Example of How to Use BELLMAN_FORD()
The following program shows how the function BELLMAN_FORD()
can be used to compute single source shortest paths. Edge costs may be
positive or negative.
Remark: The graph algorithms in LEDA are generic, that is, they
accept graphs as well as parameterized
graphs.
In main() we first create a simple graph G
with four nodes and five edges.
The costs of the edges are stored in the edge_array<int>
cost. We use int as the number type for the edge costs.
The variant of BELLMAN_FORD() for double can be
used in exactly the same way. You only need to replace int
by double in the definition of cost and dist.
#include <LEDA/graph/graph.h>
#include <LEDA/graph/shortest_path.h>
using namespace leda;
int main()
{
graph G;
node n0=G.new_node(); node n1=G.new_node();
node n2=G.new_node(); node n3=G.new_node();
edge e0=G.new_edge(n0,n1); edge e1=G.new_edge(n0,n3);
edge e2=G.new_edge(n1,n2); edge e3=G.new_edge(n2,n3);
edge e4=G.new_edge(n3,n1);
edge_array<int> cost(G);
cost[e0]=1; cost[e1]=-1; cost[e2]=-1;
cost[e3]=2; cost[e4]=1;
The node_array<edge>
pred and the node_array<int> dist for G
are used for the result of BELLMAN_FORD().
pred[v] will contain the last edge on a shortest path from the
source node s to v. This allows a construction
of the complete shortest path. dist[v] will contain the length
of a shortest path from s to v.
node_array<edge> pred(G);
node_array<int> dist(G);
bool no_negative_cycle=BELLMAN_FORD(G,n0,cost,dist,pred);
if (no_negative_cycle) {
node v;
forall_nodes(v,G) {
G.print_node(v);
if (v==n0)
std::cout << " was source node." << std::endl;
else
if (pred[v]==nil)
std::cout << " is unreachable." << std::endl;
else {
std::cout << " " << dist[v] << " ";
G.print_edge(pred[v]);
std::cout << std::endl;
}
}
}
else std::cout << "There are negative cycles!" << std::endl
<< "All dist-values unspecified!" << std::endl;
return 0;
}
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