Algorithmic Solutions > LEDA > LEDA Guide > Graph Algorithms > Shortest Path Algorithms > Bellman-Ford Algorithm for SSSP > Example BELLMAN_FORD_T()

Example of How to Use BELLMAN_FORD_T()

The following program shows how the function BELLMAN_FORD_T() can be used to compute single source shortest paths in a directed graph. 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 order to use the template function BELLMAN_FORD_T() we need to include <LEDA/templates/shortest_path.t>. We use the LEDA number type integer as the number type NT for the edge costs. In constrast to the C++ number type int, LEDA's integer does not overflow.

#include <LEDA/graph/graph.h>
#include <LEDA/graph/templates/shortest_path.h>
#include <LEDA/numbers/integer.h>

using namespace leda;

In main() we first create a simple graph G with four nodes and five edges. We use an edge_array<integer> cost to store the costs of the edges of G.

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<integer> 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<integer> dist are used for the result of BELLMAN_FORD_T(). 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<integer> dist(G);
  bool no_negative_cycle=BELLMAN_FORD_T(G,n0,cost,dist,pred);
  if (no_negative_cycle) {
    node v;
    forall_nodes(v,G) {
      if (v==n0) 
	  std::cout << " was source node." << std::endl;
	  if (pred[v]==nil) 
          std::cout << " is unreachable." << std::endl;
        else {
          std::cout << " " << dist[v] << " "; 
          std::cout << std::endl;

  else std::cout << "There are negative cycles!" << std::endl
                 << "All dist-values unspecified!" << std::endl;

  return 0;

See also:

Bellman-Ford Algorithm for SSSP


Parameterized Graphs

Edge Arrays

Node Arrays

Checking the Results of an SSSP Algorithm

Number Types

Graphs and Related Data Types

Manual Entries:

Manual Page Shortest Path Algorithms

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