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Assignment 1

Table of Contents

The following assignment is due Thursday 1/30 by 8:00 PM. You'll need to submit a .zip file containing two Cargo packages in Gradescope. You can start the setup with: 

cargo new hw1
cargo new slice

For all but the last question, put your solution in the file hw1/src/main.rs.

Note. This assignment is shorter than usual because it's the first one. It should be a litmus for you in deciding whether or not to take the course.

1. Euclidean Distance

Implement a function called distance which, given two points in \(\mathbb R^2\) of type (f64, f64) returns the Euclidean between them.

Also implement a function is_close which, given two numbers in \(\mathbb R\) of type f64, determines if they are within \(1^{-10}\) of each other.

Verify your solution (sort of) by asserting within the function main that the distance between \((5, 5)\) and \((4, 4)\) is close to \(\sqrt{2}\).

Note. This problem (as with many others) may require looking at the documentation for The Rust Standard Library.

2. nth Prime

Implement a function called nth_prime which, given a nonnegative integer \(n\) of type u32, returns the \(n^{\textsf{th}}\) prime number as a u32.

Verify your solution by asserting within main that the 22nd prime is 83.

Note: This is a problem which can be sped up quite a bit. You can solve it however you'd like, but if you're up for it, I'd definitely recommend looking into some faster algorithms.

3. Taxicab Numbers

Implement a function called is_taxicab which, given a nonnegative integer \(n\) of type u32, determines if the \(n\) can be represented as the sum of a pair of positive cubes is more than one way.

Include this function in hw/src/main.rs. Verify your solution by asserting within main that 1729 is a taxicab number.

4. Slice

You should put your solution to this problem in the Cargo package slice.

It's not uncommon to have a document containing problem and solutions to an assignment or exam, and it's to nice to have a way of extracting just the problems. One simple way of doing this is to introduce a special delimiter, e.g. 

>>>>>>>>>>>>>>>>>>>>

which can be used to delimit the solution parts of the document.

In this problem, you'll write a Rust program to do this. It should take input at stdin and remove all lines between and including the delimiters (in the case that there are an odd number of delimiters, you should take EOF to be the final delimiter). For example, given a file test.txt containing 

EXAM

Question 1. Write a function in python which squares its input.
>>>>>>>>>>>>>>>>>>>>
Solution.

def square(n):
    return n * n
>>>>>>>>>>>>>>>>>>>>

Question 2.  Show that 1 + 1 = 2.
>>>>>>>>>>>>>>>>>>>>
Solution.

I'm not sure, this one seems tricky...ask Russell.
>>>>>>>>>>>>>>>>>>>>

END OF EXAM

you should be able to run: 

cargo run < test.txt

and it should print: 

EXAM

Question 1. Write a function in python which squares its input.

Question 2.  Show that 1 + 1 = 2.

END OF EXAM

Furthermore, we will only require that the line contains the delimiter. That way, we can put delimiters in comments when we're dealing with code, e.g. 

let incr x = x + 1
(* >>>>>>>>>>>>>>>>>>>> *)

let dumb_function x = x + 1
(* not sure why I put this here *)

(* >>>>>>>>>>>>>>>>>>>> *)

should become: 

let incr x = x + 1