Homework 1 Solutions

Solution Files

You can find the solutions in hw01.py.

Required Questions

Q1: Distance

Implement a function called distance(x1, y1, x2, y2):

  • x1 and y1 form an x-y coordinate pair
  • x2 and y2 form an x-y coordinate pair

distance returns the Euclidean distance between the two points. Use the following formula:

2-D distance formula

from math import sqrt

def square(x):
    return x * x

def distance(x1, y1, x2, y2):
    """Calculates the Euclidian distance between two points (x1, y1) and (x2, y2)

    >>> distance(1, 1, 1, 2)
    1.0
    >>> distance(1, 3, 1, 1)
    2.0
    >>> distance(1, 2, 3, 4)
    2.8284271247461903
    """

    return sqrt(square(x1-x2) + square(y1-y2))

Use Ok to test your code:

python3 ok -q distance

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.