The equivalent function 2

You can easily deduce the purpose of a recursive function by looking at how it combines the result of a sub solution.

For example, fun1(a,b) will keep adding a until b goes to 0 . Each time b is reduced by 1 , the result is added with a . Hence it is equivalent to $a$ sum itself $b$ times, which is just $ab$ .

Then, fun2(a,b) is very similar except each time b is reduced by 1 , the result is multiplied by a . This is equivalen to $a$ multiplies itself $b$ times, which is just $a^b$ .

Just see the first condition for function 2- If b=0, then it will return 1. Now since only one option must be true when b=0, a^b is the answer.

two solutions the dumb and the mathematical: mathematical: we can do a=2, b=3. so is the same for the minus 1 like 2 2 2 or 2^3 dumb: def fun1(a,b): if b==0: return 0 return a + fun1(a, b-1) # a + a * (b-1) 1+1 1 or a b

def fun2(a,b): if b==0: return 1 else: return fun1(a, fun2(a, b-1)) # a (a (b-1)) 3 3 4 or a^b print(fun2(2, 3))