Struct SimultaneousIncongruences 

pub struct SimultaneousIncongruences { /* private fields */ }

Simultaneous Incongruences problem.

Given a list of pairs (aᵢ, bᵢ) with bᵢ > 0 and 1 ≤ aᵢ ≤ bᵢ, determine whether there exists a non-negative integer x such that x ≢ aᵢ (mod bᵢ) for all i simultaneously.

The search space is x ∈ {0, …, L−1} where L = lcm(b₁, …, bₙ) (one full period). config[0] encodes x directly.

Example

use problemreductions::models::algebraic::SimultaneousIncongruences;
use problemreductions::{Problem, BruteForce};

// pairs: [(2,2),(1,3),(2,5),(3,7)] — lcm=210, x=5 is a solution
let problem = SimultaneousIncongruences::new(vec![(2,2),(1,3),(2,5),(3,7)]).unwrap();
let solver = BruteForce::new();
let witness = solver.solve(&problem).unwrap();
assert!(witness.is_some());

Implementations

impl SimultaneousIncongruences

pub fn new(pairs: Vec<(i64, i64)>) -> Result<Self, ConstructionError>

Create a new SimultaneousIncongruences instance, returning an error if any pair is invalid.

pub fn num_pairs(&self) -> usize

Get the number of incongruence pairs.

pub fn pairs(&self) -> &[(i64, i64)]

Get the incongruence pairs.

pub fn lcm_moduli(&self) -> i64

Compute the LCM of all moduli.

Trait Implementations

impl BruteForceProblem for SimultaneousIncongruences

fn dimensions(&self) -> Vec<usize>

Cardinality of each coordinate in the brute-force search space.

fn num_variables(&self) -> usize

Number of coordinates in the brute-force search space.

impl Clone for SimultaneousIncongruences

fn clone(&self) -> SimultaneousIncongruences

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SimultaneousIncongruences

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl DeclaredVariant for SimultaneousIncongruences

impl<'de> Deserialize<'de> for SimultaneousIncongruences

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for SimultaneousIncongruences

const NAME: &'static str = "SimultaneousIncongruences"

Base name of this problem type (e.g., “MaximumIndependentSet”).

type Solution = i64

Mathematical witness type for this problem.

type Value = Or

The evaluation value type.

fn parameter_names() -> &'static [&'static str]

Canonical parameter names for this problem model.

fn parameters(&self) -> ProblemParameters

Measure the complete canonical parameters of this concrete instance.

fn variant() -> Vec<(&'static str, &'static str)>

Returns variant attributes derived from type parameters.

fn evaluate(&self, solution: &Self::Solution) -> Result<Or, EvaluationError>

Evaluate the problem on a solution.

fn problem_type() -> ProblemType

Look up this problem’s catalog entry.

impl ReduceTo<SimultaneousIncongruences> for KSatisfiability<K3>

type Result = Reduction3SATToSimultaneousIncongruences

The reduction result type.

fn reduce_to(&self) -> Result<Self::Result, ReductionError>

Reduce this problem to the target problem type.

fn target_construction(error: ConstructionError) -> ReductionError

where Self: Sized,

Attach this reduction edge to a target-construction failure.

fn exact_i64( value: usize, operation: impl Into<String>, ) -> Result<i64, ReductionError>

where Self: Sized,

Convert a structural count used by the target’s exact integer algebra.

impl Serialize for SimultaneousIncongruences

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.