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|
||||
checksum = "fa4f8080344d4671fb4e831a13ad1e68092748387dfc4f55e356242fae12ce3e"
|
||||
dependencies = [
|
||||
"proc-macro2",
|
||||
"quote",
|
||||
"syn",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "zerocopy-derive"
|
||||
version = "0.8.17"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "06718a168365cad3d5ff0bb133aad346959a2074bd4a85c121255a11304a8626"
|
||||
dependencies = [
|
||||
"proc-macro2",
|
||||
"quote",
|
||||
"syn",
|
||||
]
|
||||
9
Cargo.toml
Normal file
9
Cargo.toml
Normal file
|
|
@ -0,0 +1,9 @@
|
|||
[package]
|
||||
name = "perfectset"
|
||||
version = "0.1.0"
|
||||
edition = "2021"
|
||||
|
||||
[dependencies]
|
||||
nalgebra = "0.33.2"
|
||||
num = "0.4.3"
|
||||
rand = "0.9.0"
|
||||
208
src/card.rs
Normal file
208
src/card.rs
Normal file
|
|
@ -0,0 +1,208 @@
|
|||
use crate::f3::F3;
|
||||
use nalgebra::{Matrix4, Vector4};
|
||||
use num::traits::Zero;
|
||||
use rand::distr::{Distribution, StandardUniform};
|
||||
use rand::Rng;
|
||||
use std::fmt::{Display, Formatter};
|
||||
|
||||
#[derive(Copy, Clone)]
|
||||
pub struct Card {
|
||||
v: Vector4<F3>,
|
||||
}
|
||||
|
||||
impl Card {
|
||||
pub fn new(number: u8, shading: u8, color: u8, shape: u8) -> Self {
|
||||
Card {
|
||||
v: Vector4::<F3>::new(
|
||||
number.try_into().unwrap(),
|
||||
shading.try_into().unwrap(),
|
||||
color.try_into().unwrap(),
|
||||
shape.try_into().unwrap(),
|
||||
),
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl Display for Card {
|
||||
fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
|
||||
let number = match self.v.x.into() {
|
||||
0 => "one",
|
||||
1 => "two",
|
||||
2 => "three",
|
||||
_ => unreachable!(),
|
||||
};
|
||||
let shading = match self.v.y.into() {
|
||||
0 => "solid",
|
||||
1 => "striped",
|
||||
2 => "open",
|
||||
_ => unreachable!(),
|
||||
};
|
||||
let color = match self.v.z.into() {
|
||||
0 => "red",
|
||||
1 => "green",
|
||||
2 => "purple",
|
||||
_ => unreachable!(),
|
||||
};
|
||||
let shape = match self.v.w.into() {
|
||||
0 => "ovals",
|
||||
1 => "squiggles",
|
||||
2 => "diamonds",
|
||||
_ => unreachable!(),
|
||||
};
|
||||
write!(f, "{}-{}-{}-{}", number, shading, color, shape)
|
||||
}
|
||||
}
|
||||
|
||||
impl Distribution<Card> for StandardUniform {
|
||||
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Card {
|
||||
Card {
|
||||
v: Vector4::<F3>::from_fn(|_, _| rng.random()),
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
pub struct CardSet {
|
||||
cards: Vec<Card>,
|
||||
}
|
||||
|
||||
impl CardSet {
|
||||
pub fn new(cards: &[Card]) -> Self {
|
||||
CardSet {
|
||||
cards: Vec::from(cards),
|
||||
}
|
||||
}
|
||||
|
||||
fn grid(&self) -> [[[[bool; 3]; 3]; 3]; 3] {
|
||||
let mut grid = [[[[false; 3]; 3]; 3]; 3];
|
||||
for card in &self.cards {
|
||||
let number: usize = card.v.x.into();
|
||||
let shading: usize = card.v.y.into();
|
||||
let color: usize = card.v.z.into();
|
||||
let shape: usize = card.v.w.into();
|
||||
grid[number][shading][color][shape] = true;
|
||||
}
|
||||
grid
|
||||
}
|
||||
|
||||
pub fn score(&self) -> f32 {
|
||||
let grid = self.grid();
|
||||
let mut bins = [[[[0u8; 3]; 3]; 3]; 4];
|
||||
for number in 0..3 {
|
||||
for shading in 0..3 {
|
||||
for color in 0..3 {
|
||||
for shape in 0..3 {
|
||||
if grid[number][shading][color][shape] {
|
||||
bins[0][number][shading][color] += 1;
|
||||
bins[1][number][shading][shape] += 1;
|
||||
bins[2][number][color][shape] += 1;
|
||||
bins[3][shading][color][shape] += 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
let mut score = 0f32;
|
||||
for bin in bins.as_flattened().as_flattened().as_flattened() {
|
||||
if !bin.is_zero() {
|
||||
let p = f32::from(*bin) / 20.0;
|
||||
score -= p * f32::log2(p);
|
||||
}
|
||||
}
|
||||
score
|
||||
}
|
||||
|
||||
pub fn print_grid(&self) {
|
||||
let grid = self.grid();
|
||||
println!("+---+---+---+");
|
||||
for number in 0..3 {
|
||||
for color in 0..3 {
|
||||
print!("|");
|
||||
for shading in 0..3 {
|
||||
for shape in 0..3 {
|
||||
if grid[number][shading][color][shape] {
|
||||
print!("X");
|
||||
} else {
|
||||
print!(" ");
|
||||
}
|
||||
}
|
||||
print!("|");
|
||||
}
|
||||
println!("");
|
||||
}
|
||||
println!("+---+---+---+");
|
||||
}
|
||||
println!("score: {}", self.score());
|
||||
}
|
||||
}
|
||||
|
||||
pub struct CardMapping {
|
||||
m: Matrix4<F3>,
|
||||
v: Vector4<F3>,
|
||||
}
|
||||
|
||||
impl CardMapping {
|
||||
pub fn map_single(&self, card: Card) -> Card {
|
||||
Card {
|
||||
v: self.m * card.v + self.v,
|
||||
}
|
||||
}
|
||||
|
||||
pub fn map(&self, cs: CardSet) -> CardSet {
|
||||
CardSet {
|
||||
cards: cs
|
||||
.cards
|
||||
.into_iter()
|
||||
.map(|card| self.map_single(card))
|
||||
.collect(),
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Matrix4::determinant() only works for floating point types :(
|
||||
fn determinant(m: &Matrix4<F3>) -> F3 {
|
||||
let d_12 = m.m33 * m.m44 - m.m43 * m.m34;
|
||||
let d_13 = m.m23 * m.m44 - m.m43 * m.m24;
|
||||
let d_14 = m.m23 * m.m34 - m.m33 * m.m24;
|
||||
let d_23 = m.m13 * m.m44 - m.m43 * m.m14;
|
||||
let d_24 = m.m13 * m.m34 - m.m33 * m.m14;
|
||||
let d_34 = m.m13 * m.m24 - m.m23 * m.m14;
|
||||
let d_1 = m.m22 * d_12 - m.m32 * d_13 + m.m42 * d_14;
|
||||
let d_2 = m.m12 * d_12 - m.m32 * d_23 + m.m42 * d_24;
|
||||
let d_3 = m.m12 * d_13 - m.m22 * d_23 + m.m42 * d_34;
|
||||
let d_4 = m.m12 * d_14 - m.m22 * d_24 + m.m32 * d_34;
|
||||
m.m11 * d_1 - m.m21 * d_2 + m.m31 * d_3 - m.m41 * d_4
|
||||
}
|
||||
|
||||
impl Distribution<CardMapping> for StandardUniform {
|
||||
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> CardMapping {
|
||||
loop {
|
||||
let m = Matrix4::<F3>::from_fn(|_, _| rng.random());
|
||||
if !determinant(&m).is_zero() {
|
||||
return CardMapping {
|
||||
m: m,
|
||||
v: Vector4::<F3>::from_fn(|_, _| rng.random()),
|
||||
};
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
use rand::rng;
|
||||
|
||||
#[test]
|
||||
fn mapping_invertable() {
|
||||
let mut rng = rng();
|
||||
for _ in 0..1000 {
|
||||
let mapping: CardMapping = rng.sample(StandardUniform);
|
||||
for i in 0..3u8.pow(4) {
|
||||
let card = Card::new(i / 3 / 3 / 3, i / 3 / 3 % 3, i / 3 % 3, i % 3);
|
||||
if !card.v.is_zero() {
|
||||
assert_ne!(mapping.map_single(card).v, mapping.v);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
236
src/f3.rs
Normal file
236
src/f3.rs
Normal file
|
|
@ -0,0 +1,236 @@
|
|||
use num::traits::{One, Zero};
|
||||
use rand::distr::{Distribution, StandardUniform};
|
||||
use rand::Rng;
|
||||
use std::ops::{Add, AddAssign, Mul, MulAssign, Sub, SubAssign};
|
||||
|
||||
#[derive(Copy, Clone, Debug, PartialEq)]
|
||||
pub struct F3 {
|
||||
s: i8,
|
||||
}
|
||||
|
||||
impl F3 {
|
||||
pub const ELEMENTS: [F3; 3] = [F3 { s: 0 }, F3 { s: 1 }, F3 { s: 2 }];
|
||||
}
|
||||
|
||||
impl From<F3> for usize {
|
||||
fn from(f: F3) -> usize {
|
||||
f.s as usize
|
||||
}
|
||||
}
|
||||
|
||||
impl TryFrom<u8> for F3 {
|
||||
type Error = &'static str;
|
||||
|
||||
fn try_from(i: u8) -> Result<Self, Self::Error> {
|
||||
if i > 2 {
|
||||
Err("out of range")
|
||||
} else {
|
||||
Ok(F3 { s: i as i8 })
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl Add for F3 {
|
||||
type Output = F3;
|
||||
|
||||
fn add(self, rhs: Self) -> Self::Output {
|
||||
F3 {
|
||||
s: (self.s + rhs.s).rem_euclid(3),
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl AddAssign for F3 {
|
||||
fn add_assign(&mut self, rhs: Self) {
|
||||
*self = *self + rhs;
|
||||
}
|
||||
}
|
||||
|
||||
impl Zero for F3 {
|
||||
fn zero() -> Self {
|
||||
F3 { s: 0 }
|
||||
}
|
||||
|
||||
fn is_zero(&self) -> bool {
|
||||
*self == Self::zero()
|
||||
}
|
||||
}
|
||||
|
||||
impl Sub for F3 {
|
||||
type Output = F3;
|
||||
|
||||
fn sub(self, rhs: Self) -> Self::Output {
|
||||
F3 {
|
||||
s: (self.s - rhs.s).rem_euclid(3),
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl SubAssign for F3 {
|
||||
fn sub_assign(&mut self, rhs: Self) {
|
||||
*self = *self - rhs;
|
||||
}
|
||||
}
|
||||
|
||||
impl Mul for F3 {
|
||||
type Output = F3;
|
||||
|
||||
fn mul(self, rhs: Self) -> Self::Output {
|
||||
F3 {
|
||||
s: (self.s * rhs.s).rem_euclid(3),
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl MulAssign for F3 {
|
||||
fn mul_assign(&mut self, rhs: Self) {
|
||||
*self = *self * rhs;
|
||||
}
|
||||
}
|
||||
|
||||
impl One for F3 {
|
||||
fn one() -> Self {
|
||||
F3 { s: 1 }
|
||||
}
|
||||
|
||||
fn is_one(&self) -> bool {
|
||||
*self == Self::one()
|
||||
}
|
||||
}
|
||||
|
||||
impl Distribution<F3> for StandardUniform {
|
||||
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F3 {
|
||||
F3 {
|
||||
s: rng.random_range(0..3),
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
|
||||
#[test]
|
||||
fn add_associative() {
|
||||
for a in F3::ELEMENTS {
|
||||
for b in F3::ELEMENTS {
|
||||
for c in F3::ELEMENTS {
|
||||
assert_eq!((a + b) + c, a + (b + c));
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn add_identity() {
|
||||
for a in F3::ELEMENTS {
|
||||
assert_eq!(F3::zero() + a, a);
|
||||
assert_eq!(a + F3::zero(), a);
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn add_inverse() {
|
||||
for a in F3::ELEMENTS {
|
||||
let mut has_inverse = false;
|
||||
for b in F3::ELEMENTS {
|
||||
if a + b == F3::zero() {
|
||||
assert!(!has_inverse);
|
||||
has_inverse = true;
|
||||
}
|
||||
}
|
||||
assert!(has_inverse);
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn sub_is_add_inverse() {
|
||||
for a in F3::ELEMENTS {
|
||||
for b in F3::ELEMENTS {
|
||||
assert_eq!(a + b - b, a);
|
||||
assert_eq!(a - b + b, a);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn add_commutative() {
|
||||
for a in F3::ELEMENTS {
|
||||
for b in F3::ELEMENTS {
|
||||
assert_eq!(a + b, b + a);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn mul_associative() {
|
||||
for a in F3::ELEMENTS {
|
||||
for b in F3::ELEMENTS {
|
||||
for c in F3::ELEMENTS {
|
||||
assert_eq!((a * b) * c, a * (b * c));
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn mul_identity() {
|
||||
for a in F3::ELEMENTS {
|
||||
assert_eq!(F3::one() * a, a);
|
||||
assert_eq!(a * F3::one(), a);
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn mul_inverse() {
|
||||
for a in F3::ELEMENTS {
|
||||
if !a.is_zero() {
|
||||
let mut has_inverse = false;
|
||||
for b in F3::ELEMENTS {
|
||||
if a * b == F3::one() {
|
||||
assert!(!has_inverse);
|
||||
has_inverse = true;
|
||||
}
|
||||
}
|
||||
assert!(has_inverse);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn mul_commutative() {
|
||||
for a in F3::ELEMENTS {
|
||||
for b in F3::ELEMENTS {
|
||||
assert_eq!(a * b, b * a);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn distributive() {
|
||||
for a in F3::ELEMENTS {
|
||||
for b in F3::ELEMENTS {
|
||||
for c in F3::ELEMENTS {
|
||||
assert_eq!(a * (b + c), a * b + a * c);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn add_is_like_set() {
|
||||
let e = F3::ELEMENTS;
|
||||
|
||||
assert_eq!(e[0] + e[0] + e[0], F3::zero());
|
||||
assert_eq!(e[1] + e[1] + e[1], F3::zero());
|
||||
assert_eq!(e[2] + e[2] + e[2], F3::zero());
|
||||
assert_eq!(e[0] + e[1] + e[2], F3::zero());
|
||||
|
||||
assert_ne!(e[0] + e[0] + e[1], F3::zero());
|
||||
assert_ne!(e[0] + e[0] + e[2], F3::zero());
|
||||
assert_ne!(e[1] + e[1] + e[0], F3::zero());
|
||||
assert_ne!(e[1] + e[1] + e[2], F3::zero());
|
||||
assert_ne!(e[2] + e[2] + e[0], F3::zero());
|
||||
assert_ne!(e[2] + e[2] + e[1], F3::zero());
|
||||
}
|
||||
}
|
||||
44
src/main.rs
Normal file
44
src/main.rs
Normal file
|
|
@ -0,0 +1,44 @@
|
|||
mod card;
|
||||
mod f3;
|
||||
|
||||
use crate::card::{Card, CardMapping, CardSet};
|
||||
use rand::distr::StandardUniform;
|
||||
use rand::{rng, Rng};
|
||||
|
||||
fn main() {
|
||||
let mut rng = rng();
|
||||
let mut cards = CardSet::new(&[
|
||||
Card::new(0, 0, 0, 1),
|
||||
Card::new(0, 0, 1, 0),
|
||||
Card::new(0, 0, 1, 2),
|
||||
Card::new(0, 0, 2, 1),
|
||||
Card::new(0, 1, 1, 1),
|
||||
Card::new(0, 2, 0, 0),
|
||||
Card::new(0, 2, 0, 2),
|
||||
Card::new(0, 2, 2, 0),
|
||||
Card::new(0, 2, 2, 2),
|
||||
Card::new(1, 0, 1, 1),
|
||||
Card::new(1, 2, 1, 1),
|
||||
Card::new(2, 0, 0, 0),
|
||||
Card::new(2, 0, 0, 2),
|
||||
Card::new(2, 0, 2, 0),
|
||||
Card::new(2, 0, 2, 2),
|
||||
Card::new(2, 1, 1, 1),
|
||||
Card::new(2, 2, 0, 1),
|
||||
Card::new(2, 2, 1, 0),
|
||||
Card::new(2, 2, 1, 2),
|
||||
Card::new(2, 2, 2, 1),
|
||||
]);
|
||||
cards.print_grid();
|
||||
|
||||
let mut max_score = cards.score();
|
||||
loop {
|
||||
let mapping: CardMapping = rng.sample(StandardUniform);
|
||||
cards = mapping.map(cards);
|
||||
let score = cards.score();
|
||||
if score > max_score {
|
||||
max_score = score;
|
||||
cards.print_grid();
|
||||
}
|
||||
}
|
||||
}
|
||||
Loading…
Reference in a new issue