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use std::iter;
use super::polynomial::{Polynomial};
use super::ratio::{Ratio};
use super::super::{Die, Dice, Fold, Reroll};
macro_rules! probabilities {
($polynomial:expr, $dice:expr, $reroll:expr, $results:expr) => ({
let polynomial = $polynomial;
let dice = $dice;
let exponent = if $reroll.is_some() { dice.0 * 2 } else { dice.0 };
let permutations = ((dice.1).0 as i128).pow(exponent);
let results = dice.results($results).enumerate();
results.map(move |(i, r)| (r, Ratio::new(polynomial[i], permutations))).collect()
});
}
impl Dice {
pub fn minimum(&self, fold: Fold) -> i32 {
match fold {
Fold::DropMinimum | Fold::DropMaximum => self.0 as i32 - 1,
Fold::Minimum | Fold::Maximum => 1,
Fold::Sum => self.0 as i32,
}
}
pub fn maximum(&self, fold: Fold) -> i32 {
match fold {
Fold::DropMinimum | Fold::DropMaximum => ((self.0 - 1) * (self.1).0) as i32,
Fold::Minimum | Fold::Maximum => (self.1).0 as i32,
Fold::Sum => (self.0 * (self.1).0) as i32,
}
}
pub fn average(&self, reroll: Option<Reroll>, fold: Fold) -> Ratio {
if fold == Fold::Sum {
Ratio::new(self.0 as i128, 1) * self.die().average(reroll)
} else {
let probabilities = self.probabilities(reroll, fold).into_iter();
probabilities.fold(Ratio::zero(), |a, (r, p)| a + (Ratio::new(r as i128, 1) * p))
}
}
pub fn results(&self, fold: Fold) -> impl Iterator<Item=i32> {
self.minimum(fold)..(self.maximum(fold) + 1)
}
pub fn probabilities(&self, reroll: Option<Reroll>, fold: Fold) -> Vec<(i32, Ratio)> {
match fold {
Fold::DropMinimum => probabilities_drop_minimum(*self, reroll),
Fold::DropMaximum => probabilities_drop_maximum(*self, reroll),
Fold::Minimum => probabilities_minimum(*self, reroll),
Fold::Maximum => probabilities_maximum(*self, reroll),
Fold::Sum => probabilities(*self, reroll),
}
}
}
fn repeat<T>(value: T, n: usize) -> impl Iterator<Item=T> where T: Copy {
iter::repeat(value).take(n)
}
fn coefficients(die: Die, reroll: Option<Reroll>) -> Vec<i128> {
if let Some(reroll) = reroll {
let (low, high) = super::numerators(die, reroll);
let mut coefficients = Vec::with_capacity(die.0 as usize);
coefficients.extend(repeat(low, low as usize));
coefficients.extend(repeat(high, die.0 as usize - low as usize));
coefficients
} else {
vec![1; die.0 as usize]
}
}
fn probabilities(dice: Dice, reroll: Option<Reroll>) -> Vec<(i32, Ratio)> {
let polynomial = Polynomial::new(coefficients(dice.1, reroll)).pow(dice.0);
probabilities!(polynomial, dice, reroll, Fold::Sum)
}
fn polynomials_drop_minimum(dice: Dice, reroll: Option<Reroll>) -> Vec<Polynomial> {
let coefficients = coefficients(dice.1, reroll);
dice.die().results().map(|r| {
let zero = r as usize - 1;
let coefficients = repeat(0, zero).chain(coefficients.iter().cloned().skip(zero));
Polynomial::new(coefficients.collect()).pow(dice.0)
}).collect()
}
fn polynomial_drop_minimum(dice: Dice, reroll: Option<Reroll>) -> Polynomial {
let polynomials = polynomials_drop_minimum(dice, reroll);
let mut polynomial = Polynomial::new(vec![0; polynomials.last().unwrap().size()]);
for (k, left) in polynomials.iter().enumerate() {
let mut summand = left.clone();
if k + 1 < polynomials.len() {
summand -= &polynomials[k + 1];
}
summand.reduce(k);
polynomial += &summand;
}
polynomial
}
fn probabilities_drop_minimum(dice: Dice, reroll: Option<Reroll>) -> Vec<(i32, Ratio)> {
let polynomial = polynomial_drop_minimum(dice, reroll);
probabilities!(polynomial, dice, reroll, Fold::DropMinimum)
}
fn probabilities_minimum(dice: Dice, reroll: Option<Reroll>) -> Vec<(i32, Ratio)> {
let sums = polynomials_drop_minimum(dice, reroll).iter().map(|p| p.sum()).collect::<Vec<_>>();
let differences = sums.iter().enumerate().map(|(i, s)| {
if i + 1 == sums.len() { *s } else { s - sums[i + 1] }
}).collect::<Vec<_>>();
probabilities!(differences, dice, reroll, Fold::Minimum)
}
fn polynomials_drop_maximum(dice: Dice, reroll: Option<Reroll>) -> Vec<Polynomial> {
let coefficients = coefficients(dice.1, reroll);
dice.die().results().map(|r| {
let zeroes = repeat(0, ((dice.1).0 - r as u32) as usize);
let coefficients = coefficients.iter().cloned().take(r as usize).chain(zeroes);
Polynomial::new(coefficients.collect()).pow(dice.0)
}).collect()
}
fn polynomial_drop_maximum(dice: Dice, reroll: Option<Reroll>) -> Polynomial {
let polynomials = polynomials_drop_maximum(dice, reroll);
let mut polynomial = Polynomial::new(vec![0; polynomials.last().unwrap().size()]);
for (k, left) in polynomials.iter().enumerate() {
let mut summand = left.clone();
if k != 0 {
summand -= &polynomials[k - 1];
}
summand.reduce(k);
polynomial += &summand;
}
polynomial
}
fn probabilities_drop_maximum(dice: Dice, reroll: Option<Reroll>) -> Vec<(i32, Ratio)> {
let polynomial = polynomial_drop_maximum(dice, reroll);
probabilities!(polynomial, dice, reroll, Fold::DropMaximum)
}
fn probabilities_maximum(dice: Dice, reroll: Option<Reroll>) -> Vec<(i32, Ratio)> {
let sums = polynomials_drop_maximum(dice, reroll).iter().map(|p| p.sum()).collect::<Vec<_>>();
let differences = sums.iter().enumerate().map(|(i, s)| {
if i == 0 { *s } else { s - sums[i - 1] }
}).collect::<Vec<_>>();
probabilities!(differences, dice, reroll, Fold::Maximum)
}