someone please explain this program..how it works

Question

def is_even(x):
if x == 0:
print (": ", end="")
return True
else:
print ("(is_even " + str(x) + ")", end="")
return is_odd(x-1)

def is_odd(x):
print ("(not is_even " + str(x) + ")", end="")
return not is_even(x)

print(is_odd(2))
print(is_even(2))

Answer 1

We can better understand your program if we simplify the code

def is_even(x):
if x == 0: return True
return not is_even(x-1)

We can see that for example is_even(5) will recurse through
NOT is_even(4) -> NOT is_even(3) -> NOT is_even(2) -> NOT is_even(1) -> NOT is_even(0)

Starting from 0 and going in the opposite direction:
False (4) <- True (3) <- False (2) <- True (1) <- False (0)

So we can see that, if the number of recursions is odd as in case of 5 and all odd numbers, is_even() will return False; if the number of recursions is even as in case of 2 and all even numbers, is_even will return True