Package edu.princeton.cs.algs4

Class DijkstraSP

  • public class DijkstraSP
extends Object
    The DijkstraSP class represents a data type for solving the single-source shortest paths problem in edge-weighted digraphs where the edge weights are non-negative.

    This implementation uses Dijkstra's algorithm with a binary heap. The constructor takes Θ(E log V) time in the worst case, where V is the number of vertices and E is the number of edges. Each instance method takes Θ(1) time. It uses Θ(V) extra space (not including the edge-weighted digraph).

    This correctly computes shortest paths if all arithmetic performed is without floating-point rounding error or arithmetic overflow. This is the case if all edge weights are integers and if none of the intermediate results exceeds 252. Since all intermediate results are sums of edge weights, they are bounded by V C, where V is the number of vertices and C is the maximum weight of any edge.

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

    Author:
    Robert Sedgewick, Kevin Wayne

    • Constructor Detail

      • DijkstraSP

        public DijkstraSP​(EdgeWeightedDigraph G,
                  int s)
        Computes a shortest-paths tree from the source vertex s to every other vertex in the edge-weighted digraph G.
        Parameters:
        G - the edge-weighted digraph
        s - the source vertex
        Throws:
        IllegalArgumentException - if an edge weight is negative
        IllegalArgumentException - unless 0 <= s < V

    • Method Detail

      • 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:
        IllegalArgumentException - unless 0 <= v < V

      • hasPathTo

        public boolean hasPathTo​(int v)
        Returns true if there is a path from the source vertex s to vertex v.
        Parameters:
        v - the destination vertex
        Returns:
        true if there is a path from the source vertex s to vertex v; false otherwise
        Throws:
        IllegalArgumentException - unless 0 <= v < V

      • pathTo

        public Iterable<DirectedEdge> pathTo​(int v)
        Returns a shortest path from the source vertex s to vertex v.
        Parameters:
        v - the destination vertex
        Returns:
        a shortest path from the source vertex s to vertex v as an iterable of edges, and null if no such path
        Throws:
        IllegalArgumentException - unless 0 <= v < V

      • main

        public static void main​(String[] args)
        Unit tests the DijkstraSP data type.
        Parameters:
        args - the command-line arguments