# Bellman Ford Visitor Concept

This concept defines the visitor interface for `bellman_ford_shortest_paths()`. Users can define a class with the Bellman Ford Visitor interface and pass and object of the class to `bellman_ford_shortest_paths()`, thereby augmenting the actions taken during the graph search.

### Refinement of

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

### Notation

`V` | A type that is a model of Bellman Ford 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` | An object of type `boost::graph_traits<G>::vertex_descriptor`.

### Associated Types

none

### Valid Expressions

Name | Expression | Return Type | Description
--- | --- | --- | ---
Initialize Vertex | `vis.initialize_vertex(s, g)` | `void` | This is invoked on every vertex of the graph before the start of the graph search.
Examine Edge | `vis.examine_edge(e, g)` | `void` | This is invoked on every edge in the graph `num_vertices(g)` times.
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 | `edge_not_relaxed(e, g)` | `void` | Upon examination, if the edge is not relaxed (see above) then this method is invoked.
Edge Minimized | `vis.edge_minimized(e, g)` | `void` | After the `num_vertices(g)` iterations through the edge set of the graph is complete, one last iteration is made to test whether each edge was minimized. If the edge is minimized then this function is invoked.
Edge Not Minimized | `edge_not_minimized(e, g)` | `void` | If the edge is not minimized, this function is invoked. This happens when there is a negative cycle in the graph.

### Models

- `bellman_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)