# Orders of Growth: basic-level questions

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Each question has a "Toggle Solution" button -- click it to reveal that question's solution.

## Conceptual Questions

### Question 1

What is the time complexity of this function in big-Theta (θ) notation?

``````def one(n):
for a in range(n):
for b in range(n/2):
for c in range(n/4):
print(a + b + c)``````

θ(n3)

### Question 2

What is the time complexity of this function in big-Theta (θ) notation?

``````def two(n):
for a in range(n):
for b in range(1000000000):
for c in range(n):
print(a + b + c)``````

θ(n2)

### Question 3

What is the time complexity of this function in big-Theta (θ) notation?

``````def three(n):
while n > 1:
result = n * n
print(result)
n = n / 10
return False``````

θ(logn)

### Question 4

What is the time complexity of this function in big-Theta (θ) notation?

``````def four(lst):
if len(lst) < 12345:
return lst
return four(lst[1:])``````

θ(n), where n is the length of the list.

### Question 5

What is the time complexity of this function in big-Theta (θ) notation?

``````def five(n):
def helper(x):
return x + n
return helper(n/2)``````

θ(1)

### Question 6

What is the time complexity of this function in big-Theta (θ) notation?

``````def reverse(lst):
if not lst:
return []
result = reverse(lst[1:])
result.append(lst)
return result``````

θ(n), where n is the size of the list.