Boost Graph Library: Dijkstra Visitor

# Dijkstra Visitor Concept

This concept defines the visitor interface for `dijkstra_shortest_paths()` and related algorithms. The user can create a class that matches this interface, and then pass objects of the class into `dijkstra_shortest_paths()` to augment the actions taken during the search.

### Refinement of

Copy Constructible (copying a visitor should be a lightweight operation).

### Notation

`V` | A type that is a model of Dijkstra Visitor.
`vis` | An object of type `V`.
`G` | A type that is a model of Graph.
`g` | An object of type `G`.
`e` | An object of type `boost::graph_traits<G>::edge_descriptor`.
`s,u,v` | An object of type `boost::graph_traits<G>::vertex_descriptor`.
`DistanceMap` | A type that is a model of Read/Write Property Map.
`d` | An object of type `DistanceMap`.
`WeightMap` | A type that is a model of Readable Property Map.
`w` | An object of type `DistanceMap`.

### Associated Types

none

### Valid Expressions

Name | Expression | Return Type | Description
--- | --- | --- | ---
Initialize Vertex | `vis.initialize_vertex(u, g)` | `void` | This is invoked one each vertex of the graph when it is initialized.
Examine Vertex | `vis.examine_vertex(u, g)` | `void` | This is invoked on a vertex as it is popped from the queue. This happens immediately before `examine_edge()` is invoked on each of the out-edges of vertex `u`.
Examine Edge | `vis.examine_edge(e, g)` | `void` | This is invoked on every out-edge of each vertex after it is discovered.
Discover Vertex | `vis.discover_vertex(u, g)` | `void` | This is invoked when a vertex is encountered for the first time.
Edge Relaxed | `vis.edge_relaxed(e, g)` | `void` | Upon examination, if the following condition holds then the edge is relaxed (its distance is reduced), and this method is invoked. `tie(u,v) = incident(e, g); D d_u = get(d, u), d_v = get(d, v); W w_e = get(w, e); assert(compare(combine(d_u, w_e), d_v));`
Edge Not Relaxed | `vis.edge_not_relaxed(e, g)` | `void` | Upon examination, if the edge is not relaxed (see above) then this method is invoked.
Finish Vertex | `vis.finish_vertex(u, g)` | `void` | This invoked on a vertex after all of its out edges have been added to the search tree and all of the adjacent vertices have been discovered (but before their out-edges have been examined).

### Models

- `dijkstra_visitor`

Copyright © 2000-2001 | Jeremy Siek, Indiana University (jsiek@osl.iu.edu) Lie-Quan Lee, Indiana University (llee@cs.indiana.edu) Andrew Lumsdaine, Indiana University (lums@osl.iu.edu)