Example of How to Use MAX_FLOW_T()
The following program shows how the function MAX_FLOW_T()
can be used to compute a maximum flow in a directed graph.
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 MAX_FLOW_T() we need
to include <LEDA/templates/max_flow.t>. We use the LEDA
number type integer
as the number type NT for
the edge capacities. In constrast to the C++ number type int,
LEDA's integer does not overflow.
#include <LEDA/graph/graph.h>
#include <LEDA/graph/templates/max_flow.h>
#include <LEDA/numbers/integer.h>
using namespace leda;
In main() we first create a simple graph G
with four nodes and six edges. We use an edge_array<integer>
cap to store the capacities 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(n1,n3);
edge e4=G.new_edge(n3,n1); edge e5=G.new_edge(n3,n2);
edge_array<integer> cap(G);
cap[e0]=1; cap[e1]=5; cap[e2]=1;
cap[e3]=2; cap[e4]=2; cap[e5]=1;
The edge_array<integer> flow is used for the result
of MAX_FLOW_T(). flow[e] will contain the flow
over edge e in the computed maximum flow from s
to t. MAX_FLOW_T() returns the value of the
maximum flow.
After calling MAX_FLOW_T() we use the function CHECK_MAX_FLOW_T()
to check the result of the computation.
If the result is correct CHECK_MAX_FLOW_T() returns true
and we output the flow value and the flow on the edges of G.
node s=n0, t=n2;
edge_array<integer> flow(G);
integer flow_value=MAX_FLOW_T(G,s,t,cap,flow);
bool is_maximum_flow=CHECK_MAX_FLOW_T(G,s,t,cap,flow);
if (is_maximum_flow) {
std::cout << "The maximum flow has value: "
<< flow_value << std::endl;
edge e;
forall_edges(e,G) {
if (flow[e]>0) {
G.print_edge(e);
std::cout << " flow = " << flow[e] << std::endl;
}
}
}
else std::cout << "Error: MAX_FLOW_T() "
<< "did not compute a maximum flow!" << std::endl;
return 0;
}
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