Struct DirectedHamiltonianPath 

pub struct DirectedHamiltonianPath { /* private fields */ }

The Directed Hamiltonian Path problem.

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

Representation

A configuration encodes a permutation using the Lehmer code: dims() = [n, n-1, ..., 2, 1], yielding n! reachable configurations. Each configuration is decoded to a permutation of 0..n, and a solution is valid when every consecutive pair (path[i], path[i+1]) is an arc in the directed graph.

Example

use problemreductions::models::graph::DirectedHamiltonianPath;
use problemreductions::topology::DirectedGraph;
use problemreductions::{Problem, Solver, BruteForce};

// Simple directed path: 0->1->2->3
let graph = DirectedGraph::new(4, vec![(0, 1), (1, 2), (2, 3)]);
let problem = DirectedHamiltonianPath::new(graph);

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

Implementations

impl DirectedHamiltonianPath

pub fn new(graph: DirectedGraph) -> Self

Create a new Directed Hamiltonian Path problem from a directed graph.

pub fn graph(&self) -> &DirectedGraph

Get a reference to the underlying directed graph.

pub fn num_vertices(&self) -> usize

Get the number of vertices in the directed graph.

pub fn num_arcs(&self) -> usize

Get the number of arcs in the directed graph.

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

Check if a configuration is a valid directed Hamiltonian path.

Trait Implementations

impl Clone for DirectedHamiltonianPath

fn clone(&self) -> DirectedHamiltonianPath

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for DirectedHamiltonianPath

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for DirectedHamiltonianPath

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for DirectedHamiltonianPath

const NAME: &'static str = "DirectedHamiltonianPath"

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<ILP> for DirectedHamiltonianPath

type Result = ReductionDirectedHamiltonianPathToILP

The reduction result type.

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

Reduce this problem to the target problem type.

impl Serialize for DirectedHamiltonianPath

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 DirectedHamiltonianPath