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def lyric_frequencies(lyrics_db):
  '''
  create a dictionary with 
  keys = unique lyrics (words)
  vals = number of occurrences in the lyrics db
  '''
  lyrics_dict = {}
  # loop through lyrics_db elements
  for lyric in lyrics_db:
    if lyric in lyrics_dict:

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def pal_rec(s):
  '''
  check if the alphabetical characters in a string read the same backwards and forewards
  '''
    # convert the input string to a list of lowercase alphanumeric characters only (i.e., punctuation, etc, omitted)
  def to_char(s):
    ls = list(s.lower())
    labc09 = list('abcdefghijklmnopqrstuvwxyz0123456789')
    char_s = [i for i in ls if i in labc09]
    return char_s

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def pal(user_string):
  '''
  check if a word/phrase is a palindrome
  '''
  lus = list(user_string)
  max_ind = int(len(lus)/2)
  l1 = [lus[i] for i in range(max_ind)]
  l2 = [lus[-(i+1)] for i in range(max_ind)]
  if l1 == l2:
    return True

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def ispowerof(n, base):
  '''
  if n is a power of b, return True, else return False
  '''
  test = False
  if n % base == 0:
    k = int(n / base)
    for i in range(k+1):
      print(i)
      print(base**i)

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def fibo(n):
  '''return element 'i' of the Fibonacci series (its initial element is element '1')'''
  if n == 0 or n == 1:
    return 1
  elif n > 1:
    return fibo(n-2) + fibo(n-1)

if __name__ == "__main__":
  i = int(input('Which element to compute in the Fibonacci sequence?: '))
  print(f'Element {i} in the Fibonacci sequence: {fibo(i-1)}')

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def additup(num_list):
  ''' function that returns the sum of the passed list - without using loops; eg:
  sum([1, 2, 3, 4, 5]) -> 15
  sum([]) -> 0
  '''
  if len(num_list) == 1:
    return num_list[0]
  else:
    return num_list[len(num_list)-1] + additup(num_list[0:len(num_list)-1])

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def hi_index(n, l):
  if l[-1] == n:
    return len(l)-1
  else:
    return hi_index(n, l[0:len(l)-1])

if __name__ == "__main__":
  l = [3, 5, 4, 3, 4, 9, 5, 7, 7, 9]
  print(f'given the list {l}\n')
  n = int(input('pick a number to find its largest index: '))

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def towers_rec(n, home, destination, temp):
  if n == 1:
    moves.append((home+' to '+destination))
  else:
    towers_rec(n-1, home, temp, destination)
    towers_rec(1, home, destination, temp)
    towers_rec(n-1, temp, destination, home)

if __name__ == "__main__":
  print(f'Elements are stacked at position A, which is \'home\'.\nMove them to position B, which is \'destination\'.\nImportant! The home stack is ranked as:\nbottom biggest, top smallest...\nand the destination stack must be ranked the same way.\nThere\'s one spare position you can use called \'temp\' which starts at position C.\nTwo rules:\n1. move one element at a time, and\n2. never place an element on top of a smaller element.')

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def mult_rec(x, y):
  if y == 1:
    return x
  else:
    return x + mult_rec(x, y-1) 

def fact_rec(x):
  if x == 1:
    return x
  elif x > 1:

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import logging
import math #since we'll need the sqrt fn

# Create and configure logger
LOG_FORMAT = "%(levelname)s %(asctime)s - %(message)s"
logging.basicConfig(filename = "log_file.log", level = logging.DEBUG, format = LOG_FORMAT, filemode = 'w')
# we'll call the logger without a name (aka 'root logger') because there are subtle issues with logger names (*what are they?*)
logger = logging.getLogger()

def quadratic_formula(a, b, c):