Adding Network examples

examples/fsharp/equality.fsx

@@ -23,7 +23,6 @@
 
 open System
 open Google.OrTools.FSharp
-open Google.OrTools.LinearSolver
 
 let opts = SolverOpts.Default
             .Name("Equality Constraints")
@@ -36,3 +35,4 @@ let opts = SolverOpts.Default
             .Algorithm(LP CLP)
 
 let slvr = opts |> lpSolve |> SolverSummary
+slvr |> ignore

examples/fsharp/lib/Google.OrTools.FSharp.fsx

@@ -77,6 +77,37 @@ type LinearSolverAlgorithm =
   | LP of LinearProgramming
   | IP of IntegerProgramming
 
+/// Max Flow Solver Result
+module MaximumFlow =
+  let (|Optimal|IntOverflow|BadInput|BadResult|) status =
+    match status with
+    | 0 ->
+      Optimal
+    | 1 ->
+      IntOverflow
+    | 2 ->
+      BadInput
+    | 3 ->
+      BadResult
+
+/// Minimum Cost Flow Result
+module MinimumCostFlow =
+  let (|NotSolved|Optimal|Feasible|Infeasible|Unbalanced|BadResult|BadCostRange|) status =
+    match status with
+    | 0 ->
+      NotSolved
+    | 1 ->
+      Optimal
+    | 2 ->
+      Feasible
+    | 3 ->
+      Infeasible
+    | 4 ->
+      Unbalanced
+    | 5 ->
+      BadResult
+    | 6 ->
+      BadCostRange
 
 type SolverOpts = {
   /// Name of the solver

examples/fsharp/network-max-flow.fsx

@@ -0,0 +1,37 @@
+#I "./lib"
+#load "Google.OrTools.FSharp.fsx"
+
+open Google.OrTools.Graph
+open Google.OrTools.FSharp
+
+printfn "Max Flow Problem"
+let  numNodes = 6;
+let numArcs = 9;
+let tails = [0; 0; 0; 0; 1; 2; 3; 3; 4]
+let heads = [1; 2; 3; 4; 3; 4; 4; 5; 5]
+let capacities = [5L; 8L; 5L; 3L; 4L; 5L; 6L; 6L; 4L]
+let expectedFlows = [4; 4; 2; 0; 4; 4; 0; 6; 4]
+let expectedTotalFlow = 10;
+let maxFlow = new MaxFlow()
+
+for i=0 to (numArcs-1) do
+  let arc = maxFlow.AddArcWithCapacity(tails.[i], heads.[i], capacities.[i])
+  if (arc <> i) then
+    failwith "Internal error"
+
+let source = 0;
+let sink = numNodes - 1;
+printfn "Solving max flow with %i nodes, and %i arcs, source=%i, sink=%i " numNodes numArcs source sink
+let solveStatus = maxFlow.Solve(source, sink)
+
+match solveStatus with
+| MaximumFlow.Optimal ->
+    let totalFlow = maxFlow.OptimalFlow();
+    printfn "total computed flow %i, expected = %i" totalFlow expectedTotalFlow
+
+    for i=1 to numArcs do
+      printfn "Arc %i (%i -> %i), capacity=%i, computed=%i, expected=%i" i (maxFlow.Head(i-1)) (maxFlow.Tail(i-1)) (maxFlow.Capacity(i-1)) (maxFlow.Flow(i-1)) (expectedFlows.[i-1])
+| _ ->
+  printfn "Solving the max flow problem failed. Solver status: %i" solveStatus
+
+

examples/fsharp/network-min-cost-flow.fsx

@@ -0,0 +1,38 @@
+#I "./lib"
+#load "Google.OrTools.FSharp.fsx"
+
+open Google.OrTools.Graph
+open Google.OrTools.FSharp
+
+printfn "Min Cost Flow Problem"
+let numSources = 4
+let numTargets = 4
+let costs = array2D [
+                      [90L; 75L; 75L; 80L];
+                      [35L; 85L; 55L; 65L];
+                      [125L; 95L; 90L; 105L];
+                      [45L; 110L; 95L; 115L]
+                    ]
+
+let expectedCost = 275
+let minCostFlow = new MinCostFlow()
+
+for source=0 to (numSources-1) do
+  for target=0 to (numTargets-1) do
+    minCostFlow.AddArcWithCapacityAndUnitCost(source, numSources + target, 1L, costs.[source, target]) |> ignore
+
+for source=0 to (numSources-1) do
+  minCostFlow.SetNodeSupply(source, 1L)
+
+for target=0 to (numTargets-1) do
+  minCostFlow.SetNodeSupply(numSources + target, -1L);
+
+printfn "Solving min cost flow with %i sources, and %i targets." numSources numTargets
+let solveStatus = minCostFlow.Solve();
+
+match solveStatus with
+| MinimumCostFlow.Optimal ->
+  printfn "Total computed flow cost = %i, expected = %i" (minCostFlow.OptimalCost()) expectedCost
+| _ ->
+  printfn "Solving the min cost flow problem failed. Solver status: %i" solveStatus
+