Lecture Notes on 22 Feb 2023

# gets all subsets of a list a
def sub_sets (a, b, idx):
  hi = len(a)
  if (idx == hi):
    print (b)
    return
  else:
    c = b[:]
    b.append(a[idx])
    sub_sets (a, b, idx + 1)
    sub_sets (a, c, idx + 1)

def main():
  a = ['A', 'B', 'C', 'D', 'E']
  b = []
  sub_sets (a, b, 0)

main()

# gets all permutations of a list a
def permute (a, idx):
  hi = len(a)
  if (idx == hi):
    print (a)
  else:
    for i in range (idx, hi):
      a[idx], a[i] = a[i], a[idx]
      permute (a, idx + 1)
      a[idx], a[i] = a[i], a[idx]

def main():
  a = ['A', 'B', 'C', 'D']
  permute (a, 0)

main()

# use memoization to obtain the fibonacci sequence
def fib_memo (n, memo):
  if (n == 0) or (n == 1):
    return n
  else:
    if (n >= len(memo)):
      f = fib_memo (n - 1, memo) + fib_memo( n - 2, memo)
      memo.append (f)
      return f
    else:
      return memo[n]

# use recursion to obtain the fibonacci sequence
def fib_rec (n):
  if (n == 0) or (n == 1):
    return n
  else:
    return fib_rec (n - 1) + fib_rec (n - 2)

def main():
  '''
  for i in range (50):
    print (i, ' ', fib_rec(i))
  '''

  memo = [0, 1]
  for i in range (500):
    print (i, ' ', fib_memo (i, memo))

main()