Version 5.0 The LEDA User Manual

template
void DIJKSTRA T(const graph& G, node s, const edge array& cost,
node array& dist)
as above, but pred is not computed.
template
NT DIJKSTRA T(const graph& G, node s, node t, const edge array& c,
node array& pred)
computes a shortest path from s to t and returns its length.
The cost of all edges must be non-negative. The return value
is unspecified if there is no path from s to t. The array pred
records a shortest path from s to t in reverse order, i.e., pred[t]
is the last edge on the path. If there is no path from s to t
or if s = t then pred[t] = nil. The worst case running time is
O(m + n log n), but frequently much better.
template
bool BELLMAN FORD B T(const graph& G, node s, const edge array& c,
node array& dist, node array& pred)
BELLMAN FORD B solves the single source shortest path
problem in the graph G(V, E) with respect to the source node
s and the cost-function given by the edge array c.
BELLMAN FORD B returns false if there is a negative cycle
in G that is reachable from s and returns true otherwise. The
algorithm ([10]) has running time O(min(D, n)m) where D
is the maximal number of edges on any shortest path. The
algorithm is only included for pedagogical purposes.
void BF GEN(GRAPH & G, int n, int m, bool non negative = true)
generates a graph with at most n nodes and at most m edges.
The edge costs are stored as edge data. The running time
of BELLMAN FORD B on this graph is Ω(nm). The edge
weights are non-negative if non negative is true and are arbitrary
otherwise.
Precondition: m ≥ 2n and m ≤ n 2 /2.
template
bool BELLMAN FORD T(const graph& G, node s, const edge array& c,
node array& dist, node array& pred)
BELLMAN FORD T solves the single source shortest path
problem in the graph G(V, E) with respect to the source node
s and the cost-function given by the edge array c.
BELLMAN FORD T returns false if there is a negative cycle
in G that is reachable from s and returns true otherwise. The
algorithm ([10]) has running time O(min(D, n)m) where D is
the maximal number of edges in any shortest path.
The algorithm is never significantly slower than BELL-
MAN FORD B and frequently much faster.