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//! Iterator over value tuples satisfying a cage arithmetic constraint.
use crate::operator::{ArithmeticConstraint, CommutativeOperator, NonCommutativeOperator};
use crate::{N, T};
use std::collections::VecDeque;
pub type Tuple = Vec<N>;
/// Iterator over all `k`-tuples of values in `1..=n` that satisfy an arithmetic constraint.
///
/// Tuples are yielded in lexicographic order via BFS. Commutative operations
/// use the ring identity to prune the search; non-commutative operations
/// enumerate all pairs without pruning.
pub struct Tuples {
n: N,
k: N,
constraint: ArithmeticConstraint,
queue: VecDeque<Tuple>,
}
impl Tuples {
/// Creates a `Tuples` iterator for a commutative (monotonic) operation.
///
/// Used by [`Table::commutative`] (a test utility); commutative cages use
/// [`Mdd`] directly in production.
#[must_use]
#[allow(dead_code)]
pub fn commutative(n: N, k: N, operator: CommutativeOperator, target: T) -> Self {
Self {
n,
k,
constraint: ArithmeticConstraint::CommutativeConstraint(operator, target),
queue: VecDeque::from([vec![]]),
}
}
/// Creates a `Tuples` iterator for a non-commutative operation over pairs (`k = 2`).
#[must_use]
pub fn non_commutative(n: N, operator: NonCommutativeOperator, target: T) -> Self {
Self {
n,
k: 2,
constraint: ArithmeticConstraint::NonCommutativeConstraint(operator, target),
queue: VecDeque::from([vec![]]),
}
}
/// Advances one step for a commutative operation.
///
/// Prunes partial tuples whose result plus the minimum possible completion
/// already exceeds the target, using the dual operation's identity element
/// as the minimum-per-remaining-slot bound.
fn monotonic(&mut self, operator: CommutativeOperator, target: T) -> Step {
let Some(tuple) = self.queue.pop_front() else {
return Step::Exhausted;
};
if tuple.len() == self.k as usize {
if operator.apply_to_tuple(&tuple) == target {
Step::Yield(tuple)
} else {
Step::Continue
}
} else {
for i in 1..=self.n {
let mut new_tuple = tuple.clone();
new_tuple.push(i);
let s = operator.apply_to_tuple(&new_tuple);
// new_tuple.len() <= k <= 9, so this cast never truncates.
#[allow(clippy::cast_possible_truncation)]
let remaining = self.k - new_tuple.len() as N;
let residual = operator.dual().identity() * T::from(remaining);
if s + residual <= target {
self.queue.push_back(new_tuple);
}
}
Step::Continue
}
}
/// Advances one step for a non-commutative operation.
///
/// No pruning is possible since the operation is not monotonic.
fn non_monotonic(&mut self, operator: NonCommutativeOperator, target: T) -> Step {
let Some(tuple) = self.queue.pop_front() else {
return Step::Exhausted;
};
if tuple.len() == self.k as usize {
if operator.apply(tuple[0], tuple[1]) == target {
Step::Yield(tuple)
} else {
Step::Continue
}
} else {
for i in 1..=self.n {
let mut new_tuple = tuple.clone();
new_tuple.push(i);
self.queue.push_back(new_tuple);
}
Step::Continue
}
}
}
/// Result of one BFS step.
enum Step {
/// A complete tuple that satisfies the target — yield it.
Yield(Tuple),
/// Partial tuple extended or complete tuple rejected — keep going.
Continue,
/// Queue is empty — iteration is finished.
Exhausted,
}
impl Iterator for Tuples {
type Item = Tuple;
fn next(&mut self) -> Option<Self::Item> {
loop {
let step = match self.constraint {
ArithmeticConstraint::CommutativeConstraint(operator, target) => {
self.monotonic(operator, target)
}
ArithmeticConstraint::NonCommutativeConstraint(operator, target) => {
self.non_monotonic(operator, target)
}
};
match step {
Step::Yield(tuple) => return Some(tuple),
Step::Continue => {}
Step::Exhausted => return None,
}
}
}
}
#[cfg(test)]
mod tests {
use crate::operator::CommutativeOperator::{Add, Multiply};
use crate::operator::NonCommutativeOperator::{Divide, Subtract};
use crate::tuples::{Tuple, Tuples};
#[test]
fn sum_to_6() {
let tuples = Tuples::commutative(7, 3, Add, 6);
let actual: Vec<Tuple> = tuples.collect();
assert_eq!(
actual,
vec![
vec![1, 1, 4],
vec![1, 2, 3],
vec![1, 3, 2],
vec![1, 4, 1],
vec![2, 1, 3],
vec![2, 2, 2],
vec![2, 3, 1],
vec![3, 1, 2],
vec![3, 2, 1],
vec![4, 1, 1],
]
);
}
#[test]
fn multiply_to_24() {
let tuples = Tuples::commutative(7, 3, Multiply, 24);
let actual: Vec<Tuple> = tuples.collect();
// n=7 excludes e.g. [1, 3, 8] and [1, 2, 12]
assert_eq!(
actual,
vec![
vec![1, 4, 6],
vec![1, 6, 4],
vec![2, 2, 6],
vec![2, 3, 4],
vec![2, 4, 3],
vec![2, 6, 2],
vec![3, 2, 4],
vec![3, 4, 2],
vec![4, 1, 6],
vec![4, 2, 3],
vec![4, 3, 2],
vec![4, 6, 1],
vec![6, 1, 4],
vec![6, 2, 2],
vec![6, 4, 1],
]
);
}
#[test]
fn subtract_to_2() {
let tuples = Tuples::non_commutative(4, Subtract, 2);
let actual: Vec<Tuple> = tuples.collect();
assert_eq!(
actual,
vec![vec![1, 3], vec![2, 4], vec![3, 1], vec![4, 2],]
);
}
#[test]
fn divide_to_2() {
let tuples = Tuples::non_commutative(6, Divide, 2);
let actual: Vec<Tuple> = tuples.collect();
// includes integer-division pairs e.g. [2, 5] since max(2,5)/min(2,5) = 5/2 = 2
assert_eq!(
actual,
vec![
vec![1, 2],
vec![2, 1],
vec![2, 4],
vec![2, 5],
vec![3, 6],
vec![4, 2],
vec![5, 2],
vec![6, 3],
]
);
}
}