:
  num = int (input ('Enter positive number: '))

  # keep repeating till the user give correct input
  while (num <= 0):
    num = int (input ('Enter positive number: '))

  # sum digits of a number
  n = num
  sum_digits = 0
  while (n > 0):
    sum_digits += n % 10
    n = n // 10
  print ('Sum digits = ', sum_digits)

  # reverse number the number
  n = num
  rev_num = 0
  while (n > 0):
    rev_num = rev_num * 10 + n % 10
    n = n // 10
  print ('Reverse number = ', rev_num)

  # get max and min of a set of numbers
  n = int (input ('Enter a number: '))
  max_n = n
  min_n = n
  while (n > -1):
    if (n > max_n):
      max_n = n
    if (n < min_n):
      min_n = n
    n = int (input ('Enter a number: '))
  print (max_n, min_n)
  
  # determine if a number is prime or not
  is_prime = True
  limit = int (num ** 0.5) + 1
  for div in range (2, limit):
    if (num % div == 0):
      is_prime = False
      break
  if (is_prime):
    print (num, "is prime")
  else:
    print (num, "is not prime")

  # determine if a number is perfect or not
  sum_divisors = 0
  limit = num // 2 + 1
  for div in range (1, limit):
    if (num % div == 0):
      sum_divisors += div
  if (num == sum_divisors):
    print (num, "is perfect")
  else:
    print (num, "is not perfect")
  
  # print the nth Fibonacci term
  f = 0
  if (num == 0) or (num == 1):
    f = num
  else:
    f1 = 0
    f2 = 1
    for i in range (2, num + 1):
      f = f1 + f2
      f1 = f2
      f2 = f
  print (num, f)

main()