I need help for the order of growth for functions in Python 3. Please show instruction for each questions how you solved Thank you.

Q3: What is the order of growth for the following functions?

Kinds of Growth

Here are some common orders of growth, ranked from no growth to fastest growth:

1. (1) constant time takes the same amount of time regardless of input size

2. (log n) logarithmic time

3. (n) linear time

4. (n log n) linearithmic time

5. (n² )

6. (n³ )

7. (n⁴ )

8. (n⁵ )

9. (n⁶ )

10. (n⁷ ), etc. polynomial time

11. (2ⁿ), (3ⁿ), etc. exponential time (considered intractable; these are really, really horrible)

12. Something else not listed

You should create a parameter-free function called complexity and return a list with 5 numbers. You should put the corresponding growth rate (1-12) for each of the problems listed below.

Question 3.1

def foo(n): s = 0

for i in range(1, n):

for j in range(0, i*i):

for t in range(0, j):

s = s + i + j + t

Question 3.2

Calculate the complexity for sum_facts(n).

def factorial(n):

i, prod = 1, 1

while i <= n:

prod = prod * i

i = i + 1

return prod

def sum_facts(n):

sum, i = 0, 1

while i <= n:

sum += factorial(i)

i = i + 1

return sum

Question 3.3

def foo(n): i = 1 while i < n:

for j in range(i, i+2):

print(i)

i = i + 2

Question 3.4

def foo(n): if n==0:

return 1

else:

return 2 + foo(n//2)

Question 3.5

def foo(n):

i = n

while i > 1:

j = 1

while j < n:

k = 0

while k < n:

k = k + 2

j = j * 2

i = i //2