Question

Given the following two functions:

def f(n):
   if n <= 0:
      return 0
   return 1 + f(n - 1)

def g(n):
   summ = 0
   for i in range(0, n, 1):
      summ += 1
   return summ

1. (2 pts) State the runtime complexity of both f() and g()
2. (2 pts) State the memory (space) complexity for both f() and g()
3. (6 pts) Write another function called h(n) that does the same thing, but is significantly faster.

Answer 1

runtime complexity of both f() is O(n)
runtime complexity of both g() is O(n)

space complexity of both f() is O(n)
space complexity of both g() is O(1)

another function called h(n) that does the same thing is
def h(n):
    return n
    

runtime complexity of both f() is O(1)
space complexity of both f() is O(1)