CODEWITHSUNDEEP
pythonpython-3.xrecursion
Khem Myrick
Khem Myrick

Reputation: 11

Even and Odd numbers with recursion in Python

I'm trying to solve "is_even" and "is_odd" function in terms of the other with recursion. I don't understand HOW this function as written ever evaluates to False, or how anything that isn't 0 ever evaluates to True. I double-checked it in teamtreehouse.com workspaces to make sure it works at all, but I can't figure out HOW it works.

I understand that it's decrementing through recursion, but I don't understand how is_odd(x) works. If is_odd(x) just negates everything in is_even, why don't all numbers evaluate to True? Or False?

def is_even(x):
    if x == 0:
        return True

    else:
        return is_odd(x-1)

def is_odd(x):
    return not is_even(x)
    # Does this negate the function of is_even(x)?
    # Does that negating mean returning False, or sending to else block?
    # If the negating does automatically sends to the else block
    # After we get here, do we ever land at True in is_even(x)?
    # If not, how do we ever land at False?

print(is_even(1))
print(is_even(2))
print(is_even(3))

Upvotes: 0

Views: 1170

Answers (3)

Nrzonline
Nrzonline

Reputation: 1618

What Sasha said is correct, however it does not fully illustrate the recursive call-stack.

x = 3

is_even(3):
  return is_odd(2)
    call is_even(2)
      return is_odd(1)
        call is_even(1)
          return is_odd(0)
            return is_even(0): True
        return not True: False
    return not False: True
return not True: False

Upvotes: 0

edu
edu

Reputation: 126

Let's take an example of the function is_even(1). What happens?

(1)

  1. Enter in is_even(1)
  2. Enter in is_odd(1-1), i.e. enter in is_odd(0)
  3. Return not is_even(0). Enter in is_even(0)
  4. x==0 -> this returns True
  5. You have a not, remember in Step 3? So: not True -> False
  6. is_even(1) = False

Let's now take an example of is_even(2). What happens?

(2)

  1. Enter in is_even(2)
  2. Enter in is_odd(2-1), i.e. enter in is_odd(1)
  3. return not is_even(1)
  4. We know from (1) that is_even(1) is False, so not False = True

Now with is_even(3)

(3)

  1. Enter in is_even(3)
  2. Enter in is_odd(3-1), i.e. enter in is_odd(2)
  3. return not is_even(2)
  4. We knot from (2) that is_even(2) is True, so not True = False

To your questions again:

  • Does this negate the function of is_even(x)?

Yes: not is_even(x) negates the result of is_even(x), as you saw in my examples.

  • Does that negating mean returning False, or sending to else block?

No. If the function is_even(x) returns True, not True returns False. If the function is_even(x) returns False, not False returns True. So it negates the result of is_even(x)

  • After we get here, do we ever land at True in is_even(x)?

Since you always decrease the argument with (x-1), you will always eventually get to x=0, as you also saw in my examples.

Upvotes: 0

sasha199568
sasha199568

Reputation: 1153

x = 0
 is_even: True

x = 1
 is_even:
   is_odd(0):
     is_even(0): True
   not True: False
 False

x = 2
 is_even:
   is_odd(1):
     is_even(1): False
   not False: True
 True

x = 3
  is_even:
    is_odd(2):
      is_even(2): True
    not True: False
  False

Upvotes: 2

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