java - 使用 Dijkstra 检测多条最短路径

Question

给定一个加权有向图，如何修改 Dijkstra 算法以测试给定节点对之间是否存在多个最低成本路径？

我目前的算法如下：（归功于 Weiss）

/**
 * Single-source weighted shortest-path algorithm. (Dijkstra) 
 * using priority queues based on the binary heap
 */
public void dijkstra( String startName )
{
    PriorityQueue<Path> pq = new PriorityQueue<Path>( );

    Vertex start = vertexMap.get( startName );
    if( start == null )
        throw new NoSuchElementException( "Start vertex not found" );

    clearAll( );
    pq.add( new Path( start, 0 ) ); start.dist = 0;

    int nodesSeen = 0;
    while( !pq.isEmpty( ) && nodesSeen < vertexMap.size( ) )
    {
        Path vrec = pq.remove( );
        Vertex v = vrec.dest;
        if( v.scratch != 0 )  // already processed v
            continue;

        v.scratch = 1;
        nodesSeen++;

        for( Edge e : v.adj )
        {
            Vertex w = e.dest;
            double cvw = e.cost;

            if( cvw < 0 )
                throw new GraphException( "Graph has negative edges" );

            if( w.dist > v.dist + cvw )
            {
                w.dist = v.dist +cvw;
                w.prev = v;
                pq.add( new Path( w, w.dist ) );
            }
        }
    }
}

标签： javagraph-theoryshortest-pathdijkstra

Answer 1

替换 field prev，用集合链接到上一个顶点prevs，并稍微更改代码：

...

        if( w.dist >= v.dist + cvw ) {
            if ( w.dist > v.dist + cvw ) {
                w.dist = v.dist +cvw;
                w.prevs.clear();
            }
            w.prevs.add(v);
            pq.add( new Path( w, w.dist ) );
        }

...