Struct HamiltonianPath 

pub struct HamiltonianPath<G> { /* private fields */ }

The Hamiltonian Path problem.

Given a graph G = (V, E), determine whether G contains a Hamiltonian path, i.e., a simple path that visits every vertex exactly once.

Representation

A configuration is a sequence of n vertex indices representing a vertex ordering (permutation). Each position i in the configuration holds the vertex visited at step i. A valid solution must be a permutation of 0..n where consecutive entries are adjacent in the graph.

The search space has dims() = [n; n] (each position can hold any of n vertices), so brute-force enumerates n^n configurations. Only n! permutations can satisfy the constraints, but the encoding avoids complex variable-domain schemes and matches the problem’s natural formulation.

Type Parameters

• G - Graph type (e.g., SimpleGraph)

Example

use problemreductions::models::graph::HamiltonianPath;
use problemreductions::topology::SimpleGraph;
use problemreductions::{Problem, Solver, BruteForce};

// Path graph: 0-1-2-3
let graph = SimpleGraph::new(4, vec![(0, 1), (1, 2), (2, 3)]);
let problem = HamiltonianPath::new(graph);

let solver = BruteForce::new();
let solution = solver.find_witness(&problem);
assert!(solution.is_some());

Implementations

impl<G: Graph> HamiltonianPath<G>

pub fn new(graph: G) -> Self

Create a new Hamiltonian Path problem from a graph.

pub fn graph(&self) -> &G

Get a reference to the underlying graph.

pub fn num_vertices(&self) -> usize

Get the number of vertices in the underlying graph.

pub fn num_edges(&self) -> usize

Get the number of edges in the underlying graph.

pub fn is_valid_solution(&self, config: &[usize]) -> bool

Check if a configuration is a valid Hamiltonian path.

Trait Implementations

impl<G: Clone> Clone for HamiltonianPath<G>

fn clone(&self) -> HamiltonianPath<G>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<G: Debug> Debug for HamiltonianPath<G>

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

Formats the value using the given formatter.

impl<'de, G> Deserialize<'de> for HamiltonianPath<G>

where G: Deserialize<'de>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<G> Problem for HamiltonianPath<G>

where G: Graph + VariantParam,

const NAME: &'static str = "HamiltonianPath"

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

type Value = Or

The evaluation value type.

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

Returns variant attributes derived from type parameters.

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

Configuration space dimensions. Each entry is the cardinality of that variable.

fn evaluate(&self, config: &[usize]) -> Or

Evaluate the problem on a configuration.

fn num_variables(&self) -> usize

Number of variables (derived from dims).

fn problem_type() -> ProblemType

Look up this problem’s catalog entry.

impl ReduceTo<DegreeConstrainedSpanningTree<SimpleGraph>> for HamiltonianPath<SimpleGraph>

type Result = ReductionHamiltonianPathToDegreeConstrainedSpanningTree

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl ReduceTo<HamiltonianPath<SimpleGraph>> for HamiltonianCircuit<SimpleGraph>

type Result = ReductionHamiltonianCircuitToHamiltonianPath

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl ReduceTo<ILP> for HamiltonianPath<SimpleGraph>

type Result = ReductionHamiltonianPathToILP

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl ReduceTo<IsomorphicSpanningTree<SimpleGraph>> for HamiltonianPath<SimpleGraph>

type Result = ReductionHPToIST

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl<G> Serialize for HamiltonianPath<G>

where G: Serialize,

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl DeclaredVariant for HamiltonianPath<SimpleGraph>