Point-Line Distance

• Write a function point_line_distance (or pointLineDistance, according to your language's case convention) that takes six 64-bit floating point numbers:

  • $x_0$, $y_0$, $x_1$, $y_1$ --- coordinates of two distinct points $(x_0, y_0)$ and $(x_1, y_1)$ on a line
  • $p$, $q$ --- the coordinates of a point $(p, q)$ and returns the distance from the point to the line through $(x_0, y_0)$ and $(x_1, y_1)$.

• Consider introducing local variables to break the computation into several steps.

• Hint 1: the distance between line $ax + by + c = 0$ and point $(p, q)$ is

$$ \frac{|ap + bq + c|}{ \sqrt{a^2 + b^2} }. $$

• Hint 2: For line $ax + by + c = 0$, $(a, b)$ is perpendicular to the line. That is, it is perpendicular to $(x_1 - x_0, y_1 - y_0)$.

• Use 64-bit floating point numbers for both inputs and the output.

• Boilerplate source files {go,jl,ml,rs}/point_line_distance.{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/point_line_distance.go
package main
import "fmt"
import "math"

/** begin my answer */

func pointLineDistance(x0, y0, x1, y1, p, q float64) float64 {
	dx := x1 - x0
	dy := y1 - y0
	a := dy
	b := -dx
	num := math.Abs(a * (p - x0) + b * (q - y0))
	den := math.Sqrt(a * a + b * b)
	return num / den
}
/** end my answer */
func main() {
	if !(math.Abs(pointLineDistance(-3.0, 1.0, 1.0, -2.0, 4.0, -3.0) - 1.0) < 1.0e-5) { panic("wrong") }
	if !(math.Abs(pointLineDistance( 2.0, 2.0, 4.0,  0.0, 1.0,  0.0) - 2.12132) < 1.0e-5) { panic("wrong") }
	if !(math.Abs(pointLineDistance( 1.0, 1.0, 4.0,  3.0, 3.0, -2.0) - 3.60555) < 1.0e-5) { panic("wrong") }
	fmt.Println("OK")
}

2-2. Compile

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

2-4. Ask Questions or Get Feedback

%%hey problem_file=point_line_distance.md answer_file=go/point_line_distance.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/point_line_distance.jl
### begin my answer

function point_line_distance(x0, y0, x1, y1, p, q)
    dx, dy = x1 - x0, y1 - y0
    a, b = dy, -dx
    num = abs(a * (p - x0) + b * (q - y0))
    den = sqrt(a * a + b * b)
    num / den
end
### end my answer

function main()
    @assert abs(point_line_distance(-3.0, 1.0, 1.0, -2.0, 4.0, -3.0) - 1.0) < 1.0e-5
    @assert abs(point_line_distance( 2.0, 2.0, 4.0,  0.0, 1.0,  0.0) - 2.12132) < 1.0e-5
    @assert abs(point_line_distance( 1.0, 1.0, 4.0,  3.0, 3.0, -2.0) - 3.60555) < 1.0e-5
    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/point_line_distance.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/point_line_distance.jl

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

3-5. Ask Questions or Get Feedback

%%hey problem_file=point_line_distance.md answer_file=jl/point_line_distance.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/point_line_distance.ml
(** begin my answer *)

let point_line_distance x0 y0 x1 y1 p q =
  let dx = x1 -. x0 in
  let dy = y1 -. y0 in
  let a = dy in
  let b = -. dx in
  let num = abs_float (a *. (p -. x0) +. b *. (q -. y0)) in
  let den = sqrt (a *. a +. b *. b) in
  num /. den;;
(** end my answer *)

let main () =
  assert (abs_float (point_line_distance (-3.0) 1.0 1.0 (-2.0) 4.0 (-3.0) -. 1.0) < 1.0e-5);
  assert (abs_float (point_line_distance   2.0  2.0 4.0   0.0  1.0   0.0  -. 2.12132) < 1.0e-5);
  assert (abs_float (point_line_distance   1.0  1.0 4.0   3.0  3.0 (-2.0) -. 3.60555) < 1.0e-5);
  Printf.printf "OK\n"
;;

main()

4-2. Compile

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

• 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/point_line_distance

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/point_line_distance.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/point_line_distance.ml

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

4-5. Ask Questions or Get Feedback

%%hey problem_file=point_line_distance.md answer_file=ml/point_line_distance.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/point_line_distance.rs
/** begin my answer */

fn point_line_distance(x0: f64, y0: f64, x1: f64, y1: f64, p: f64, q: f64) -> f64 {
    let dx = x1 - x0;
    let dy = y1 - y0;
    let a = dy;
    let b = -dx;
    let num = (a * (p - x0) + b * (q - y0)).abs();
    let den = (a * a + b * b).sqrt();
    num / den
}
/** end my answer */

fn main() {
    assert!((point_line_distance(-3.0, 1.0, 1.0, -2.0, 4.0, -3.0) - 1.0).abs() < 1.0e-5);
    assert!((point_line_distance( 2.0, 2.0, 4.0,  0.0, 1.0,  0.0) - 2.12132).abs() < 1.0e-5);
    assert!((point_line_distance( 1.0, 1.0, 4.0,  3.0, 3.0, -2.0) - 3.60555).abs() < 1.0e-5);
    println!("OK")
}

5-2. Compile

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

• 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/point_line_distance

5-4. Ask Questions or Get Feedback

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

Problem:
{problem}

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

Give me a feedback to my answer.