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

## 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;
}```

Bellman-Ford Algorithm for SSSP

Graphs

Parameterized Graphs

Edge Arrays

Node Arrays

Checking the Results of an SSSP Algorithm

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