Day 3: Advanced Conditionals

CMSC 201: Conditionals P2

HW1

Still exists. Still due 2024-09-13 23:59.99999.... Any more questions?

"Fun": Compsci "laws"

People in computer science love making up or referencing "laws" (and effects, and rules, and such). Here are some of my favorites:

Who cares (about advanced conditionals)?

Advanced conditionals (and logic gates) make up literally all of computing! And leads to one of the hardest problems in computer science. But this example code is going to be a bit more boring... Let's do some programming interview practice problems! (FizzBuzz)

Advanced Conditionals

Review: Conditionals take an action based on a condition. Think: IF this, then THAT.

if temperature > 70:
    print("summer clothes!")

if temperature > 70:
    print("summer clothes!")
else:
    print("maybe wear a jacket")

if temperature > 70:
    print("summer clothes!")
elif hvac_working:
    print("who cares, technology saves us from the environment")
else:
    print("maybe wear a jacket")

The None type

Python has a special "type" or object: None. It's the closest thing Python has to a NULL or empty value. It represents a value of nothingness. It is always considered false (False).

Truthy/Falsy values

Python tries to be helpful by having things that are not booleans still evaluate to true or false.

• ints and floats: anything except 0 is true
• string: any non-empty string
• None: always false
• ...not None: always true?

Truthy/falsy values only happen in a "boolean context". (What does that mean? Whenever it's used by itself in some conditonal.)

# Not truthy/falsy
if 5 == int(input()):
	print("Nice number!")

# Truthy/falsy!
if int(input()):
	print("Nice number!")

Negation

Want the opposite of something? Use not!

not True == False

if not 100 >= 1000:
    print("100 is not >= 1000!")

Combining conditions

Python keywords and and or let us combine multiple conditionals into one statement.

Truth tables

if temperature > 70 and ac_broken == True:
    print("summer clothes!")

We can group these with parentheses. Normally they are evaluated left to right.

True and False

True and (False or True)

De Morgan's law

When you negate something, there is an equivalence rule you can use (known as De Morgan's laws). Sometimes this is useful for simplifying expressions. It is:

not (A or B) --(is equivalent to)--> (not A) and (not B)
not (A and B) --(is equivalent to)--> (not A) or (not B)

Some intuition: A AND B will only be if both A or B and true. To negate this (NOT AND), we need to have either A or B be true-- but not both! (Think: we're inverting the table.)

Let's simplify this:

if not (user_input > 10 and user_input % 2 == 0) \
   and user_input != 12:
	print("I like that number!")

if user_input <= 10 or user_input % 2 != 0 \
   and user_input != 12:
	print("I like that number!")

Short circuiting

When the outcome of a condition with multiple parts is obvious, Python won't bother evaulating unnecessary parts.

Why are these two code blocks different?

temperature = 60
if temperature > 70 and ac_broken == True:
    print("summer clothes!")

temperature = 80
if temperature > 70 and ac_broken == True:
    print("summer clothes!")

Combining our Type lore knowledge: What would this print?

if print("condition one") and print("condition two"):
    print("wow!")

What about this one:

if (print("condition one") or not print("condition two")) \
	 and print("condition three") \
	 and not print("condition four"):
    print("wow!")

Speaking of circuits...

AND, OR, and NOT gates make up all of computation. Using just those three logic gates gates, you can do anything with a computer. CMPE people are destined to learn all about that in gratuitous detail... but the rest of us can too! (Recommended resources if you're interested: nand2tetris and Code by Charles Petzold).

if (print("condition one") or not print("condition two")) \
	 and print("condition three") \
	 and not print("condition four"):
    print("wow!")

if (A or not B) \
    and C \
    and not D:
    print("wow!")

if (A or not B) \
    and C \
    and Z or not Y \
    or E or W and Z \
    or (Z and A and C or X):
    print("wow!")

(declare-const A Bool)
(declare-const B Bool)
(declare-const C Bool)
(declare-const D Bool)
(assert (and (and (or A (not B)) C) (not D)))
(check-sat)
(get-model)

sat
(
  (define-fun A () Bool
    false)
  (define-fun D () Bool
    false)
  (define-fun B () Bool
    false)
  (define-fun C () Bool
    true)
)

(declare-const a Bool)
(declare-const b Bool)
(define-fun demorgan () Bool
    (= (and a b) (not (or (not a) (not b)))))
(assert (not demorgan))
(check-sat)

unsat

for x in range(1, 101):
    if x % 3 == 0:
        print("Fizz", end="")
    if x % 5 == 0:
        print("Buzz", end="")
    if not (x % 3 == 0) and not (x % 5 == 0):
        print(x, end="")
    print()