edu.princeton.cs.algorithms

Class BellmanFordSP

java.lang.Object

edu.princeton.cs.algorithms.BellmanFordSP

public class BellmanFordSP
extends Object

The BellmanFordSP class represents a data type for solving the single-source shortest paths problem in edge-weighted digraphs with no negative cycles. The edge weights can be positive, negative, or zero. This class finds either a shortest path from the source vertex s to every other vertex or a negative cycle reachable from the source vertex.

This implementation uses the Bellman-Ford-Moore algorithm. The constructor takes time proportional to V (V + E) in the worst case, where V is the number of vertices and E is the number of edges. Afterwards, the distTo(), hasPathTo(), and hasNegativeCycle() methods take constant time; the pathTo() and negativeCycle() method takes time proportional to the number of edges returned.

For additional documentation, see Section 4.4 of Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.

Author:

Robert Sedgewick, Kevin Wayne

Constructor Summary

Constructors

Constructor and Description
BellmanFordSP(EdgeWeightedDigraph G, int s) Computes a shortest paths tree from s to every other vertex in the edge-weighted digraph G.

Method Summary

Methods

Modifier and Type	Method and Description
double	distTo(int v) Returns the length of a shortest path from the source vertex s to vertex v.
boolean	hasNegativeCycle() Is there a negative cycle reachable from the source vertex s?
boolean	hasPathTo(int v) Is there a path from the source s to vertex v?
static void	main(String[] args) Unit tests the BellmanFordSP data type.
Iterable<DirectedEdge>	negativeCycle() Returns a negative cycle reachable from the source vertex s, or null if there is no such cycle.
Iterable<DirectedEdge>	pathTo(int v) Returns a shortest path from the source s to vertex v.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

BellmanFordSP

public BellmanFordSP(EdgeWeightedDigraph G,
             int s)

Computes a shortest paths tree from s to every other vertex in the edge-weighted digraph G.

Parameters:

G - the acyclic digraph

s - the source vertex

Throws:

IllegalArgumentException - unless 0 ≤ s ≤ V - 1

Method Detail

hasNegativeCycle

public boolean hasNegativeCycle()

Is there a negative cycle reachable from the source vertex s?

Returns:

true if there is a negative cycle reachable from the source vertex s, and false otherwise

negativeCycle

public Iterable<DirectedEdge> negativeCycle()

Returns a negative cycle reachable from the source vertex s, or null if there is no such cycle.

Returns:

a negative cycle reachable from the soruce vertex s as an iterable of edges, and null if there is no such cycle

distTo

public double distTo(int v)

Returns the length of a shortest path from the source vertex s to vertex v.

Parameters:

v - the destination vertex

Returns:

the length of a shortest path from the source vertex s to vertex v; Double.POSITIVE_INFINITY if no such path

Throws:

UnsupportedOperationException - if there is a negative cost cycle reachable from the source vertex s

hasPathTo

public boolean hasPathTo(int v)

Is there a path from the source s to vertex v?

Parameters:

v - the destination vertex

Returns:

true if there is a path from the source vertex s to vertex v, and false otherwise

pathTo

public Iterable<DirectedEdge> pathTo(int v)

Returns a shortest path from the source s to vertex v.

Parameters:

v - the destination vertex

Returns:

a shortest path from the source s to vertex v as an iterable of edges, and null if no such path

Throws:

UnsupportedOperationException - if there is a negative cost cycle reachable from the source vertex s

main

public static void main(String[] args)

Unit tests the BellmanFordSP data type.