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## 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(n^{3})

### 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(n^{2})

### 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(log*n*)

### Question 4

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

```
def four(lst):
if len(lst) < 12345:
return lst[0]
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[0])
return result
```

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