Greatest Common Divisor

• Write a function gcd that takes two non-negative integers $a$ and $b$ ($a \ge b$, not both zero) and returns their greatest common divisor

• Hint: for $b > 0$:

$$ \gcd(a, b) = \gcd(b, a \bmod b) $$

• Do not use loops or mutable variables; the observation above should allow you to formulate gcd recursively, almost trivially

• If you have worked on gcd before (in the iteration topic), which approach do you find easier?

• Boilerplate source files {go,jl,ml,rs}/gcd.{go,jl,ml,rs} containing the test code is generated and shown below.

• Edit the source files either by opening them in a text editor (e.g., vscode), or editing the cells below and executing them.

1. AI tutor

1-1. Prepare

• Your personal AI tutor is provided for questions and feedback
• Execute the following cell before you use it

import heytutor

1-2. Examples

1-2-1. A general question

%%hey
How to write a function in Go?

1-2-2. A hint on this specific problem

%%hey
Give me a hint on this problem for Rust

1-2-3. NEW: A few builtin variables

• {file:FILENAME} is the content of FILE
• {bash[-1]} is the output of the last %%bash_ cell, {bash[-2]} that of the second last %%bash_ cell, etc.
• {problem} is the content of the file you specified by %%hey problem_file=foo.md
• {answer} is the content of the file you specified by %%hey answer_file=go/foo.go

1-2-4. Help when you struggle

%%hey answer_file=go/foo.go
I get this error when I compile it. What's wrong?"

My program:
{answer}

Error message:
{bash[-1]}

1-2-5. Ask feedback

• You are encouraged to ask a feedback once you think you are done with the problem, to know if there is a better answer. You can do so by something like:

%%hey problem_file=foo.md answer_file=go/foo.md
Give me a feedback to my answer.

Problem:
{problem}

My Answer:
{answer}

2. Go

2-1. Baseline code

import heytutor

%%writefile_ go/gcd.go
package main
import "fmt"

/** begin my answer */

func gcd(a, b int64) int64 {
	if b == 0 {
		return a
	} else {
		return gcd(b, a % b)
	}
}
/** end my answer */

func main() {
	if !(gcd(1499276220,   463728183)   == 6873) { panic("wrong") }
	if !(gcd(256381708674, 48941846742) == 35094) { panic("wrong") }
	if !(gcd(8619803849,   3861314192)  == 11437) { panic("wrong") }
	fmt.Println("OK")
}

2-2. Compile

%%bash_
export PATH=${PATH}:~/.local/go/bin:~/go/bin
go build -o go/gcd go/gcd.go

• Note: when you run go or other Go commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (export PATH=${PATH}:~/go/bin)
• You may consider adding that line in your ~/.bash_profile

2-3. Run

%%bash_
go/gcd

2-4. Ask Questions or Get Feedback

%%hey problem_file=gcd.md answer_file=go/gcd.go

Problem:
{problem}
My Answer (between /** begin my answer */ and /** end my answer */):
{answer}

Give me a feedback to my answer.

3. Julia

3-1. Baseline code

import heytutor

%%writefile_ jl/gcd.jl
### begin my answer

function gcd(a, b)
    if b == 0
        a
    else
        gcd(b, a % b)
    end
end
### end my answer

function main()
    @assert gcd(1499276220,   463728183) == 6873
    @assert gcd(256381708674, 48941846742) == 35094
    @assert gcd(8619803849,   3861314192) == 11437
    println("OK")
end

main()

3-2. Compile

• Julia code is compiled "just in time" (compiled upon executed), so does not need a specific action for compilation before you run

3-3. Run

%%bash_
export PATH=${PATH}:~/.juliaup/bin
julia jl/gcd.jl

• Note: when you run julia or other Julia commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (export PATH=${PATH}:~/.juliaup/bin)
• You may consider adding that line in your ~/.bash_profile

3-4. Interactive execution

• julia command also serves is an interactive command for Julia programs

• You can run a source code and continue interaction

$ julia -i jl/gcd.jl

• For trial and error, you may also consider creating a Julia notebook

3-5. Ask Questions or Get Feedback

%%hey problem_file=gcd.md answer_file=jl/gcd.jl

Problem:
{problem}

My Answer (between ### begin my answer and ### end my answer):
{answer}

Give me a feedback to my answer.

4. OCaml

4-1. Baseline code

import heytutor

%%writefile_ ml/gcd.ml
(** begin my answer *)

let rec gcd a b =
  if b = 0 then
    a
  else
    gcd b (a mod b);;
(** end my answer *)

let main () =
  assert (gcd 1499276220   463728183   = 6873);
  assert (gcd 256381708674 48941846742 = 35094);
  assert (gcd 8619803849   3861314192  = 11437);
  Printf.printf "OK\n"
;;

main()

4-2. Compile

%%bash_
eval $(opam env)
ocamlc ml/gcd.ml -o ml/gcd

• Note: when you run ocamlc or other OCaml commands (see below) in a terminal (SSH or Jupyter terminal), you need to execute the first line (eval $(opam env))
• You may consider adding that line in your ~/.bash_profile

4-3. Run

%%bash_
ml/gcd

4-4. Interactive execution

• ocaml command is an interactive command for OCaml programs

• In terminal (Jupyter or SSH), you can directly run a source code

$ eval $(opam env)   # once in your session or put it in ~/.bash_profile
$ ocaml ml/gcd.ml

• You can run a source code and continue interaction

$ eval $(opam env)   # once in your session or put it in ~/.bash_profile
$ ocaml -init ml/gcd.ml

• For trial and error, you may also consider creating an OCaml notebook

4-5. Ask Questions or Get Feedback

%%hey problem_file=gcd.md answer_file=ml/gcd.ml

Problem:
{problem}

My Answer (between (** begin my answer *) and (** end my answer *)):
{answer}

Give me a feedback to my answer.

5. Rust

5-1. Baseline code

import heytutor

%%writefile_ rs/gcd.rs
/** begin my answer */

fn gcd(a: i64, b: i64) -> i64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}
/** end my answer */

fn main() {
    assert!(gcd(1499276220,   463728183) == 6873);
    assert!(gcd(256381708674, 48941846742) == 35094);
    assert!(gcd(8619803849,   3861314192) == 11437);
    println!("OK");
}

5-2. Compile

%%bash_
. ~/.cargo/env
rustc rs/gcd.rs -o rs/gcd

• Note: when you run rustc or other Rust commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (. ~/.cargo/env)
• You may consider adding that line in your ~/.bash_profile

5-3. Run

%%bash_
rs/gcd

5-4. Ask Questions or Get Feedback

%%hey problem_file=gcd.md answer_file=rs/gcd.rs

Problem:
{problem}

My Answer (between /** begin my answer */ and /** end my answer */):
{answer}

Give me a feedback to my answer.