#
Homework 2

*Due at 11:59:59 pm on 09/14/2023.*

## Instructions

Download hw02.zip. Inside the archive, you will find starter files for the questions in this homework, along with a copy of the OK autograder.

**Readings:** This homework relies on following references:

## Questions

### Question 1: Fibonacci

The Fibonacci sequence is a famous sequence in mathematics. The first
element in the sequence is 0 and the second element is 1. The *n*th
element is defined as *F _{n} = F_{n-1} +
F_{n-2}*.

Implement the `fib`

function, which takes an integer `n`

and returns
the `n`

th Fibonacci number. Use a `while`

loop in your solution.

```
def fib(n):
"""Returns the nth Fibonacci number.
>>> fib(0)
0
>>> fib(1)
1
>>> fib(2)
1
>>> fib(3)
2
>>> fib(4)
3
>>> fib(5)
5
>>> fib(6)
8
>>> fib(100)
354224848179261915075
"""
"*** YOUR CODE HERE ***"
```

Use OK to test your code:

`python3 ok -q fib`

### Question 2: Nonzero

Write a function that takes in a list and returns the first nonzero entry.

```
def nonzero(lst):
""" Returns the first nonzero element of a list
>>> nonzero([1, 2, 3])
1
>>> nonzero([0, 1, 2])
1
>>> nonzero([0, 0, 0, 0, 0, 0, 5, 0, 6])
5
"""
"*** YOUR CODE HERE ***"
```

Use OK to test your code:

`python3 ok -q nonzero`

### Question 3: Contains N

Write a function that takes in a list and a number, and returns whether or not the list contains the value n.

```
def has_n(lst, n):
""" Returns whether or not a list contains the value n.
>>> has_n([1, 2, 2], 2)
True
>>> has_n([0, 1, 2], 3)
False
>>> has_n([], 5)
False
"""
"*** YOUR CODE HERE ***"
```

Use OK to test your code:

`python3 ok -q has_n`

### Question 4: Total Price

Implement the function `total_price`

, which takes in a list of prices of individual products and needs to find the total price. Unfortunately, any product that is priced greater than or equal to $20 has a 50 percent tax, so include that in the final price.

Try to do this in one line!

Cast your final answer to an **integer** to avoid floating point precision errors. For example, if `x`

contains your final answer, `return int(x)`

!

```
def total_price(prices):
"""
Finds the total price of all products in prices including a
50% tax on products with a price greater than or equal to 20.
>>> total_price([5, 20, 30, 7])
87
>>> total_price([8, 4, 3])
15
>>> total_price([10, 100, 4])
164
"""
"*** YOUR CODE HERE ***"
```

Use OK to test your code:

`python3 ok -q total_price`

### Question 5: arange

Implement the function `arange`

, which behaves just like np.arange(start, end, step) from Data 8. You only need to support positive values for step.

```
def arange(start, end, step=1):
"""
arange behaves just like np.arange(start, end, step).
You only need to support positive values for step.
>>> arange(1, 3)
[1, 2]
>>> arange(0, 25, 2)
[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24]
>>> arange(999, 1231, 34)
[999, 1033, 1067, 1101, 1135, 1169, 1203]
"""
"*** YOUR CODE HERE ***"
```

Use OK to test your code:

`python3 ok -q arange`

### Question 6: Reverse (iteratively)

Write a function `reverse_iter_for`

that takes a list and returns a new
list that is the reverse of the original using a `for`

loop. You should not
need any indexing notation.

```
def reverse_iter_for(lst):
"""Returns the reverse of the given list.
>>> reverse_iter_for([1, 2, 3, 4])
[4, 3, 2, 1]
"""
"*** YOUR CODE HERE ***"
```

Use OK to test your code:

`python3 ok -q reverse_iter_for`

Complete the function `reverse_iter_while`

that behaves identically to
`reverse_iter_for`

but is implemented as using a `while`

loop.
You may use indexing or slicing notation. Do not use `lst[::-1]`

!

```
def reverse_iter_while(lst):
"""Returns the reverse of the given list.
>>> reverse_iter_while([1, 2, 3, 4])
[4, 3, 2, 1]
"""
rev_lst = []
i = 0
while i < len(lst):
"*** YOUR CODE HERE ***"
```

Use OK to test your code:

`python3 ok -q reverse_iter_while`

## Submission

When you are done, submit your file to Gradescope. You only need to upload the following files:

`hw02.py`