# Homework 1 Solutions

## Solution Files

You can find the solutions in hw01.py.

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# Required Questions

### Q1: A Plus Abs B

Python's `operator`

module contains two-argument functions such as `add`

and
`sub`

for Python's built-in arithmetic operators. For example, `add(2, 3)`

evalutes to 5, just like the expression `2 + 3`

.

Fill in the blanks in the following function for adding `a`

to the
absolute value of `b`

, without calling `abs`

. You may **not** modify any
of the provided code other than the two blanks.

```
def a_plus_abs_b(a, b):
"""Return a+abs(b), but without calling abs.
>>> a_plus_abs_b(2, 3)
5
>>> a_plus_abs_b(2, -3)
5
>>> a_plus_abs_b(-1, 4)
3
>>> a_plus_abs_b(-1, -4)
3
"""
if b < 0:
f = sub else:
f = add return f(a, b)
```

Use Ok to test your code:

`python3 ok -q a_plus_abs_b`

Use Ok to run the local syntax checker (which checks that you didn't modify any of the provided code other than the two blanks):

`python3 ok -q a_plus_abs_b_syntax_check`

If `b`

is positive, we add the numbers together. If `b`

is negative, we
subtract the numbers. Therefore, we choose the operator `add`

or `sub`

based on the sign of `b`

.

### Q2: Two of Three

Write a function that takes three *positive* numbers as arguments and returns
the sum of the squares of the two smallest numbers. **Use only a single line
for the body of the function.**

```
def two_of_three(i, j, k):
"""Return m*m + n*n, where m and n are the two smallest members of the
positive numbers i, j, and k.
>>> two_of_three(1, 2, 3)
5
>>> two_of_three(5, 3, 1)
10
>>> two_of_three(10, 2, 8)
68
>>> two_of_three(5, 5, 5)
50
"""
return min(i*i+j*j, i*i+k*k, j*j+k*k)
# Alternate solution
def two_of_three_alternate(i, j, k):
return i**2 + j**2 + k**2 - max(i, j, k)**2
```

Hint:Consider using the`max`

or`min`

function:`>>> max(1, 2, 3) 3 >>> min(-1, -2, -3) -3`

Use Ok to test your code:

`python3 ok -q two_of_three`

Use Ok to run the local syntax checker (which checks that you used only a single line for the body of the function):

`python3 ok -q two_of_three_syntax_check`

We use the fact that if `x>y`

and `y>0`

, then `square(x)>square(y)`

.
So, we can take the `min`

of the sum of squares of all pairs. The
`min`

function can take an arbitrary number of arguments.

Alternatively, we can do the sum of squares of all the numbers. Then we pick the largest value, and subtract the square of that.

## Check Your Score Locally

You can locally check your score on each question of this assignment by running

`python3 ok --score`

**This does NOT submit the assignment!** When you are satisfied with your score, submit the assignment to Gradescope to receive credit for it.

# Submit Assignment

Submit this assignment by uploading any files you've edited **to the appropriate Gradescope assignment.** Lab 00 has detailed instructions.