图之单源Dijkstra算法、带负权值最短路径算法

1、图类基本组成

存储在邻接表中的基本项

 /**
  * Represents an edge in the graph
  *
  */
 class Edge implements Comparable<Edge> {
     public Vertex dest;　　//Second vertex in Edge
     public double cost;　　//Edge cost

     public Edge(Vertex d, double c) {
         dest = d;
         cost = c;
     }

     @Override
     public int compareTo(Edge o) {
         double otherCost = o.cost;
         return cost < otherCost ? -1 : cost > otherCost ? 1 : 0;
     }

     @Override
     public String toString() {
         return "Edge{" + "dest=" + dest + ", cost=" + cost + '}';
     }
 }

存储每个顶点信息

 /**
  * Represents a vertex in the graph
  */
 class Vertex {
     public String name;
     public List<Edge> adj;//Adjacent vertices
     public double dist;
     public Vertex prev;
     public int scratch;//Extra variable used in algorithm

     public Vertex(String name) {
         this.name = name;
         adj = new LinkedList<Edge>();
         reset();
     }

     public void reset() {
         dist = Graph.INFINITY;
         prev = null;
         scratch = 0;
     }

     @Override
     public String toString() {
         return "Vertex{" + "name='" + name + '\'' + ", prev=" + prev + ", adj=" + adj + ", dist=" + dist + '}';
     }
 }

图类的框架

 import java.util.*;

 /**
  * Created by Vanguard on 2017/4/6.
  */
 public class Graph {
     public static final double INFINITY = Double.MAX_VALUE;
     private Map<String, Vertex> vertexMap = new HashMap<String, Vertex>();

     public void addEdge(String sourceName, String destName, double cost) {
         Vertex v = getVertex(sourceName);
         Vertex w = getVertex(destName);
         v.adj.add(new Edge(w, cost));
     }

     /**
      * 通过查询图的表，打印最短路径
      *
      * @param destName
      */
     public void printPath(String destName) {
         Vertex w = vertexMap.get(destName);
         if (w == null) {
             System.out.println("NoSuchElementException");
             return;
         } else if (w.dist == INFINITY) {
             System.out.println(destName + " is unreachable.");
         } else {
             System.out.print("(Cost is: " + w.dist + ") ");
             printPath(w);
             System.out.println();
         }
     }

     private void printPath(Vertex dest) {
         if (dest.prev != null) {
             printPath(dest.prev);
             System.out.print(" --> ");
         }
         System.out.print(dest.name);
     }

     private Vertex getVertex(String vertexName) {
         Vertex v = vertexMap.get(vertexName);
         if (v == null) {    //create if not exist.
             v = new Vertex(vertexName);
             vertexMap.put(vertexName, v);
         }
         return v;
     }

     private void clearAll() {
         for (Vertex v : vertexMap.values()) {
             v.reset();
         }
     }
 }

2、最短路径算法

广度优先搜索

 /**
  * Single-source unweighted shortest-path algorithm.
  * 无权单源最短路径算法——广度优先搜索
  *
  * @param startName
  */
 public void unweighted(String startName) {
     clearAll();
     Vertex start = vertexMap.get(startName);
     if (start == null) {
         throw new NoSuchElementException("Start vertex not fond.");
     }
     Queue<Vertex> q = new LinkedList<Vertex>();
     q.add(start);
     start.dist = 0;
     while (!q.isEmpty()) {
         Vertex v = q.remove();
         for (Edge e : v.adj) {
             Vertex w = e.dest;
             if (w.dist == INFINITY) {
                 w.dist = v.dist + 1;
                 w.prev = v;
                 q.add(w);
             }
         }
     }
 }

Dijstra算法

 /**
  * Single-source unweighted shortest-path algorithm.
  * 无权单源最短路径算法——广度优先搜索
  *
  * @param startName
  */
 public void unweighted(String startName) {
     clearAll();
     Vertex start = vertexMap.get(startName);
     if (start == null) {
         throw new NoSuchElementException("Start vertex not fond.");
     }
     Queue<Vertex> q = new LinkedList<Vertex>();
     q.add(start);
     start.dist = 0;
     while (!q.isEmpty()) {
         Vertex v = q.remove();
         for (Edge e : v.adj) {
             Vertex w = e.dest;
             if (w.dist == INFINITY) {
                 w.dist = v.dist + 1;
                 w.prev = v;
                 q.add(w);
             }
         }
     }
 }

带负权值得最短路径算法

 /**
  * Single-source negative-weighted shortest-path algorithm.
  * 带负权值得最短路径算法
  *
  * @param startName
  */
 public void negative(String startName) {
     clearAll();

     Vertex start = vertexMap.get(startName);
     if (start == null) {
         throw new NoSuchElementException("Start vertex not fond.");
     }
     Queue<Vertex> q = new LinkedList<>();
     q.add(start);
     start.dist = 0;
     start.scratch++;
     while (!q.isEmpty()) {
         Vertex v = q.remove();
         if (v.scratch++ > 2 * vertexMap.size()) {
             System.out.println("Negative cycle detected.");
         }
         for (Edge e : v.adj) {
             Vertex w = e.dest;
             double costvw = e.cost;
             if (w.dist > v.dist + costvw) {
                 w.dist = v.dist + costvw;
                 w.prev = v;
                 //Enqueue only if not already on the queue
                 if (w.scratch++ % 2 == 0)
                     q.add(w);
                 else
                     w.scratch--;
             }
         }

     }
 }

THE END.